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