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# Calculate Distance Between Two Gps Coordinates Python

4km in that example? On Jun 19, 2015 3:58 PM, "pashtika" [email protected] Type in two addresses or click on the map to start. Im using Leonardo with GPS data logger; im wondering if this code works for this equipment? My application is that i have to save on the SD Card the distance and the time (begging and ending time). Points are written in the (x,y) format, where x is the x-coordinate and y is the y-coordinate. the earth's radius is R = 6372. Calculating distance between two points represented by lat,long upto 15 feet accuracy (Java in General forum at Coderanch). In my blog, I demonstrate a technique where you first create a bounding box (min/max lat/long). 8, which is the radius of Earth. Inputs can be in several formats: GPS Coordinates (like N 42 59. Draw a line to join them and form a right triangle with this line as the hypotenuse. You cannot determine distance between two zip codes without additional information. the first part is the latitude; the second part is the longitude; don't use ° ' " signs, W E N S letters and spaces. Calculate distance between two points. of the starting point. This script calculates distances, bearing and more between the two Latitude/Longitude points. import pyproj geod = pyproj. In polar coordinates there is literally an infinite number of coordinates for a given point. See distance to other cities from Houston – Texas – USA measured in kilometers (km), miles and nautical miles and their local time. The distance between any two points with coordinates (x1, y1) and (x2,y2) is given by: d=sq root of d =(x2-x1)2+ - Answered by a verified Tutor We use cookies to give you the best possible experience on our website. So the distance between the longitude of two points is dependent on the latitude of those points. Enter either: decimal latitudes/longitudes with minus sign for South and West; degrees minutes seconds in a format like E 32 14 9 (32°14'9" East longitude). A geographic coordinate system defines two-dimensional coordinates based on the Earth’s surface. Best Answer: R = radius earth = 6. Corbettmaths Videos, worksheets, 5-a-day and much more. Additionally, this tool will convert your decimal coordinates to degrees minutes seconds (DMS). Measure your distance in miles or km, see elevation graphs, and track calorie burn all one one page. double haversine_km(double lat1, double long1. Save them as a KML file (not KMZ), and open them in GE-Path. Calculate the distance as-the-crow-flies between two Latitude/Longitude points on Earth You can enter the Latitude (East - West) and Longitude (North - South) coordinates as given by Google Earth software. Skip to content. If this distance is no more than the radius that you have chosen for the mystery circle, then the user has found the circle! You can use getShift as written, or modify it into a function getDistance that directly returns the distance between two points. hello everyone, I am a newbie on python. The output table can be quite large. We don't upload 34 Calculate The Distance Between Two Points Locations Coordinates In Power Bi, We just retail information from other sources & hyperlink to them. Hijmans, Ed Williams, and Chris Vennes, which I could use to do just. The class accepts coordinates in any of the following formats: 1. just under 117 and a half degrees. A problem that arises when performing geographically weighted regression is determining the distance between GPS coordinates. Also, I use ‘create points’ tool to get the longitude and latitude. You can try to calculate distance of two locations (based on GPS coordinates: longitude and latitude) with following libraries: geopy : supports Great Circle and Vincenty formulas; additionally, it uses Karney geodesic formula as default function to calculate distance. Note that the distances are not the shortest distance between two coordinates, but rather the distances of the fastest routes. Then according to Lesson 31, Problem 5, the coördinates at the right angle are (15, 3). This distance calculator is not only for South Africans, anyone from all over the globe is welcome to use the calculator, it was developed as a free tool to calculate the distance between two points. However, if you want to learn the distance between two coordinates, you may use the distance between coordinates tool. The distance calculator will then display a measurerment of the length in feet, meters, miles and kilometers. There are many options available if you want to import these in a GIS and run analysis. The coordinate values of the data point are x=45 and y=50. That is not the case in python 3 (return an approximation. For example, if the two points have coordinates (-3, 7) and (1, 2), then the difference between 7 and 2 is 5, and so Y = 5. Don't ask why, totally a new more complicated discussion. Distance in 2 Dimensions. The tool creates a table with distances between two sets of points. Note the use of the two-argument form of the arctangent, atan2(y,x), which ensures that the resulting angle is in the correct quadrant: θ = atan2( sin(δλ) * cos(φ 2 ), cos(φ 1) * sin (φ 2) * cos(δλ). public domain: def calculate i messed up the x and y and i wasn't aware that i can use the wgs84 coordinates. If an address corresponds to those coordinates, you can then set this point as your starting point or destination for your driving directions request. distancesfrom. Because of this, Great Circles are important for the study of migration and other human interactions and activities including shipping and airline routes. geopy is a Python 2 and 3 client for several popular geocoding web services. All gists Back to GitHub. The algorithm used to calculate distances is described in detail here. Using the formula for the distance between two points, this is The width is the distance between the points B and C. If you want to know the distance between two points along the map, then the Distance – Find my distance is the best app for the purpose. Measure distances. Like the Project menu, Distance can take input in one of the two ways; via locking on to your current location, or through selecting a location on map. Or if you are traveling via plane as it ignores earth curvature. Given n integer coordinates. Steps: Start ArcMap. Most GPS devices provide coordinates in the Degrees, Minutes and Seconds (DMS) format, or most commonly the Decimal Degrees (DD) format. The application allows also the reversed conversion (H to h), and the conversion between two vertical datums. calculate distance between 2 gps coordinates. Developers today experiment and implement various kind of features including the feature to calculate distance between two GPS coordinates in the Android mobile app. Here is the equation:. I believe it's in WGS 84, a geographic coordinate system vs. This script calculates distances, bearing and more between the two Latitude/Longitude points. Switch between intersection types by clicking on the title. In Virtual Earth the radial distance is the radius of the Earth, the zenith angle is the latitude, and the azimuth angle is the longitude. The first step is expressing each Latitude/Longitude of both of the coordinates in radians: lat1. Calculate travel time and distance between two addresses using. To calculate distances between points given by latitudes and longitudes precisely, you need to know which geoid was used as a reference in specifying them. distance() Examples. In this case, we’re going to define distance between two pixels as the Euclidean distance between their x,y coordinates in the image. To calculate the distance between two points we use the inv function, which calculates an inverse transformation and returns forward and back azimuths and distance. Need to get the distance between two addresses/cities/zip-codes but don't want to/can't use an API? Here's a macro I wrote that scrapes HTML from Google Maps Edit: Thanks to user /u/aikoaiko who pointed out an alternative to getting mileage from Google without using Maps. of the starting point. WHAT YOU NEED TO USE THE STATE PLANE COORDINATE SYSTEMS N & E State Plane Coordinates for Control Points AZIMUTHS - True, Geodetic, or Grid - Conversion from Astronomic to Geodetic (LaPlace Correction) - Conversion from Geodetic to Grid (Mapping Angle) DISTANCES - Reduction from Horizontal to Ellipsoid “Sea-Level Reduction Factor”. How far is it from (4, 3) to (15, 8)? Consider the distance d as the hypotenuse of a right triangle. Request for Question Clarification by leapinglizard-ga on 08 Apr 2004 01:22 PDT Are you asking for the straight-line distance between two points in space? In other words, do you want to know the length of a line segment whose endpoints are specified in polar coordinates?. With this power bi. Distance calculator between cities on Map. When the histogram is not uniform ( uniform=false ), then each of ranges[i] contains histSize[i]+1 elements:. The Haversine formula accounts for the. 1 What is the best way to calculate the great circle distance (ignoring elevation differences) between 2 points? If the distance is less than about 20 km and the locations of the 2 points in Cartesian coordinates are X1,Y1 and X2,Y2 then the Pythagorean Theorem. Find altitude filling in input fields (latitude, longitude) or doing click on the map. Estimate distance between two latitude/longitude locations (Python) Since there is a limit qouta for Google API daily requests, so I decided to use manual calculation for the distance between two points on the map. There are various ways to handle this calculation problem. Nothing else makes sense and I see that you were able to calculate a distance in ft. Comment • 7; I am using ArcGIS Desktop 10. if anyone can also guide me how to do this then also I will be highly thankful. Calculate dy, the difference in the points y-coordinates. 939997 Point2: -19. This online calculator will compute and plot the distance and midpoint for two points in two dimensions. Python Exercises, Practice and Solution: Write a Python program to compute the distance between the points (x1, y1) and (x2, y2). Many languages have this function. In the last column, type the formula using the GetDistanceH function, and then copy it to the remaining cells in the table. if the default search radius is used, distances from all input points to all near points are calculated. This code outputs the distance between 2 GPS points showing also the vertical and horizontal bearing between them. Dimensions are heavily used in design, engineering, and facilities applications for GIS. If you like it just leave a message please. I needed to calculate the angle between two points on the same circle. In this article, we will develop an Android application which displays driving distance and travel time between two locations in Google Map Android API V2. This is also known as a great circle line if based on a sphere rather than an ellipsoid. Initial and reverse headings (in degrees) can be calculated in a similar way using the. As you start to write the name of a city or place, distance calculator will suggest you place names automatically, you may choose from them to calculate distance. This formula gives a signed distance which is positive on one side of the plane and negative on the other. Secondly are all latitdue lines equidistant per degree,including 89 deg to a pole?. By continuing to browse this site, you agree to this use. Java program to calculate the distance between two points. The code has been written in five different formats using standard values, taking inputs through scanner class, command line arguments, while loop and, do while loop, creating a separate class. Hi i do have a homework that it needs to calculate the distance between two points on earth. Coordinates. Calculate distance between 2 sets of longitude / latitude coordinates. Search for jobs related to Python program to calculate distance between two points or hire on the world's largest freelancing marketplace with 17m+ jobs. Javascript program to calculate great circle distance using latitude and longitude points on the earth. In this article, we will see how to calculate the distance between 2 points on the earth in two ways. So you first need to use Maps to geocode the airport code into latitude/longitude, and then use the Haversine formula to calculate the distance between the two locations. 2) You are mixing up two different variables. This page shows how to calculate the geographic midpoint (also known as the geographic center, or center of gravity) for two or more points on the earth's surface. com offers free software downloads for Windows, Mac, iOS and Android computers and mobile devices. I built this primarily to make it easy to check if a Locationless (Reverse) Cache has already been found. I believe it's in WGS 84, a geographic coordinate system vs. Calculate the great circle distance between two points. The default is false. Given two GPS lat/lon/altitude coordinates of two aircraft, how do I compute the slant range (line of sight distance) between them? Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their. As mentioned above, we simply deserialize the data to get a List object that is fully populated with all of. Using 2 sets of Gobal Satilite Positioning coordinates, how would you determine the direct distance between the 2 locations. (about 20+ targets) The user would enter their coordinates or a current location in a certain box. Virtually all of it is within 100 miles of the surface. I determined the minimum distance from this centriod to the state border. import pyproj geod = pyproj. (You can also choose. If you are planning a road trip and want to learn the mileage distance between two locations, you can use this location tool to help you. Write a Python program to compute Euclidean distance. From investigating my location history, it seems that unless my phone is off or without reception, Android reports my location exactly every 60 seconds. Simply enter the from address and to address and the distance between the two address will be calculated in milage and kilometers. From the known position of three satellites and the measured distances between them and the receiver, coordinates of receiver position can be calculated. The Bearing Distance Calculator function calculates the forward and backward azimuths between two specified coordinates as well as the distance. However, if the data frame is using a geographic coordinate system, the measurements will always be geodesic and you don't need to hold down Shift. How far is it from (4, 3) to (15, 8)? Consider the distance d as the hypotenuse of a right triangle. 5 depicts the. Python Exercises, Practice and Solution: Write a Python program to compute the distance between the points (x1, y1) and (x2, y2). python - calculating a gps coordinate given a point, bearing and distance; algorithm - Calculate distance between two latitude-longitude points? (Haversine formula) geolocation - distance and bearing between two geopoints in android; How to calculate the distance between two places using Haversine Formula in iPhone?. This is the method recommended for calculating short distances by Bob Chamberlain. The distance between any two points with coordinates (x1, y1) and (x2,y2) is given by: d=sq root of d =(x2-x1)2+ - Answered by a verified Tutor We use cookies to give you the best possible experience on our website. Then I wrote a script in Python (LondonGPS. GPS: Position, Time and Distance - 09/06/2005. The spherical formula for this is d=cos-1 [cos(90° - VT) cos(90° - PT) + sin(90° - VT) sin(90° - PT) cos(VN - PN)]. I turned to my web browser and googled it, sure enough, there was this R package called ‘geosphere’ from Robert J. Start ArcMap. Python’s complex type uses rectangular coordinates where a number on the complex plain is defined by two floats, the real part and the imaginary part. The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes. Distance can be calculated in terms of speed and time as well where distance is given by speed/time and frequently used for mathematics or physics calculations. Given geographic coordinates, returns distance in kilometers. e NOT flat). [MySQL, PHP, JAVA, JavaScript, Python, Node. Barbara Raney May 18, 2014 Microsoft It has all the needed trig functions to calculate the distance in miles between two points using Longitude and Latitude where they are expressed in decimal form. Outputting the result in a table Distances in km between each of the two points. Request for Question Clarification by leapinglizard-ga on 08 Apr 2004 01:22 PDT Are you asking for the straight-line distance between two points in space? In other words, do you want to know the length of a line segment whose endpoints are specified in polar coordinates?. The easiest way to get a distance and an azimuth between two known points is an inverse calculation. You want to calculate the distance between two coordinates in consecutive rows. Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a) They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods such as great-circle distance which. As you can see from the example of Mt. From investigating my location history, it seems that unless my phone is off or without reception, Android reports my location exactly every 60 seconds. Latitude/Longitude Calculator - by Don Cross. Distance Calculation Introduction. Message: This is a GRADUATE question ???? The solution to this problem may be found in all standard surveying books, as it is a fundamental problem in geodesy. calculate distance between 2 gps coordinates. The code above is valid in Python 2. This script is able to calculate angle between planes, directions of different crystal system. Convert Coordinates - Calculate a position in a variety of formats. Please write the origin and destination city name, choose the distance unit and press calculate. This can be achieved through Google Maps API. Global Coordinates Measuring Distance Using latitude and longitude, can calculate the great circle distance between two points as follows: – d = R arccos(sin(ϕ 1) * sin(ϕ 2) + cos (ϕ 1) * cos (λ 1 - λ 2)) – Where R is the radius of the earth This assumes the earth is a sphere. Or if you are traveling via plane as it ignores earth curvature. The second one calculates the total distance between a list of locations. Shows work with distance formula and graph. The waypoint is also given as a GPS coordinate pair. This article provides a code snippet for calculating distance between two points taking latitude and longitude values as example. CalculateDistance(Location, Location, DistanceUnits) Calculate distance between two locations. Hatching Area between two graphics p_handle = hatching(f,g,xx,option) with : f,g : functions to plot xx : graphic support. Calculate the distance (d) between the two points (length of the hypotenuse). Distances between Points using GPS Coordinates Figure 1. So, one has to take the absolute value to get an absolute distance. A C# class library that will calculate distance and cardinal direction between two sets of coordinates and provides the lat/long boundaries around an origin coordinate allowing for simple SQL or LINQ selection of locations within the given radius. Haversine Formula []. Steps: Start ArcMap. Calculate the distance between two addresses gets confused when you input GPS coordinates. 939997 Point2: -19. Based on formula from http://www. The answers to Haversine Formula in Python (Bearing and Distance between two GPS points) provide Python implementations that answer your question. Theses free samples assist in understanding its usage. ppt), PDF File (. Quick demo to calculate distance between two points using GPS and SQL Server. In this video I will show you how to calculate the distances between two points (geographical locations, latitud longitud, zip codes, etc) using Google Maps API service. the earth's radius is R = 6372. A user account is not needed for the features on this web page. if the default search radius is used, distances from all input points to all near points are calculated. This page shows how to calculate the geographic midpoint (also known as the geographic center, or center of gravity) for two or more points on the earth's surface. For a deeper discussion of the source code, I recommend reading my blog entry: C#, GPS Receivers, and Geocaching: Vincenty’s Formula. if anyone can also guide me how to do this then also I will be highly thankful. Calculating distances between two points 27 Jun 2016, 07:04 compute all the possible distances between every single drownig event and the coastal border of the countries stated above. double haversine_km(double lat1, double long1. The RP number is the RP X-coordinate divided by DBRPS (distance between RPs) and truncating to an integer. Determining the position of a user using GPS is essentially a triangulation problem. Like the Project menu, Distance can take input in one of the two ways; via locking on to your current location, or through selecting a location on map. The distance formula is $\text{ Distance } = \sqrt{(x_2 -x_1)^2 + (y_2- y_1)^2}$. Distance calculator. Python | Calculate Distance between two places using Geopy GeoPy is a Python library that makes geographical calculations easier for the users. Posts: 24996. Rule 1: The distance between two points is the straight line connecting the points. Calculating the Distance Between Two GPS Coordinates with Python (Haversine Formula) September 7, 2016. But essentially the program should gather two sets of coordinates from a GPS module and the users phone (using the 1Sheeld) and work out the bearing and distance between them. Distance between two points and the midpoint. Methods of Calculating Distance. e NOT flat). We don't upload 34 Calculate The Distance Between Two Points Locations Coordinates In Power Bi, We just retail information from other sources & hyperlink to them. 912498 I have tried using the following formulas, which I found online, but it is clear I am using them incorrectly. This code was originally made for an Automatic Tracking Antenna Aimer. Then according to Lesson 31, Problem 5, the coördinates at the right angle are (15, 3). With this power bi. In case of datum transformation, select the desired datum in the target column(s) 4. Two results will be displayed - showing the great-circle distance between two points, and the initial compass bearing/heading from the origin to the destination. Calculating distance between two points represented by lat,long upto 15 feet accuracy I have been given the requirement calculating the distance from GPS coordinates. Questions: Problem I would like to know how to get the distance and bearing between 2 GPS points. It is easy to calculate Euclidean distance based on pythagorean theorem. The spherical formula for this is d=cos-1 [cos(90° - VT) cos(90° - PT) + sin(90° - VT) sin(90° - PT) cos(VN - PN)]. Or if you are traveling via plane as it ignores earth curvature. To find the distance between two points in three-dimensional space, use d = √((x 2 - x 1) 2 + (y 2 - y 1) 2 + (z 2 - z 1) 2). so i have to ask the user to input the two coordinates and based on hav. Most of Python geographic libraries provide those distance formula. In that case, when the input and near features are the same record, that result will be skipped so as not to report that each feature is 0 units from itself. Developers today experiment and implement various kind of features including the feature to calculate distance between two GPS coordinates in the Android mobile app. Calculating distance between two LAT long coordinates hi, i have a pair of latitude and longitude and i want to calculate the distance between these two points. In vbscript i achieved in the following wayNow i want to implement this in unix shell scri | The UNIX and Linux Forums. com is the free, no login required, route planner for runners cyclists and walkers. You can save the points in the history of GPS area or distance calculated. San Gorgonio observed at a distance of 87 miles, if you ignored the curvature of the Earth you would calculate an elevation angle that would be too large by nearly a factor of two. 157 miles, and a second is 1. This can be used to place features so they are relative to one another. just under 117 and a half degrees. The distance measuring can be done between two points or between your current position and one other point. In simple way of saying it is the absolute sum of difference between the x-coordinates and y-coordinates. Given the coordinates of an origin point on the Earth, along with a compass direction (azimuth) and a distance from that point, this calculator determines the coordinates of a target point. In Crystal Reports there is no built in function that does that calculation, so this blog post will walk you through creating a Custom Function based on the. It takes the latitude and longitude coordinates of two points represented in decimal format and calculates the length of a straight line between them. You can calculate the length of a path, running route, fence, border, or the perimeter of any object that appears on a google map. Intersection of Two Parabolas. Subject: Using latitude, longitude, and altitude to determine distance Category: Science > Instruments and Methods Asked by In any case, you were interested in calculating the distance between two points specified by longitude, latitude, and altitude. Calculate Distance and Bearing from Latitudes and Longitudes of two points (Geoscience Australia's website) Calculate Latitude and Longitude of a second point given Latitude and Longitude of first point and Distance and Bearing (Geoscience Australia's website) Transformation of Coordinates. To talk about points living in two dimensions, we specify them using two coordinates (the Cartesian coordinate system), the x coordinate and the y coordinate. The Global Positioning System (GPS) is a worldwide radio-navigation system formed from a constellation of 24 satellites, each in its own orbit 11,000 nautical miles above the Earth, and five ground stations that make sure the satellites are working properly. Calculate Direction and Distance between 2 points Sign in to follow this. Please refer to this. It involves first plotting your two GPS points on a spherical model of the earth, calculating the angle between them using a dot product, calculating distance using this angle and the earth's radius and finally dividing by the elapsed time to approximate the speed. Sum of Manhattan distances between all pairs of points. Calculate the Distance Between Two GPS Points with Python (Vincenty’s Inverse Formula) 2D Airfoil Geometry Manipulation via Composite Quadratic Bézier Curves and Python; Calculating the Distance Between Two GPS Coordinates with Python (Haversine Formula) Particle Swarm Optimization from Scratch with Python; Everything Else. plane to analyze and solve problems (e. Using the NMEA data above, I now need a way to calculate the direction and distance the robot needs to go in order to reach a desired waypoint. Note that the Vicenty algorithm for (ellipsoidal) course and distance may fail to converge correctly, or at all, if the final point is within 37' of. used to calculate max_segment_length. Excel vba calculate distance between two addresses or coordinates. Measure distances. 352901604 kilometers using the default ellipsoid WGS-84. Clustering geo location coordinates (lat,long pairs) Ask Question Asked 5 years, The python package has support for haversine distance which will properly compute distances between lat/lon points. There are occasions when the calculator will not be able to predict your journey, this could be if there is no valid route between the points or our service cannot determine the distance based on the given start and end points. Basically I want to know that with the difference of one degree how much will be the difference in Distance. Ask Question We are going to use this GPS module in a vehicle. The program measure the distance D in the first frame of the video, but not continiously as the objects move. if the default search radius is used, distances from all input points to all near points are calculated. Note that the World Geodetic System WGS84 and the European Reference System ETRS89 are virtually identical and that coordinate transformation between the two systems in practical navigation is unnecessary. It is a special case of a more general formula in spherical trigonometry, the law of haversines, relating the sides and angles of spherical "triangles". On the real data I need to calculate the number of Events that happen at 1km, 2km and 3km form each Location. Most GPS devices provide coordinates in the Degrees, Minutes and Seconds (DMS) format, or most commonly the Decimal Degrees (DD) format. For example navigators are one of those “every-day” applications where routing using specific algorithms is used to find the optimal route between two (or multiple) points. Calculate these first two angles in degrees (VN,VT). The Distance Matrix API is a service that provides travel distance and time for a matrix of origins and destinations. This can be used to place features so they are relative to one another. The distance between any two points with coordinates (x1, y1) and (x2,y2) is given by: d=sq root of d =(x2-x1)2+ - Answered by a verified Tutor We use cookies to give you the best possible experience on our website. Capable estimates total distance between any location using haversine formula and route method provided by the map and display location coordinates and location address. python gps distance latitude-longitude. Hatching Area between two graphics p_handle = hatching(f,g,xx,option) with : f,g : functions to plot xx : graphic support. Blog Post created by flat-Earth formulas for calculating the distance between two points start showing noticeable errors when the distance is more than about 20 kilometers. To talk about points living in two dimensions, we specify them using two coordinates (the Cartesian coordinate system), the x coordinate and the y coordinate. Suppose the value of K is 3. Since the earth is a sphere, you can't use the distance formula that works for two points in a plane. In this case, we’re going to define distance between two pixels as the Euclidean distance between their x,y coordinates in the image. Every Point on a Graph has Two Coordinates. Calculate distance of 2 points in 3 dimensional space. Dimensions— A special kind of annotation that shows specific lengths or distances, for example, to indicate the length of a side of a building, a land parcel, or the distance between two features. GPS Visualizer's map, profile, and conversion programs have the ability to instantly add elevation data — from a DEM (digital elevation model) database — to any type of GPS file. It can be used for weapons attack since the targeted things from the weapons are on the different plane. The distance between any two points. The code has been written in five different formats using standard values, taking inputs through scanner class, command line arguments, while loop and, do while loop, creating a separate class. Someone told me that I could also find the bearing using the same data. Distance calculations are based on the great circle distance between points, and do not account for differences in elevation. The distance between each degree of latitude is about 69 m. def calculate_initial_compass_bearing (pointA, pointB): """ i messed up the x and y and i wasn't aware that i can use the wgs84 coordinates without transforming to a 2D. 5 depicts the. Latitude/Longitude Distance Calculation. This makes plotting latitude quite straight forward. in more than 20 kms. Or if you are traveling via plane as it ignores earth curvature. Drag to change location and find new elevation. to calculate the GPS distance between two points using GPS coordinates. Use python to build a scrip which takes those coordinates (centers of each team member's face) and determines the distance from the center of the image to the center of team member's faces. but will return wrong value in Python 3 That comes from the fact that it uses the controversial "/" division operator which in python 2 returns the floor division when used with 2 integers. How far is it from (4, 3) to (15, 8)? Consider the distance d as the hypotenuse of a right triangle. Calculate the distance between two coordinates by latitude and longitude, including a Javascript implementation. This code outputs the distance between 2 GPS points showing also the vertical and horizontal bearing between them. In this article, we will see how to calculate the distance between 2 points on the earth in two ways. Calculate distance and true bearing between two latitude/longitude coordinates and show in Google Map : This service allows you to calculate the shortest distance over the earth's surface between two locations A and B. In that case, when the input and near features are the same record, that result will be skipped so as not to report that each feature is 0 units from itself. If they intersect, then at that line of intersection, they have no distance -- 0 distance -- between them. If the distance of the user from three or more satellites is known, then the 3D position can be calculated using triangulation. This post is rather old but as I came across an issue testing it I thought it would be good to add a precision. I was trying to determine, understand, and compare the latitude and longitude of Pohnpei in the Federated States of Micronesia with relation to Toledo,Ohio and Miami Beach,Florida, two places where I have lived. Intersections can be performed between any two points with a non-zero horizontal distance between them. The Haversine formula accounts for the. Using the Haversin formula. 939550 The distance between them is around 86 meters. To calculate distances between points given by latitudes and longitudes precisely, you need to know which geoid was used as a reference in specifying them. I've a set of GPS coordinates in Decimal Degree format. The term is the number of points we have that are separated by the distance. Don't ask why, totally a new more complicated discussion. I already have the GPS coordinates of the image itself (center) and the distance between the center and the object, as well as the pixel location of the object. It involves first plotting your two GPS points on a spherical model of the earth, calculating the angle between them using a dot product, calculating distance using this angle and the earth's radius and finally dividing by the elapsed time to approximate the speed. Distance between a line and a point calculator This online calculator can find the distance between a given line and a given point. See distance to other cities from Houston – Texas – USA measured in kilometers (km), miles and nautical miles and their local time. GPS provides the accuracy about 10 meters, but DGPS can provide accuracy around 1 meter, even beyond that 10 cm. WxPython supports wxPoint and wxRect, but it lacks many basic functions (such as, say, adding two points together to produce a third point. calculate distance between 2 gps coordinates. Given two LatLng objects and value between 0 and 1, you may also calculate a destination between them using the interpolate() method, which performs spherical linear interpolation between the two locations, where the value indicates the fractional distance to travel along the path from the origin to the destination. This is the angular distance, in radians, relative to the center of the earth. if the default search radius is used, distances from all input points to all near points are calculated. com offers free software downloads for Windows, Mac, iOS and Android computers and mobile devices. A rough approximation is : 1 deg of longitude = 111. That all leads to an implementation of what is known as the T. This means that when a feature is inside a polygon, the distance between the feature and the surrounding polygon is zero. Edit: I made a correction to move from -180->180 to 0->360 North1,East1 are your reference coordinates, North2, east2 the target. Rect) This code is lacking a zillion essential features (but interpoint distance can now be calculated).

