Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In teaching simulation, the Buffon's needle is a popular experiment to use for designing a Monte Carlo simulation to approximate the number  π . Simulating the Buffon's needle experiment is a perfect example for demonstrating the beauty of a Monte Carlo simulation in a classroom. Hover, there is a common misconception concerning the Buffon's needle simulation. Erroneously, the simulation of the needle drop cannot be used to evaluate  π .  have to simulate the needle's angle from an uniform (0, π/2) distribution. It is self-referential in theory, since it requires the number  π  as the input value to approximate  π . In this study,  propose a new method using the fixed-point iteration to remove the inherent paradox of the Buffon's needle simulation. A new algorithm with Python implementation is proposed. The simulation outputs indicate that our new method is as good as if  use the true  π  value as an input.
['Maximilian J. Wang', 'Jin Wang']
I am writing a research paper on a idea Removing the inherent paradox of the Buffon's needle monte carlo simulation using fixed-point iteration method
[{"from": "human", "value": "I am writing a research paper on a idea Removing the inherent paradox of the Buffon's needle monte carlo simulation using fixed-point iteration method"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In teaching simulation, the Buffon's needle is a popular experiment to use for designing a Monte Carlo simulation to approximate the number  \u03c0 . Simulating the Buffon's needle experiment is a perfect example for demonstrating the beauty of a Monte Carlo simulation in a classroom. Hover, there is a common misconception concerning the Buffon's needle simulation. Erroneously, the simulation of the needle drop cannot be used to evaluate  \u03c0 .  have to simulate the needle's angle from an uniform (0, \u03c0/2) distribution. It is self-referential in theory, since it requires the number  \u03c0  as the input value to approximate  \u03c0 . In this study,  propose a new method using the fixed-point iteration to remove the inherent paradox of the Buffon's needle simulation. A new algorithm with Python implementation is proposed. The simulation outputs indicate that our new method is as good as if  use the true  \u03c0  value as an input."}]