All Posts
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Mechanical Television: John Logie Baird
How a spinning disc with a spiral of holes and a single flickering neon lamp produced the world's first television picture — an interactive look at the physics and engineering of mechanical TV.
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Pell’s Equation and the Chakravala Method
How medieval Indian mathematicians solved integer solutions of hyperbolas centuries before Europe, using Brahmagupta’s composition law and Bhaskara’s cyclic Chakravala algorithm.
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Counting Walks with Adjacency Matrices
How powers of a graph's adjacency matrix encode the number of walks between vertices — with an interactive walkthrough and a proof by induction.
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Degree Sequences and Graphical Scores
What makes a sequence of integers the degree sequence of some graph? An interactive look at graphical sequences and how to test them.
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The Euler Number of a Binary Image
How the Euler number — connected components minus holes — can be computed locally over a binary image using three simple 2×2 pixel patterns.
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How to Prove the Infinity of Primes
Two elegant proofs that primes never end — Euclid’s classical argument by contradiction, and Goldbach’s 1730 proof using Fermat numbers and pairwise relative primality.