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There is a theory due to Tresse, which is unfortunately fairly complicated. It is explained, at least partly, in the book of Arnol'd, Geometric Methods in the Theory of Ordinary Differential Equations. Elie Cartan wrote a difficult paper on it, and this paper was explained more clearly in a paper of Bryant, Griffiths and Hsu, Toward a Geometry of Differential Equations. The possibility of finding coordinates in which both systems of curves are straight lines is precisely the vanishing of Tresse's invariants, which occurs just when your space $Z$ is given by a single quadratic equation in the space $X \times Y$, in some system of coordinates. Explicit formulae for Tresse's invariants are in the sources I mentioned. I wrote a paper on the relation of this problem to complex algebraic geometry: http://arxiv.org/pdf/math/0507087v5.
There is a theory due to Tresse, which is unfortunately fairly complicated. It is explained, at least partly, in the book of Arnol'd, Geometric Methods in the Theory of Ordinary Differential Equations. Elie Cartan wrote a difficult paper on it, and this paper was explained more clearly in a paper of Bryant, Griffiths and Hsu, Toward a Geometry of Differential Equations. The possibility of finding coordinates in which both systems of curves are straight lines is precisely the vanishing of Tresse's invariants, which occurs just when your space $Z$ is given by a single quadratic equation in the space $X \times Y$. Explicit formulae for Tresse's invariants are in the sources I mentioned.


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# iOS - Localizing strings in a project

Localization is an often overlooked problem. We start a project, we know that we only have to support one language and we approach our string-handling based on that requirement. When the time comes to support a second language, the project grew so much that adapting to that second language causes pain and frustration.

## Doing it right from the beginning

iOS and Xcode support localized strings in a rudimentary-but-pragmatic way: we can define a Localizable.strings file, and localize that file in n languages. For each language we will have a key-value file that will contain all our strings:

// German strings

"ok_button_title" = "OK";
"cancel_button_title" = "Abbrechen";

/*Main Screen*/
"main_title" = "Willkommen";

// Spanish strings

"ok_button_title" = "Vale";
"cancel_button_title" = "Cancelar";

/*Main Screen*/
"main_title" = "Bienvenido";

For accessing these strings all we need to do is to use NSLocalizedString(key, comment: "") and pass the key we are interested in. Eg. NSLocalizedString("ok_button_title", comment: "")

This is going to work nicely and, if we were to launch the app in German or Spanish, the system will know which strings to use.

## Getting they keys under control

The main drawback of that approach is that keys are strings and if they start going around, that could be prone to error.

This can be easily solved as well. Let’s define a new type called Strings which will contain all our keys:

enum Strings: String {
case okButtonTitle = "ok_button_title"
case cancelButtonTitle = "cancel_button_title"
case mainTitle = "main_title"
case mainSubtitle = "main_subtitle"
}

We can even define an extension to get the localized string for every key in the Strings enum:

extension Strings {
var localized: String {
return NSLocalizedString(rawValue, comment: "")
}
}

Now all we need to do to use a string in a UILabel, for example, is to call:

label.text = Strings.mainTitle.localized

## Bringing it to the next level: extracting the strings

Keeping strings and wordings up to date is usually a burden for developers. Designers would produce a mockup which some wordings than then the product manager will need to check/update. The developer is usually left with the task of making sure that these wordings are in sync. If a project is run in several platforms (iOS, Android, web…), keeping the wordings up to date and synchronized can get out of control easily.

A wiser approach would be to move these strings out of the project and place them in a centralized tool that every platform could access. You could build such a service or you can use a commercial solution. For the sake of this tutorial I’m going to use POEditor: an online tool which allows you define terms and their translations and provides an API to access that information.

### Setting up the project

This step is very straight-forward: we create a project, we add new entries (called terms in POEditor) and provide the translations. That’s all it is.

POEditor

### Automatizing the fetching of the strings

The underlying idea is that, on every build, we want to fetch the latest strings, generating our Strings enum automatically (listing all available keys), and download the translations in the different supported languages.

To do so I’m using Python, hacking my way into it (please, don’t judge my Python knowledge: I know nothing about nothing).

400: Invalid request

The script does two main things: first, it fetches all the terms listed in the project. With that we create our Strings class (we are also taking care of the case conversion from snake to camel case).

This script is run during the build phase:

Build Phases

## Conclusion

This can be easily improved, but with a couple of neat tricks we were able to create a setup where developers don’t really need to worry about strings anymore. A PM or marketing person could go into that tool and update these strings and the app will pick-up on the changes during the next build.

