### Triangles Containing the Origin

You may have found this site by searching for information regarding Project Euler Problem 184. This is not a solution to that problem. In fact, it really bothers me when I find people who post their solutions to these problems online, especially the higher level ones. In this blog post, I talk about a simple problem from probability that was motivated from this Project Euler problem, but the solution to this problem is not likely to help you solve that one.

I wanted to create the animation/simulation for this problem

I eventually want to extend this problem to explore all convex polygons instead of just triangles (which is a more difficult problem) and I will be able to easily reference this problem if needed

As promised, here is the animation that describes this process. I created this animation with Racket: a functional programming language that makes it extremely easy to work with images. In a future blog post, I will probably talk more about Racket and what I like to use it for, but for now here is the animation.

Pick three points uniformly at random along the circumference of a unit circle centered at the origin. What is the probability that the triangle connecting these three points contains the origin?Like I said, this problem is not as difficult as the problems that I usually write about, but I decided to write a blog post about it for two main reasons:

I wanted to create the animation/simulation for this problem

I eventually want to extend this problem to explore all convex polygons instead of just triangles (which is a more difficult problem) and I will be able to easily reference this problem if needed

As promised, here is the animation that describes this process. I created this animation with Racket: a functional programming language that makes it extremely easy to work with images. In a future blog post, I will probably talk more about Racket and what I like to use it for, but for now here is the animation.

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