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 sphere
This open problem taught me what topology isThe inscribed rectangle problem, and how it leads to studying Mobius strips, klein bottles and topology.
Why slicing a cone gives an ellipseA beautiful proof of why slicing a cone gives an ellipse.
Visualizing quaternions (4d numbers) with stereographic projectionHow to visualize quaternions, a 4d number system, in our 3d world
Quaternions and 3d rotation, explained interactivelyAn introduction to an interactive experience on why quaternions describe 3d rotations
Sneaky Topology | The Borsuk-Ulam theorem and stolen necklacesSolving a discrete math puzzle, namely the stolen necklace problem, using topology, namely the Borsuk Ulam theorem
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.
The AI that solved IMO Geometry ProblemsGuest video by Aleph0 on how AlphaGeometry combines logic and intuition.
Why ruler and compass?Guest video by Ben Syversen, discussing the history of Euclid’s Elements, and the role ruler and compass constructions really served.