The tool also supports other formats for the export file (JSON, Android XML, etc.), so this script could be easily adapted to your project/platform requirements.


text:
# LU Decomposition Method – Algorithm, Implementation in C With Solved Examples

LU Decomposition Method
LU Decomposition Method is also known as factorization or Crout’s reduction method. Let the system of linear equations be
$Ax=b……….(1)$
Where A,


text:
# Polynomial and exponential growth in groups and algebras

Let $S ^ \prime = \{ g _ {1} \dots g _ {n} \}$ be a set of generators for a finitely-generated group $G$. Consider $S = \{ g _ {1} \dots g _ {n} , g _ {1} ^ {-} 1 \dots g _ {n} ^ {-} 1 \}$. Let $S ^ {(} n)$ be the collection of all elements of $G$ which can be written as a word in $S$ of length $\leq n$, and let $f _ {G} ( n) = \# S ^ {(} n)$ be the number of elements of $S ^ {(} n)$. The function $f _ {G} ( n)$ is called the growth function of $G$( with respect to the chosen generators). A similar definition can be given for algebras, cf. below. The subject of growth functions for algebras and groups studies the order of growth of functions like $f _ {G} ( n)$ and relates this to group-theoretic properties of $G$.

Consider a non-negative function $f: \mathbf N \rightarrow \mathbf R$, $f( n) \geq 0$ for all $n$. Let $f, g$ be such "growth functions" . The function $f$ is of lesser growth than $g$, $f < g$, if there exist a $c > 0$ and an $m \in \mathbf N = \{ 1, 2 ,\dots \}$ such that $f( n) \leq cg( nm)$ for all $n \in \mathbf N$. Two growth functions $f, g$ are of the same order of growth if $f < g$ and $g < f$. The equivalence class of $f$ for this relation is denoted by $[ f ]$ and is called the growth of $f$. As in analytic function theory, one considers

$$\rho ( f ) = { {\lim\limits \sup } } _ {n \rightarrow \infty } \ \frac{ \mathop{\rm log} \mathop{\rm log} f( n) }{ \mathop{\rm log} n } ,$$

the order of growth of $f$, which only depends on $[ f ]$. The function $n \mapsto 2 ^ {n}$ has order of growth 1, or exponential growth. This is the highest that is of interest (and can occur) in the present context. A function $f$ is of polynomial growth, or power growth, $r$ if $f \in [ n ^ {r} ]$. Given that $\rho ( f ) = 0$, the polynomial growth power $r$ is found from

$$r( f ) = {\lim\limits \sup } _ {n \rightarrow \infty } \ \frac{ \mathop{\rm log} f( n) }{ \mathop{\rm log} n } .$$

If the growth of $f$ satisfies the inequalities $[ 2 ^ {n} ] > [ f ] > [ n ^ {r} ]$ for all $r > 0$, the function $f$ is said to be of intermediate growth.

The growth function for a finitely-generated group was defined above. The growth of $[ f _ {G} ]$ does not depend on the chosen system of generators and is hence an invariant of $G$. The growth of a finitely-generated free group on $\geq 2$ generators is exponential. A finitely-generated nilpotent group has polynomial growth.

For an algebra $A$ over a field $k$( associative, Lie, etc.) the definition is as follows.

Let $a _ {1} \dots a _ {r}$ be a set of generators of $A$ over $k$, so that every $a \in A$ is a $k$- linear combination of monomials in the $a _ {i}$. Let $V$ be the vector space spanned by the $a _ {i}$. Let $V ^ {k}$ be the vector subspace of $A$ of all $k$- linear combinations of products $v _ {1} \dots v _ {k}$, $v _ {i} \in V$. Then the function

$$f _ {A} ( n) = \sum _ { i= } 1 ^ { n } \mathop{\rm dim} V ^ {i}$$

is the growth function of $A$( with respect to the generating subspace $V$). The growth of $f _ {A}$ does not depend on the choice of $V$. The growth of the group algebra $k[ G]$ is the growth of $G$.

If $W = \oplus _ {n=} 0 ^ \infty W ^ {n}$ is a graded vector space, one defines the series

$$h _ {W} ( z) = \sum _ { n= } 0 ^ \infty \mathop{\rm dim} ( W ^ {n} ) z ^ {n} .$$

This series is called the Hilbert series, Poincaré series, Hilbert–Poincaré series, or Poincaré–Betti series, depending on the context. There is an associated growth function

$$g _ {W} ( n) = \sum _ { i= } 0 ^ { n } \mathop{\rm dim} ( W ^ {i} ).$$

If $A = \oplus _ {n=} 0 ^ \infty A ^ {(} n)$ is a finitely-generated graded algebra, then the growth function coming from the grading and any growth function defined by a finite-dimensional generating vector space have the same growth.

For graphs one also defines a growth function. Let $G = ( V, E)$ be a finite oriented graph, possibly with loops and multiple edges. Let $c _ {G} ( m)$ be the number of paths of length $m$. Then the Poincaré series of the graph $G$ is

$$P _ {G} ( z) = \sum _ { m= } 0 ^ \infty c _ {G} ( m) z ^ {m} ,$$

and the growth function of $G$ is $f _ {G} ( m) = \sum _ {i=} 0 ^ {m} c _ {G} ( m)$. Here a path of length $m$ is a sequence of vertices and edges $v _ {1} e _ {1} v _ {2} \dots e _ {m-} 1 v _ {m}$ such that $e _ {i}$ goes from $v _ {i}$ to $v _ {i+} 1$.

There are two central questions concerning Poincaré series and growth functions.

i) In the graded case: Is the Poincaré series rational?

ii) In all cases: Is it true for a suitable class of algebras or groups that all objects either have polynomial or exponential growth?

A positive answer to i) (in the graded case) implies a positive answer to ii).

The Poincaré series of a graph is a rational function of the form $P _ {G} ( z) = q( z) p( z) ^ {-} 1$ with $p( z) = 1- a _ {1} z - \dots - a _ {n} z ^ {n}$, the reciprocal polynomial to the minimal polynomial $m( z) = z ^ {n} - a _ {1} z ^ {n-} 1 - \dots - a _ {n}$ of the incidence matrix $B$ of $G$, where $b _ {ij}$ is the number of edges from vertex $i$ to vertex $j$. In particular, the growth of a graph is either polynomial or exponential, [a13].

There are many algebras for which the associated growth functions and Poincaré series have been considered. For instance, for a local ring, $( A, m)$, the Poincaré series of $\oplus m ^ {i} / m ^ {i+} 1$, cf. Local ring. For an associative nilpotent ring over $k$ one considers the graded algebra $\mathop{\rm Ext} _ {\widetilde{N} } {} ^ {*} ( k , k)$, the Yoneda $\mathop{\rm Ext}$- algebra, where $\widetilde{N} = N \oplus k$ is the algebra over $k$ obtained by adjoining a unit. For a local ring $R$ one also considers $\mathop{\rm Ext} _ {R} ^ {*} ( k, k)$, where now $k$ is the residue field of $R$. In topology one consider the graded algebra of the homology (or cohomology) of the loop space $\Omega X$ of a space $X$. In all these cases there are relations (established or conjectured) between the properties of the Poincaré series (such as rationality, rate of convergence, etc.) and properties of the algebras or topological spaces involved.

There are a variety of constructions associating graphs to algebras, spaces to algebras, algebras to spaces, algebras to graphs, and corresponding relations between the associated growth functions and Poincaré series, cf. [a1], [a13][a15].

The growth problem for commutative local rings is settled by the following result. Let $( R, \mathfrak m )$ be a local ring and consider its Betti numbers $b _ {i} ( R) = \mathop{\rm dim} _ {k} ( \mathop{\rm Ext} _ {R} ^ {i} ( k, k)) = \mathop{\rm dim} _ {k} \mathop{\rm Tor} _ {i} ^ {R} ( k, k)$, i.e. the coefficients of its Poincaré series. Then there are two possibilities, [a16]: either $b _ {i}$ is a polynomial in $i$, which happens if and only if $R$ is a complete intersection, or there exist integers $N$ and $d > c > 1$ such that $c ^ {i} < b _ {i} < d ^ {i}$ for all $i \geq N$. This implies immediately a positive solution to the Golod–Gulliksen conjecture, which stated that a local ring is a complete intersection if and only if the radius of convergence of its Poincaré series is $\geq 1$. Indeed one has, [a16], [a17], that the radius of convergence is $\infty$ if and only if $R$ is regular (cf. Local ring), that it is precisely 1 if and only if $R$ is an irregular complete intersection and that it is strictly between 0 and 1 otherwise.

The concept of a complete intersection local ring corresponds to a complete intersection in algebraic geometry, i.e. varieties in $\mathbf P ^ {N}$ of codimension $i$ determined by $i$ equations. In algebraic terms this can be described as follows.

Let $( R, \mathfrak m )$ be a commutative Noetherian local ring, $n = \mathop{\rm dim} _ {k} \mathfrak m / \mathfrak m ^ {2}$( sometimes called the embedding dimension of $R$). Choose a basis for $\mathfrak m / \mathfrak m ^ {2}$ and consider the corresponding Koszul complex $E _ {*}$. Let $\epsilon _ {j} = \mathop{\rm dim} _ {k} H _ {j} ( E _ {*} )$. The local ring $( R, \mathfrak m )$ is a complete intersection if $e _ {1} = n- \mathop{\rm dim} R$. A Noetherian local ring is a complete intersection if and only if its completion $( \widehat{R} , \widehat{ {\mathfrak m }} )$ is a complete intersection, and this is the case if and only if $\widehat{R}$ is a quotient of a complete regular local ring $\widetilde{R}$ by an ideal generated by a regular $\widetilde{R}$- sequence (cf. Koszul complex). For commutative Noetherian local rings one has the chain of implications: regular $\Rightarrow$ complete intersection $\Rightarrow$ Gorenstein $\Rightarrow$ Cohen–Macaulay. Cf. also Gorenstein ring and Cohen–Macaulay ring.

Cf. [a1] for a recent survey concerning these and other results on growth and rationality for algebras and spaces.

For groups there are, among others, the following theorems.

The Milnor–Wolf theorem: A finitely-generated solvable group is either of polynomial growth or of exponential growth. In the first case it is polycyclic and almost nilpotent (i.e. has a nilpotent subgroup of finite index), [a8], [a9].

The Gromov–Milnor theorem: A finitely-generated group is of polynomial growth if and only if it is almost nilpotent, [a9], [a6].

There are groups of intermediate growth [a2].

Tits' theorem: A finitely-generated subgroup of a connected Lie group has either exponential growth or is almost nilpotent (and hence has polynomial growth), [a7].

There are relations between the geometry of manifolds and the growth of its fundamental group. Probably the oldest one is due to A.S. Shvarts, [a5]. Let $M$ be a connected compact manifold with fundamental group $G = \pi _ {1} ( M)$. Let $\widetilde{M}$ be the universal covering space of $M$. Give $M$ a Riemannian metric $g$ and consider the induced metric $\widetilde{g}$ on $\widetilde{M}$. ( $M$ and $\widetilde{M}$ are locally the same.) Take an arbitrary point $\widetilde{p} \in \widetilde{M}$ and let $v( s)$ be the volume of the ball of radius $s$ in $\widetilde{M}$ with centre $\widetilde{p}$. The growth of $v$ does not depend on $g$ or $\widetilde{p}$ and is hence an invariant of $M$. It is called the volume invariant, [a4]. The Shvarts theorem now says that the volume invariant of $M$ is the growth of $\pi _ {1} ( M)$.

