Monthly Archives: December 2020

Rigid heptagon linkage

In January 2000, Erich Friedman considered the problem of finding a rigid unit-distance graph G containing a regular heptagon as a subgraph. That is to say, the graph is immersed in the plane such that: every edge of G must … Continue reading

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Barreto-Naehrig curves and cryptographic pairings

There’s a very elegant cryptographic construction discovered by Barreto and Naehrig in a 2005 paper. It is beautiful from a pure mathematical perspective, but also has an impressive application: it was* part of the ingenious mechanism by which zCash supports … Continue reading

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Shallow trees with heavy leaves

There are two very different state-of-the-art chess engines: Stockfish and Leela Chess Zero. Stockfish searches many more positions (100 000 000 per second) and evaluates them using computationally cheap heuristics. The tree search methodology is a refinement of alpha-beta pruning. … Continue reading

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Let the circumcentre be your origin

Suppose we have two vectors, u and v, in a Euclidean vector space. If we wanted to somehow quantify the proximity of these two vectors, there are two particularly appealing choices: the squared distance, |u − v|²; the inner product, … Continue reading

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