Math Terms

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  • Lemma: a “helping theorem” or lemma (plural lemmata or lemmas) from the Ancient Greekλῆμμα (lemma, “anything which is received, such as a gift, profit, or a bribe”) is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself. (Source: Wikipedia)

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A Platonic/Catalan Compound and Its Dual, a Platonic/Archimedean Compound

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Compound of Rhombic Dodeca and Icosa

Shown above: the compound of the icosahedron and the rhombic dodecahedron. Below is its dual, the compound of the dodecahedron and the cuboctahedron.

Compound of Dodeca and Cubocta

Both these compounds were created using the “add/blend polyhedron from memory” function in Stella 4d: Polyhedron Navigator. To check out this program for yourself, just follow this link.

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Introduction to Wasserstein metric (earth mover’s distance)

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This is a short introduction to the notion of Wasserstein metric but presented in a way that explicitly highlights the earth mover intuition on the definition.

1. the cost of moving one particle

Throughout the post, we fix a metric space (X,d). Suppose a particle of mass $latex w ge 0$ is placed at position $latex x in X$. The cost of moving this particle to a new position $latex y in X$ is defined to be $latex w d(x,y)$. With this definition, you see:

  • The cost of moving a particle from place x to the same place x is zero.
  • The cost of…

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