A mapping $\phi$ from a metric space $( M, d)$ to another $( M ^ \prime , d ^ \prime )$ is called globally expanding if $d ^ \prime ( \phi ( x), \phi ( y)) > d( x, y)$ for all $x \neq y$. It is called locally expanding, or just expanding, if each point has an open neighbourhood on which $\phi$ is globally expanding. The mapping $z \mapsto z ^ {2}$ from the circle into itself is locally expanding (but not globally). Franks' polynomial growth theorem says that if a compact manifold admits an expanding self-mapping, then its fundamental group is of polynomial growth, cf. [a6].

The Milnor fundamental group growth theorems are the following, [a3]. If $M$ is a complete $n$- dimensional Riemannian manifold with an everywhere positive semi-definite mean curvature tensor $R _ {ij}$, then the growth of every finitely-generated subgroup of $\pi _ {1} ( M)$ is polynomial. On the other hand, if $M$ is a compact Riemannian manifold with all sectional curvatures less than zero, then the fundamental group is of exponential growth.

One application of growth theory was to the class field tower problem, cf. Class field theory and Tower of fields. Let $G$ be a group and $\mathbf F _ {p}$ the field of $p$ elements, $p$ a prime number. Let $A = \mathbf F _ {p} [ G]$ be the group algebra of $G$ over $\mathbf F _ {p}$ and let $\mathfrak a$ be the augmentation ideal of $A$, i.e. the ideal generated by the elements $g- 1 \in R$, $g \in G$. The Zassenhaus filtration is the sequence of characteristic subgroups $G _ {n} = \{ {g \in G } : {g- 1 \in \mathfrak a ^ {n} } \}$. The sequence $\{ G _ {n} \}$ is also called the lower $p$- central series of $G$. Let $\widehat{A}$ be the associated graded ring defined by $\mathfrak a$, i.e.

$$\widehat{A} = \oplus _ { n= } 0 ^ \infty {\widehat{A} } _ {n} ,\ \ {\widehat{A} } _ {n} = \mathfrak a ^ {n} / \mathfrak a ^ {n+} 1 .$$

Let $f _ {G} ( z)$ be the associated Hilbert series

$$f _ {G} ( z) = \sum _ { n= } 0 ^ \infty \mathop{\rm dim} ( {\widehat{A} } _ {n} ) z ^ {n} ,$$

where $\mathop{\rm dim} = \mathop{\rm dim} _ {\mathbf F _ {p} }$ and it is assumed that $\mathop{\rm dim} {\widehat{A} } _ {n} < \infty$, which is guaranteed if $\mathop{\rm dim} {\widehat{A} } _ {1} < \infty$. Let $G = F/R$, where $F$ is a free group on $d \geq 2$ generators, and let $S$ be a set of defining words for $G$. For each $s \in S$, let $d ( s) = \sup \{ {n } : {s \in F _ {n} } \}$, where $F _ {n}$ is the Zassenhaus filtration of $F$. Let $l _ {n} = \# \{ {s \in S } : {d( s) = n } \}$, $l _ {0} = 1$. Then the Golod–Shafarevich theorem says: 1) $\mathop{\rm dim} {\widehat{A} } _ {n} \geq d( \mathop{\rm dim} ( {\widehat{A} } _ {n-} 1 )) - \sum _ {k=} 0 ^ {n-} 1 l _ {n-} k$; and 2) if $l _ {n} \leq ( d- 1) ^ {2} /4$ for all $n$, then the algebra $A$ is infinite dimensional, [a11], [a12]. This theorem was a main ingredient in the negative solution of the class field tower problem; that is, in the construction of infinite class field towers.

Still another application is Lazard's theorem [a10], which provides a criterion for the analyticity of a pro- $p$- group in terms of the Hilbert series of the associated algebra.

#### References

 [a1] I.K. Babenko, "Problems of growth and rationality in algebra and topology" Russian Math. Surv. , 41 : 2 (1986) pp. 117–175 Uspekhi Mat. Nauk , 41 : 2 (1986) pp. 95–142 MR0842162 Zbl 0607.55007 [a2] R.I. Grigorchuk, "On Milnor's problem of group growth" Soviet Math. Dokl. , 28 (1983) pp. 23–26 Dokl. Akad. Nauk SSSR , 271 (1983) pp. 30–33 MR712546 [a3] J. Milnor, "A note on curvature and fundamental group" J. Diff. Geom. , 2 (1968) pp. 1–7 MR0232311 Zbl 0162.25401 [a4] V. Efremovich, "On proximity geometry of Riemannian manifolds" Transl. Amer. Math. Soc. (2) , 39 (1964) pp. 167–170 Uspekhi Mat. Nauk , 8 (1953) pp. 189–191 Zbl 0152.39201 [a5] A. Shvarts, "A volume invariant of coverings" Dokl. Akad. Nauk SSSR , 105 (1955) pp. 32–34 (In Russian) Zbl 0066.15903 [a6] M. Gromov, "Groups of polynomial growth and expanding maps" Publ. Math. IHES , 53 (1981) pp. 53–73 MR0623535 MR0623534 Zbl 0474.20018 [a7] J. Tits, "Free subgroups in linear groups" J. of Algebra , 20 (1972) pp. 250–270 MR0286898 Zbl 0257.20031 Zbl 0236.20032 [a8] J.A. Wolf, "Growth of finitely generated solvable groups and curvature of Riemannian manifolds" J. Diff. Geom. , 2 (1968) pp. 421–446 Zbl 0207.51803 [a9] J.W. Milnor, "Growth of finitely generated solvable groups" J. Diff. Geom. , 2 (1968) pp. 447–449 MR0244899 Zbl 0176.29803 [a10] M. Lazard, "Groupes analytiques -adiques" Publ. Math. IHES , 26 (1965) pp. 389–603 MR209286 [a11] E.S. Golod, I.R. Shafarevich, "On class field towers" Transl. Amer. Math. Soc. (2) , 48 (1965) pp. 91–102 Izv. Akad. Nauk SSSR Ser. Mat. , 28 (1964) pp. 261–272 Zbl 0148.28101 [a12] H. Koch, "Galoissche Theorie der -Erweiterungen" , Deutsch. Verlag Wissenschaft. (1970) [a13] V.A. Ufnarovskii, "A criterion for the growth of graphs and algebras defined by words" Math. Notes , 31 (1982) pp. 238–241 Mat. Zametki , 31 (1982) pp. 465–472 [a14] J.-E. Roos, "Relations between the Poincaré–Betti series of loop spaces and of local rings" M.P. Malliavin (ed.) , Sem. Alg. P. Dubreil , Lect. notes in math. , 740 , Springer (1979) pp. 285–322 MR563510 Zbl 0415.13012 [a15] C. Löfwall, "On the subalgebra generated by one dimensional elements in the Yoneda Ext-algebra" , Preprint Dept. Math. , Univ. Stockholm (1976) Zbl 0429.13008 [a16] L. Avramov, "Local algebra and rational homotopy" Astérisque , 113–114 (1984) pp. 15–43 MR0749041 Zbl 0552.13003 [a17] L. Avramov, "Local rings of finite simplicial dimension" Bull. Amer. Math. Soc. , 10 (1984) pp. 289–291 MR0733698 Zbl 0552.13005
How to Cite This Entry:
Polynomial and exponential growth in groups and algebras. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polynomial_and_exponential_growth_in_groups_and_algebras&oldid=48236


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# How to show that $B^{-1}\cdot A^{-1}=B\cdot A$?

I can't find the solution of this problem:

Given two $n\times n$ square matrices $A,B$ such that $A^2\cdot B^2=I_n$, show that $B^{-1}\cdot A^{-1}=B\cdot A$.

• If $A^2 B^2 =I$ then $B^2 A^2 = I$. – copper.hat Jan 8 '15 at 16:44

Since $A^{2}B^{2}=I_{n}$ note that taking $A^{-1}=ABB$ we have that $A\cdot A^{-1}=I_n$. For square matrices this is enough to show $A$ is invertible. The same follows for $B$ by taking $B^{-1}=AAB$. Using the facts that $A^{-1}\cdot A=I_{n}$ and $B\cdot B^{-1}=I_{n}$ we get that \begin{eqnarray*} A^{2}B^{2}=I_{n} & \iff & AB^{2}=A^{-1}I_{n},\mbox{ by left multiplication}\\ & \iff & AB=A^{-1}I_{n}B^{-1},\,\mbox{ by right multiplication}\\ & \iff & AB=A^{-1}B^{-1}. \end{eqnarray*} Taking inverses of both sides and using the property $(AB)^{-1}=B^{-1}A^{-1}$ gives the desired result.

• Can you clarify? – Phanu9000 Jan 8 '15 at 16:54
• Well I should have really said, take inverses of both sides, and then use socks-shoes property? – Phanu9000 Jan 8 '15 at 16:57
• I can't judge that. I don't know what is called socks-shoes property. – Pp.. Jan 8 '15 at 16:58
• The usual property of inverses: $(AB)^{-1}=B^{-1}A^{-1}$ – Phanu9000 Jan 8 '15 at 17:00
• Cool name! Yes, that does make it. And actually it makes it a nicer answer than the other. Just add also the observation that $A^2B^2=I$ implies $A,B$ are invertible. – Pp.. Jan 8 '15 at 17:05

$A^2 \cdot B^2 = I \Rightarrow A, B$ are invertible. The set of all invertible matrices forms a group. So we also have $B^2 \cdot A^2 = I.$ Hence $B \cdot A = B^{-1}\cdot A^{-1}.$

I'm assuming that the entries of the matrices are from a field.

EDIT: $A^2 \cdot B^2 = I \Rightarrow \text{det}(A^2) \cdot \text{det}(B^2) = \text{det}(A^2 \cdot B^2) = 1 \Rightarrow \text{det}(A^2) \neq 0.$ Now $(\text{det}(A))^2 = \text{det}(A^2) \Rightarrow \text{det}(A) \neq 0.$ Similarly for $B.$

• Thank you for your answer. Can you please explain why $A^{2}⋅B^{2}=I\Rightarrow A,B$ are invertible? – igil Jan 8 '15 at 16:57
• ok! thanks for the remark! – igil Jan 8 '15 at 17:06
• @ioll: you are welcome. :) – Krish Jan 8 '15 at 17:07


text:
ï»¿ A body of mass m accelerates uniformly from rest to v1 in time t1. The instantaneous power delivered to the body as a function of time t is from Physics Motion in A Plane Class 11 Manipur Board

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A body of mass m accelerates uniformly from rest to v1 in time t1. The instantaneous power delivered to the body as a function of time t is

B.

