
> 
> **Question:**
> 
> 
> * how did the classification of quadrilaterals come into being? Was there a single major contributor who coined terms like "rectangle", "square", "trapez/ium/oid", "kite", "deltoid", etc. or were these definitions contributed by several individuals over a longer stretch of time?
> * what was the motivation for adding quadrilaterals with specific properties to the taxonomy; is it because the validity of certain theorems is restricted to them or is the motivation something else and what is it then?
> * why are by far fewer kinds of deltoids classified than convex quadrilaterals?
> 
> 
> 



History of the Taxonomy of Quadrilaterals
**Q1.** If one wishes to single out one main early contributor to the systematic classification of convex quadrilaterals it would have to be the 9th century Indian mathematician [Mahavira](https://en.wikipedia.org/wiki/Mah%C4%81v%C4%ABra_(mathematician)), who divided quadrilaterals into five classes: those with unequal sides (mainly cyclic quadrilaterals, having a circumcircle), all sides equal (rhombus and square), opposite sides equal (parallelogram and rectangle), two opposite sides equal (isosceles trapezium), and three sides equal (trapezium with three equal sides). See for example [Mathematical Achievements of Pre-modern Indian Mathematicians.](https://books.google.nl/books?id=DAPLaxw-53IC&pg=PA257) 


The names used by Mahavira (e.g. "*sama*" for a square and "*dvidsama*" for a rectangle) were of course not the Latin names we use today, but that seems of less significance. Some of these Latin names have a remarkably late date of first use, it seems "*rhombus*" was not used until the 16th century ([source](http://jeff560.tripod.com/r.html)).


In response to Timothy Chow's question: the two different definitions of trapezium versus trapezoid appear to originate from the 1795 [Mathematical and Philosophical Dictionary](https://books.google.nl/books?id=035RAAAAYAAJ) by Charles Hutton, in which the definitions of the two terms were reversed. The US followed that reversed definition, the UK did not ([source](http://jeff560.tripod.com/t.html)).


**Q2.** In a fun and inspiring [posting](http://mzone.mweb.co.za/residents/profmd/classify.pdf), Ben Hambrecht argues for "length-angle" duality as the key organizing principle that motivates the taxonomy.


![](https://ilorentz.org/beenakker/MO/quadrirectnangles.png)


