This compound was created using *Stella 4d*, software you can try here.

# Daily Archives: April 9, 2015

# Quora: What is an Intuitive Explanation of Combinatorial Species?

# NO DIFFERENCE

best poetry blog in the cosmos

when it

comes to

a struggle

as monumental as

this

best not to pick

but snipe at both sides

but if

cornered by faction

claim Möbius Strip

inside, outside

both side

no difference

# Math Terms

- Lemma: a “helping theorem” or
**lemma**(plural**lemmata**or**lemmas**) from the Ancient Greek*λῆμμα*(*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)

# THINGS MATH STUDENTS WILL UNDERSTAND

# Course notes from Fall 2012 to Fall 2014

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

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.

# Chess Rook Paths and squares1

# Nested Trigonometric Functions: Sine and Cosine

The sine and cosine curves themselves are shown for reference, and all four possible combinations of sine and/or cosine which nest one function inside another (with values for the outer function to evaluate ranging from -2π to 2π) are also shown.

# Introduction to Wasserstein metric (earth mover’s distance)

## 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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