Geometry

If we try to cut a square into finitely many triangles (possibly of different shapes) of equal area. You would find that no matter what the shapes are the number of triangles is always even. Here is an example: There is some interesting history behind the discovery of the above…

By Ashley Langham‍ American high schoolers have Robert Simson, the Scottish mathematician, to thank for their geometry curriculum. He wrote the first English adaptation of Euclid’s Elements, published in 1723, that would lead to the creation of their mathematical curriculum today.‍ Robert Simson fell in love with geometry at an…

I needed to flatten a 3D mesh to 2D using only Python for a project. I scorched the internet but couldn’t find anything relevant. In this article, I’ll explain a way to flatten a 3D mesh like this:

The value of pi (=3.1415926535….) is one of those ubiquitous yet mysterious constants of nature. We can’t live without it yet we have no idea why it has the value it has. In this post I would like to give an intuitive explanation for why it takes its peculiar value. Prelude …

Dimers on Riemann surfaces II: conformal invariance and scaling limit(arXiv) Author : Nathanaël Berestycki, Benoit Laslier, Gourab Ray Abstract : Given a bounded Riemann surface M of finite topological type, we show the existence of a universal and conformally invariant scaling limit for the Temperleyan cycle-rooted spanning forest on any…

By Ashley Langham‍ Euclid is often conflated as the father of geometry, though given we know very little about the validity of his biography, it is hard to consider him with that title. His Elements is, however, by far, the most famous publication for the creation of modern geometry. …

Euclid defines the “right angle” as being the angle formed by two intersecting lines when the two angles formed at the intersection are equal to each other. …