Let the constant acceleration of body of mass m is a.
From equation of motion

v1 = 0 + at1
â‡’ a = t2/t1Â = ...... (i)
At an instant t, the velocity v of the body v = 0 + at

Let the constant acceleration of body of mass m is a.
From equation of motion

v1 = 0 + at1
â‡’ a = t2/t1Â = ...... (i)
At an instant t, the velocity v of the body v = 0 + at

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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
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Give three examples of vector quantities.

Force, impulse and momentum.
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Give three examples of scalar quantities.

Mass, temperature and energy
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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors.Â

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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
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text:
# Mathematical induction question

1. Apr 5, 2013

### Googl

Hi all,

I am revising on Proof by mathematical induction and I have came across a question I haven't found a way to work it out.

$$\sum_{r=1}^n r(r!) = (n + 1)! -1$$

I understand the steps of proving by mathematical induction question. The ! is causing the confusion.

2. Apr 5, 2013

### Staff: Mentor

In which way? It is a Factorial.

3. Apr 5, 2013

### Bacle2

Maybe you can rewrite the general summand as:

(r+1)r!-r! and expand the sum, see what happens.


text:
# Math Help - [SOLVED] Optimization Problem

1. ## [SOLVED] Optimization Problem

Hi,

I just need a clue to what to do next for this question:
Each rectangular page of a book must contain 43.890625 cm$^2$ of printed text, and each page must have 2.5 cm margins at top and bottom, and 1.6 cm margin at each side. What is the minimum possible area of such a page?

Solution: Let $x$ be the width and let $y$ be the height of the page. Then the width of the printed area is given by $l =$ x-3.2 and the height of the printed area is given by $h$ = y-5 . We note that the area of the printed text is given by $p$ = (x-3.2)(y-5) . The problem is to find $x$ and $y$ to minimize xy under the condition p= (x-3.2)(y-5) = 43.890625.

The problem I am stuck with, is finding the area in terms of x...
We aren't given another equation to isolate y, and I tried isolating for y in terms of the area which gave me
43.890625 + 5x - 16 = y
but the only possible answers all contained 43.890625 without being maniulated...

2. Originally Posted by alleysan
Hi,

I just need a clue to what to do next for this question:
Each rectangular page of a book must contain 43.890625 cm$^2$ of printed text, and each page must have 2.5 cm margins at top and bottom, and 1.6 cm margin at each side. What is the minimum possible area of such a page?

Solution: Let $x$ be the width and let $y$ be the height of the page. Then the width of the printed area is given by $l =$ x-3.2 and the height of the printed area is given by $h$ = y-5 . We note that the area of the printed text is given by $p$ = (x-3.2)(y-5) . The problem is to find $x$ and $y$ to minimize xy under the condition p= (x-3.2)(y-5) = 43.890625.

The problem I am stuck with, is finding the area in terms of x...
We aren't given another equation to isolate y, and I tried isolating for y in terms of the area which gave me
43.890625 + 5x - 16 = y
but the only possible answers all contained 43.890625 without being maniulated...

the printed area is fixed ... the problem wants to minimize the area of the entire page.

let x = width of printed part
y = length of printed part

$A = (x+3.2)(y+5)$

$xy = 43.890625$ cm$^2$ ... call that ugly area constant, $k$

$y = \frac{k}{x}
$

$A = (x + 3.2)\left(\frac{k}{x} + 5\right)$

find $\frac{dA}{dx}$ and optimize


text:
## Sunday, March 20, 2016

### Adding disclosures to Wikidata with Bioclipse

Last week the huge, bi-annual ACS meeting took place (#ACSSanDiego), during which commonly new drug (leads) are disclosed. This time too, like this one tweeted by Bethany Halford:

Because getting this information out in the open is important, I think it's a good idea to add them to Wikidata (see doi:10.3897/rio.1.e7573). So, with Bioclipse (doi:10.1186/1471-2105-8-59) I redrew the structure:

I previously blogged about how to add chemicals to Wikidata, but I realized that I wanted to also use Bioclipse to automate this process a bit. So, I wrote this script to generated the SMILES, InChI, InChIKey, double check the compound is not already in Wikidata (using the Wikidata SPARQL endpoint), an look up the PubChem compound identifier (example SMILES).

smiles = "CCCC"

mol = cdk.fromSMILES(smiles)
ui.open(mol)

inchiObj = inchi.generate(mol)
inchiShort = inchiObj.value.substring(6)
key = inchiObj.key // key = "GDGXJFJBRMKYDL-FYWRMAATSA-N"

sparql = """
PREFIX wdt: <http://www.wikidata.org/prop/direct/>
SELECT ?compound WHERE {
?compound wdt:P235 "$key" . } """ if (bioclipse.isOnline()) { results = rdf.sparqlRemote( "https://query.wikidata.org/sparql", sparql ) missing = results.rowCount == 0 } else { missing = true } formula = cdk.molecularFormula(mol) // Create the Wikidata QuickStatement, // see https://tools.wmflabs.org/wikidata-todo/quick_statements.php item = "LAST" // set to Qxxxx if you need to append info, // e.g. item = "Q22579236" pubchemLine = "" if (bioclipse.isOnline()) { pcResults = pubchem.search(key) if (pcResults.size == 1) { cid = pcResults[0] pubchemLine = "$item\tP662\t\"$cid\"" } } if (!missing) { println "====================" println "Already in Wikidata as " + results.get(1,"compound") println "====================" } else { statement = """ CREATE$item\tDen\t\"chemical compound\"
$item\tP233\t\"$smiles\"
$item\tP274\t\"$formula\"
$item\tP234\t\"$inchiShort\"
$item\tP235\t\"$key\"
\$pubchemLine
"""

println "===================="
println statement
println "===================="
}

The output of this script is a QuickStatement for Magnus Manske's tool (IMPORTANT: it's not meant to automate editing Wikidata! I only automate creating the input, which I carefully check (e.g. checking all stereochemistry is defined)! Note, how Bioclipse opens up the structure in a viewer with ui.open()), which is a list of commands to create and edit entries in Wikidata. You need to enable it first, but if you have an account, this is not too hard. Of course, the advantage is that it is a lot quicker. I have similar script to create QuickStatements starting with only a ChEMBL identifier.

The QuickStatement for GDC-0853 looks like:

CREATE

LAST Den "chemical compound"
LAST P233 "O=C1C(=CC(=CN1C)c2ccnc(c2CO)N4C(=O)c3cc5c(n3CC4)CC(C)(C)C5)Nc6ncc(cc6)N7CCN(C[C@@H]7C)C8COC8"
LAST P274 "C37H44N8O4"
LAST P234 "1S/C37H44N8O4/c1-23-18-42(27-21-49-22-27)9-10-43(23)26-5-6-33(39-17-26)40-30-13-25(19-41(4)35(30)47)28-7-8-38-34(29(28)20-46)45-12-11-44-31(36(45)48)14-24-15-37(2,3)16-32(24)44/h5-8,13-14,17,19,23,27,46H,9-12,15-16,18,20-22H2,1-4H3,(H,39,40)/t23-/m0/s1"
LAST P235 "WNEODWDFDXWOLU-QHCPKHFHSA-N"
LAST P662 "86567195"

The first line creates a new Wikidata item, while the next ones add information about this compound. GDC-0853 is now also Q23304817. The label I added manually afterwards. Note how the Bioclipse script found the PubChem identifier, using the InChIKey. I also use this approach to add compounds to Wikidata that we have in WikiPathways.


text:
How can I limit the amount of curvature of a bezier curve?

I've been creating bezier curves in a program according to a user clicking where the endpoints ought to be with success. Now, I wonder if there is a way to restrict the shapes of the beziers such that their sharpness is minimized.

I know that a cubic bezier curve needs four pairs of coordinates: the start point, the endpoint, and two control points. My question then, is how do I calculate the best control points to minimize the amount of curvature in my bezier if the only requirements are the endpoints? And then how can I calculate that curvature so that I can altogether reject endpoints that produce too sharp of a curve? Assume I have a minimum radius that I want to honor.

I also know the tangents at the endpoints (at least one of them is known) so straight lines are ruled out.

• Why does a Bezier curve have to have 4 pairs of coordinates? – JessicaK Nov 14 '14 at 8:37
• @JessicaK 4 pairs are standard (cubic splines are what all graphics systems understand). – orion Nov 14 '14 at 8:40
• The question is quite badly phrased. You want to have cubic bezier curves with minimum curvature, which means "straight lines", then you describe "minimum radius". I don't think you've thought about what you actually want carefully so I don't think this is a good question. – Suzu Hirose Nov 14 '14 at 8:43
• @Suzu, adding one sentence has clarified your concern. – Octopus Nov 14 '14 at 8:44
• @orion I do not disagree with your comment, but having a canonical implementation in graphics does not mean you cannot have things such as more control points or a non-uniform knot sequence. – JessicaK Nov 14 '14 at 8:56

First of all, you need to match the endpoints, as you said. I will assume that you also need to match the tangents (especially if it's a part of a spline). If the control points are A,B,C,D, the tangent in A points along vector AB, and the tangent in D points in DC direction.

You can therefore freely move B and C along the tangent direction, which changes the "sharpness" but keeps the tangents and endpoints intact.

There are three typical cases:

1) The tangents converge. This means that intersection of lines AB and CD is where the curve is. The closer B and C are to this intersection, the sharper the curve. If B or C is farther away than the intersection, you have a self-intersecting curve or at least something extremely sharp. If your condition is "soft" (not mathematical, but you just want some heuristic to limit the curvature), you can for instance, just forbid B and C to be more than half way from A/D to the intersection. If you want mathematically rigorous condition, you can vary the two parameters (AB and CD distances) and calculate the minimal radius of curvature for each case until you go over the desired limit.

2) the tangents diverge on the same side. This case produces a "bubble". The farther away the B and C are, the larger the circle-like bump is. This kind of a spline is usually not something you want (at least in graphics), you have more control if you split it in half and get two "conventional" beziers. In any case, here, the curve is sharprer if AB and CD are smaller, but varying these parameters makes drastic changes in the shape.

3) the tangents point in opposite directions (the curve intersects the A-D straight line). This is a horrible case (S-shape). Still, you can only vary AB and CD distances if you want to keep the tangents, so you can vary them until you honor the condition. This case again has subcases (like the two above), depending on whether the angles BAD and ADC are obtuse or acute.

I hope this helps. Essentially, you have two free parameters that you can vary in order to minimize sharpness. It also makes sense (to preserve the general shape) to keep the ratio AB/CD fixed and scale the distances simultaneously. Then you have a 1-parametric case which you can solve algorithmically without ambiguity (in 2-parametric case, you have too many solutions).

