# Geometry

An assortment of topics related to geometry and higher dimensions

But why is a sphere's surface area four times its shadow?Two proofs for the surface area of a sphereDec 2, 2018

Why slicing a cone gives an ellipseA beautiful proof of why slicing a cone gives an ellipse.Aug 1, 2018

Thinking outside the 10-dimensional boxA method for thinking about high-dimensional spheres, introduced in the context of a classic example involving a high-dimensional sphere inside a high-dimensional box.Aug 11, 2017

All possible pythagorean triples, visualizedThere are a few special right triangles many of us learn about in school, like the 3-4-5 triangle or the 5-12-13 triangle. Is there a way to understand all triplets of numbers (a, b, c) that satisfy a^2 + b^2 = c^2? There is! And it uses complex numbers in a clever way.May 26, 2017

Visualizing quaternions (4d numbers) with stereographic projectionHow to visualize quaternions, a 4d number system, in our 3d worldSep 6, 2018

Quaternions and 3d rotation, explained interactivelyAn introduction to an interactive experience on why quaternions describe 3d rotationsOct 26, 2018

Euler's Formula and Graph DualityA very clever proof of Euler's characteristic formula using spanning trees.Jun 21, 2015

Darts in Higher DimensionsA game of darts yields an interesting connection to higher dimensional geometry.Nov 19, 2019