Geometry
An assortment of topics related to geometry and higher dimensions
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But why is a sphere's surface area four times its shadow?Two proofs for the surface area of a sphereDec 2, 2018
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Why slicing a cone gives an ellipseA beautiful proof of why slicing a cone gives an ellipse.Aug 1, 2018
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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
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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
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Visualizing quaternions (4d numbers) with stereographic projectionHow to visualize quaternions, a 4d number system, in our 3d worldSep 6, 2018
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Quaternions and 3d rotation, explained interactivelyAn introduction to an interactive experience on why quaternions describe 3d rotationsOct 26, 2018
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Euler's Formula and Graph DualityA very clever proof of Euler's characteristic formula using spanning trees.Jun 21, 2015
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Darts in Higher DimensionsA game of darts yields an interesting connection to higher dimensional geometry.Nov 19, 2019