Edit: I was hoping to avoid explicit math because it's easy to know what to do, but it's tedious to write down and do anything analytically, better to let the computer do it. However, here we go:

A cubic bezier is parameterized like this: $$\vec{r}(t)=(1-t)^3 A + 3(1-t)^2 t B+ 3(1-t)t^2 C +t^3 D$$ the first derivative: $$\vec{r}'(t)=3(1-t)^2(B-A)+6(1-t)t(C-B)+3t^2(D-C)$$ the second derivative is $$\vec{r}''(t)=6(1-t)(C-2B+A)+6t(D-2C+B)$$

Now, the curvature is expressed as such: $$\kappa=\frac{|\vec{r}'\times\vec{r}''|}{|\vec{r}'|^{3}}$$

You pretty much need to calculate this numerically and also find the maximum over $t$ numerically. It's too ugly to do anything "on paper". See the discussion here:

maximum curvature of 2D Cubic Bezier

My suggestion was to "correct" your control points as such: $$B_u=A+(B-A)u$$ $$C_u=D+(C-D)u$$ where you are looking for $u$ which minimizes your maximum curvature. $u=1$ is your original curve. This parametrization lets you keep the approximate shape of the curve.

• I was really hoping to see some actual math. – Octopus Nov 14 '14 at 9:01
• I set up the idea what to vary. I'll add some math. – orion Nov 14 '14 at 9:04
• Thanks for the math. This is awesome. – Octopus Nov 14 '14 at 23:45

If you would like to minimize the "sharpness" of the cubic Bezier curve honoring two end points and two end tangent directions, there is something called "optimized geometric Hermite curve" (OGH curve) that might be interested to you. The OGH curve does not minimize the maximum curvature of the curve. Instead, it minimizes the overall "strain energy" of the curve, which is

$$\int_0^1 [f^"(t)]^2 \;\mathrm{dt}$$

You can refer to this paper link for details. For cubic OGH curve, you can find out the "optimal" magnitudes of the end derivatives analytically. The formula is listed in this paper as equation (4).


text:
# Séminaire PAS

Organisateurs : Erwan Saint-Loubert Bié et Christoph Kriegler
Les exposés ont lieu le mardi à 14h45 en salle 218 du bâtiment de mathématiques (consulter le plan d'accès au laboratoire).
Agenda global au format

### Mars 2023

• Mardi 28 mars 2023 - Athanasios Kouroupis (NTNU Trondheim, Norvège)

Beurling primes and Hardy spaces of Dirichlet series

Given an arbitrary increasing sequence q = {qn},
1 < qn → ∞, such that {log qn}
is linearly independent over the rationals, we will denote by Nq = {νn} the set of numbers that
can be written (uniquely) as finite products with factors from q, ordered in an increasing
manner. The numbers qn are known as Beurling primes, and the numbers νn are Beurling
integers. The corresponding generalized Dirichlet series are of the form
f (s) = ∑ an vn^(-s).

The talk comprises a first part on Bohr's theorem
(joint work with Frederik Broucke and Karl–Mikael Perfekt)
and a second part on composition operators on
the Dirichlet Hardy space H2.

Afficher le contenu...

• Mardi 07 mars 2023 - Carlos Gomez Cabello, Universidad de Sevilla

Semigroups of composition operators on Banach spaces of Dirichlet series

In this talk, we shall consider continuous semigroups of analytic functions $\{\Phi_t\}_{t\geq0}$ in the so-called \emph{Gordon-Hedenmalm class} $\mathcal{G}$, that is, the family of analytic functions $\Phi:\mathbb{C}_+\to\mathbb{C}_+$ giving rise to bounded composition operators in the Hardy space of Dirichlet series $\mathcal{H}^2$. We will show the existence of a one-to-one correspondence between continuous semigroups $\{\Phi_{t}\}_{t\geq0}$ in the class $\mathcal G$ and strongly continuous semigroups of composition operators $\{T_t\}_{t\geq0}$, where $T_t(f)=f\circ\Phi_t$, $f\in\mathcal{H}^2$. Then, we will characterise the infinitesimal generators of continuous semigroups in the class $\mathcal G$ as the Dirichlet series sending $\mathbb C_{+}$ into its closure. We will extend these results to the range $p\in[1,\infty)$ and for the case $p=\infty$, we shall prove that there are no non-trivial strongly continuous semigroups of composition operators in $\mathcal{H}^\infty$. If time permits, a brief comment will be made regarding the symbols of the bounded composition operators in the algebra $\mathcal{A}(\mathbb C_+)$ of Dirichlet series as well as the interplay between the corresponding semigroups of these symbols and the associated semigroups of composition operators.

Afficher le contenu...

### Novembre 2022

• Mardi 15 novembre 2022 - Rémi BOUTIN, Université Paris Cité

Embedded Topics in the Stochastic Block Model

Communication networks such as emails or social networks are now ubiquitous and their analysis has become a strategic field. In many applications, the goal is to automatically extract relevant information by looking at the nodes and their connections. Unfortunately, most of the existing methods focus on analysing the presence or absence of edges and textual data is often discarded. However, all communication networks actually come with textual data on the edges. In order to take into account this specificity, we consider in this paper networks for which two nodes are linked if and only if they share textual data. We introduce a deep latent variable model allowing embedded topics to be handled called ETSBM to simultaneously perform clustering on the nodes while modelling the topics used between the different clusters. ETSBM extends both the stochastic block model (SBM) and the embedded topic model (ETM) which are core models for studying networks and corpora, respectively. The inference is done using a variational-Bayes expectation-maximisation algorithm combined with a stochastic gradient descent. The methodology is evaluated on synthetic data and on a real world dataset.

Afficher le contenu...

• Mardi 08 novembre 2022 - Claire BRECHETEAU, Université de Rennes 2, 14h00

Approcher des données par une union de boules ou d'ellipsoïdes et partitionnement

Dans cet exposé, il sera question de construire un proxy de le fonction
distance à un compact, à partir d'un nuage de points générés sur ce
compact, avec du bruit.
Ce proxy sera construit à partir d'un critère de type k-means, avec une
divergence de Bregman. Ses sous-niveaux seront des unions de boules. Je
présenterai l'utilisation de ce proxy à des fins de partitionnement de
données.

Il s'agit de travaux publiés dans :
- Claire Brécheteau and Clément Levrard, A k-points-based distance for
robust geometric inference. Bernoulli 2020, Vol. 26, No. 4, 3017-3050
- Claire Brécheteau and Aurélie Fischer and Clément Levrard, Robust
Bregman Clustering. Annals of Statistics 2021, Vol. 49, No. 3, 1679-1701

Afficher le contenu...

### Octobre 2022

• Vendredi 14 octobre 2022 - GUNNAR TARALDSEN

Mathematics of improper priors and posteriors

Taraldsen et al (2022) have recently proved a generalization of Bayes theorem that includes both
improper priors and improper posteriors. This theory links the Renyi (1955) conditional probability
spaces with the theory of disintegration presented by Bourbaki (1959). In this talk, the Basu
theorem, the factorization theorem, and optimal frequentist inference based on Bayesian or fiducial
arguments are reconsidered in this more general context

Afficher le contenu...


text:
# Properties of the Geometric Mean

The main properties of the geometric mean are:

• The geometric mean is less than the arithmetic mean, $G.M < A.M$
• The product of the items remains unchanged if each item is replaced by the geometric mean.
• The geometric mean of the ratio of corresponding observations in two series is equal to the ratios of their geometric means.
• The geometric mean of the products of corresponding items in two series is equal to the product of their geometric mean.


text:
# Water in the Manometer.

The system shown in the diagram is at equilibrium at $$300K$$ and the volume of the bulb is $$150 ml$$ which contains Oxygen gas and some amount of liquid water. If the bulb contains $$0.001$$ $$mol$$ of $${ 0 }_{ 2 }(g)$$, then the volume of liquid water is approximately ______ $$ml$$.

$$Details$$ $$and$$ $$Assumptions$$

At $$300K$$ Vapour pressure of water is $$28 mm$$ $$of$$ $$Hg$$.

$$h=161 mm$$.

The manometer is closed and the space above the other end is a Vacuum.

×


text:
# ←→

Methodological notes

# On choosing the energy—momentum tensor in electrodynamics and on the Abraham force

Research and Design Institute of Radioelectronic Engineering, Branch of M.V. Protsenko Federal Research and Development Center Production Association &guot;Start&guot;, Mira str. 1/1, Zarechnyi, Penza region, 442965, Russian Federation

The well-debated problem of choosing the energy—momentum tensor in electrodynamics is examined. Electromagnetic forces in a continuum medium that follow from Minkowski's and Abraham's tensors are considered. It is shown that the conservation equations for both Minkovski's momentum density and for Abraham's impulse simultaneously follow from Minkowski's tensor and that they are the components of a composite electromagnetic pulse in the medium. It is shown that choosing canonical material equations reduces the Abraham force to zero. Considerations are presented which uniquely favor choosing the Minkowski tensor and show the incompleteness of the Abraham tensor.


text:
# Grid $k$-coloring without monochromatic rectangles

Update: The obstruction set (i.e. the NxM "barrier" between colorable and uncolorable grid sizes) for all monochromatic-rectangle-free 4-colorings is now known.

Anyone feel up to trying 5-colorings? ;)

The following question arises out of Ramsey Theory.

Consider a $k$-coloring of the $n$-by-$m$ grid graph. A monochromatic rectangle exists whenever four cells with the same color are arranged as the corners of some rectangle. For example, $(0,0), (0,1), (1,1),$ and $(1,0)$ form a monochromatic rectangle if they have the same color. Similarly, $(2,2), (2,6), (3,6),$ and $(3,2)$ form a monochromatic rectangle, if colored with the same color.

Question: Does there exist a $4$-coloring of the $17$-by-$17$ grid graph that does not contain a monochromatic rectangle? If so, provide the explicit coloring.

Some known facts:

• $16$-by-$17$ is $4$-colorable without a monochromatic rectangle, but the known coloring scheme does not appear to extend to the $17$-by-$17$ case. (I'm omitting the known $16$-by-$17$ coloring because it would very likely be a red herring for deciding $17$-by-$17$.)
• $18$-by-$19$ is NOT $4$-colorable without a monochromatic rectangle.
• $17$-by-$18$ and $18$-by-$18$ are also unknown cases; an answer to these would be interesting as well.

