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.