Disclaimer: Bill Gasarch has a $289 (USD) bounty on a positive answer to this question; you can reach him through his blog. A note on etiquette: I'll make sure he knows the source of any correct answer (should one arise). He brought it up again during a rump session at Barriers II, and I find it interesting, so I'm forwarding the question here (without his knowledge; though I highly doubt he would mind). - Just want to add some references/pointers: apart from the blog posts[1,2], the updates at the bit-player blog[3,4] are detailed and insightful. There has been substantial discussion on all of these posts. [1]: blog.computationalcomplexity.org/2009/11/… [2]: blog.computationalcomplexity.org/2009/12/… [3]: bit-player.org/2009/the-17x17-challenge [4]: bit-player.org/2009/17-x-17-a-nonprogress-report Note: No markdown formatting in comments? How can I make pretty links? – Neeldhara Aug 31 '10 at 14:01 Those are some great links. Thanks Neeldhara! :) – Daniel Apon Aug 31 '10 at 14:47 Likewise, thanks for posting this here - I followed the developments on this for some time, and this should rekindle interest in the problem! – Neeldhara Sep 1 '10 at 5:37 @Moron: Yes, you only need to consider those rectangles whose sides are parallel to the axes. BTW, there is also a complexity-theory angle to this: Bill has speculated that given a partial k-coloring of an m by n grid, determining whether the coloring can be completed in a rectangle-free manner is NP-complete. – Kurt Sep 2 '10 at 21:07 The automorphism group of the problem is large:$2\times 4! \times(17!)^2=6.1\times 10^{30}$solution-preserving symmetries, counting the row-column swap, permutations of the colors, permutations of the rows, and permutations of the columns. Is it known how many distinct rectangle-free subsets there are of size$71,72,73,...$? – mjqxxxx Mar 23 '11 at 3:11 ## 6 Answers Some of you are probably aware of this, but the 17 x 17 coloring problem has been solved by Bernd Steinbach and Christian Posthoff. See Gasarch's blog post here. - Also the 18x18 grid is 4-colorable without monochromatic rectangles ... now, the only "missing tile" is the 21x12 grid – Marzio De Biasi Feb 8 '12 at 14:55 This is not really an answer to the question, but I've encoded the 17x17 4-coloring problem as a 4-CNF (in the standard DIMACS format for SAT-solvers) and uploaded it here. If anyone has access to a good SAT solver (and a supercomputer!) maybe we can make some progress. Note: in my encoding, if gridpoint$(i,j)$is assigned color$c \in \{0,1,2,3\}$, then the variable$(17i+j+289c+1)$takes the value$1$, and$0$otherwise. - Awesome. (I do indeed have access to a supercomputer.) Next step's running numbers to estimate this thing's runtime on the specific machine. Who knows if this is in the ballpark of reasonable, but it's a different approach I'd been looking at. Now, time to go find that recent question on SAT-solvers so I can read up... :) – Daniel Apon Sep 27 '10 at 13:52 Turns out the problem I was thinking of was on #SAT, so I've started a new question on SAT solvers at cstheory.stackexchange.com/questions/1719/… – Daniel Apon Sep 27 '10 at 14:35 Great - let me know how it goes! – Lev Reyzin Sep 27 '10 at 21:28 @Lev, just a random update: it appears the runtime of the 17x17, even using the best possible supercomputer and a really fast SAT solver, is still astronomical. Plus side: it appears within the realm of reason to attack this with a supercomputer in a targeted way, i.e. find the exact partial 1-colorings that will work (already done by hand by Beth Kupkin at Rutgers), then find the exact partial 2-colorings that will work from that, etc. Down side: there's no "quick solution"; it'll have to be a long-term project with multiple stages of supercomputer execution – Daniel Apon Nov 16 '10 at 11:44 @Joe, however! Here is a "leaderboard" of the current best approximate colorings: Leaderboard -- It appears simulated annealing works quite well for finding approximate colorings. – Daniel Apon Mar 23 '11 at 19:31 This is not a real answer, either. Certainly the problem here is the presence of an astronomical number of symmetries, which fool even the best SAT solvers on the best supercomputers. Such symmetries map solutions to solutions and non-solutions to non-solutions: in this case probably there is an immense number of almost-solutions (i.e. assignments satisfying all but a small amount of clauses), each of which can be obtained by any other applying a proper symmetry. Hence the solver wastes an enormous amount of time trying each of these almost-solutions, while in a certain sense they are all the same. Exploiting symmetries (see this paper) should be an avenue to explore in order to attack this hard 17x17 instance and make some progress on it. I wonder if anyone already tried to do so. - Hey, that's pretty sweet! :) Hadn't seen it before. – Daniel Apon Mar 23 '11 at 19:42 @Daniel: You're welcome! ;-) Hope it helps. – Giorgio Camerani Mar 23 '11 at 21:19 I used Aloul's "Shatter" program on multiple encodings of the 17x17 problem and put some CPU weeks into a few different SAT solvers and had no luck. The paper Walter referenced is actually the first of maybe a dozen or something he's written on the subject, so there might be something in there that'll do the job, but it's no low hanging fruit. – Jay Kominek Apr 8 '11 at 6:44 Again, not a real answer, but anyway, here are some thoughts on adopting graph colouring algorithms for this problem. Let us say that a set$I$of grid positions is an independent set if set$I$does not contain all four corners of some rectangle. Define a maximal independent set in the obvious way. Now the following are equivalent claims: 1.$n$-by-$m$grid can be coloured with$k$colours. 2.$n$-by-$m$grid can be covered with$k$independent sets. 3.$n$-by-$m$grid can be covered with$k$maximal independent sets. Now, the interesting thing is that covering with independent sets can be done in time$\log k\ \text{poly}(nm)2^{nm}$using fast covering product algorithm (Björklund et al. 2007). This is certainly is an improvement over trivial$k^{mn}$algorithm, though$2^{289}$seems still unsurmountable. If the family of all (maximal) independent set has sufficiently nice structure, it might also be possible to fine-tune the covering product algorithm. - How is claim 3 equivalent to claim 2? The maximal independent set for 17x17 is of size 74, by the way, as shown in Elizabeth Kupin's paper (pdf). There is only one such set, not counting permutations of the rows and columns as distinct. – Null Set May 22 '11 at 20:47 I mean maximal in the sense that no proper superset is independent, as it is customary in computer science. Maximum is the word usually used when meaning "of largest possible size". – Janne Korhonen May 22 '11 at 21:15 In that case, the set of maximal independent sets contains all the row/column permutations of the unique size 74 set, and no size 73 independent sets, because they are all subsets of the size 74 set. I'm not sure what it has from sizes 67 to 72. – Null Set May 22 '11 at 21:31 The 21x12 grid is 4-colorable without monochromatic rectangles, as well !!! - This is Bill Bouris. Hi, Dan. I'm working on a program that searches for a suitable 17x17 matrix which exhibits no-4-coloring according to Ramsey's Theory. I use a positional matrix depicting all connections between points and fix the main diagonal and allow the top row of the matrix to run through all of the possible 16choose8 combinations; I capture only the matrices that pass regarding the following criteria... no-XRRR, no-RXRR, no-RRXR, no-RRRX, no-XBBB, no-BXBB, etc., then I sweep through the matrix using the next weakest criteria... no-XBRR, noBXRR, no-BBXR, no-BBRX, no-XRBB, no-RXBB, etc. for a total of 32 sweeps until the computer fills in the coloring automatically. I've noticed that there's a possible candidate per every 400 matrices out of a total 12780, and it takes .95 hours to find the candidate or 1 per every 8.644 seconds. It's coming along, but I don't have much time to program it... as I work full-time. We should work together... I could use the$289.00!

-
Bill Gasarch should only be paying out $128. – William Bouris May 23 '11 at 0:49 sorry about that... 272/2 or$136 –  William Bouris May 23 '11 at 1:10
This is not an answer to the question. best as a comment. –  Suresh Venkat May 23 '11 at 6:57


text:
Compound Interest Problem

• Jul 15th 2013, 05:40 PM
Espionage
Compound Interest Problem
Kathy deposits $10,000 in her retirement account, which compounds interest continually. If she has$19,600 in the account after four years, how much money will she have in the account after another two years?

I'm not familiar with the compound interest formula.
• Jul 15th 2013, 06:28 PM
Prove It
Re: Compound Interest Problem
The compound interest formula is \displaystyle \begin{align*} A = P \left( 1 + R \right) ^n \end{align*}, where P is your principal, R is your interest rate for each time period of compounding, and n is the number of time periods that the interest compounds over.

• Jul 15th 2013, 07:05 PM
Espionage
Re: Compound Interest Problem
Alright, so I solved for R, which got me (sqrt(35)/5)-1 and plugging it back into the equation and setting n to 6, I got 27,440. That's right, right? • Jul 15th 2013, 07:10 PM Prove It Re: Compound Interest Problem Actually, I apologise, I have made an error. What I have given you is the compound interest formula over a discrete number of time intervals, not over a continuous period. If the interest compounds continually, then the formula is \displaystyle \begin{align*} A = P \, e^{r\,t} \end{align*}, where P is the principle, e is Euler's number, r is the annual interest rate, and t is the number of years. • Jul 15th 2013, 07:43 PM Espionage Re: Compound Interest Problem I don't see how I would solve that second equation (and get a natural number, approximately) without the use of some sort of calculator. The studying material I've been using has all natural numbers for answers and by using the discrete compound interest formula, the answer27,440 is an option.
• Jul 15th 2013, 09:36 PM
Prove It
Re: Compound Interest Problem
You are given the amount after four years and the principle, so substitute into the equation to get the yearly interest rate. Then you can substitute the value of 6. You should find that if you keep everything in terms of exponentials and logarithms, that things will simplify, and so you won't need a calculator.
• Jul 17th 2013, 05:29 AM
bjhopper
Re: Compound Interest Problem
A=P*e^rt
19600=10000e^4r
ln 1.96=ln e^4r
0.673=4r
r=0.168
change P to 19600 and calculate the new amount after 2 years


text:
I would like to run the association rule mining algorithm of the Orange library on a dataset that is stored in a PostgreSQL database. The table 'buildingset' contains the itemsets for each user, thus each record is related to a user, and each field is related to an item. The values are either 1 (smallint) or missing. The table has about 14,000 records and 31 fields.

When I try to run the algorithm on this dataset, I get the following error:

ValueError Traceback (most recent call last): File "/opt/orange/orange3/Orange/canvas/scheme/widgetsscheme.py", line 722, in process_signals_for_widget handler(*args) File "/home/bdukai/.local/lib/python3.4/site-packages/orangecontrib/associate/widgets/owassociate.py", line 444, in set_data self.X = data.X File "/opt/orange/orange3/Orange/data/sql/table.py", line 353, in X self.download_data(AUTO_DL_LIMIT) File "/opt/orange/orange3/Orange/data/sql/table.py", line 333, in download_data raise ValueError("Too many rows to download the data into memory.") ValueError: Too many rows to download the data into memory.

Thus is there any way overcome this limitation, without upgrading the hardware?

• could you share how you could connect with SQL table, I downloaded freeDTS ( don't know how to install it) as well as running pip install pymssql in command line ( completed with no issue). But nothing change. I try to use file widget, but I could only get 60K row out of 1 Million. thanks – oveno Jun 5 '18 at 9:54
• I haven't used Orange since then and I honestly don't remember, sorry – Balazs Dukai Jun 14 '18 at 12:48


text:
# Touch x-axis

Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.

Result

a = (Correct answer is: a=(x+2)^2+(y-2)^2=4)
b = (Correct answer is: b=(x-6)^2+(y-10)^2=100)

#### Solution:

$b=\left(x-6{\right)}^{2}+\left(y-10{\right)}^{2}=100$

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Showing 1 comment:
Math student
how do you end up with n=r ?

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