Category Archives: Random

On a set that detects the convergence of a sum of reciprocals using relative density: A proposal for an indicator set and a proof of its nonexistence.

Natural Density Suppose we take a subset of the natural numbers and look at the sum of the reciprocals of its elements: One question we can ask here is: for which subsets does this sum converge? Though there are many routes … Continue reading

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Integration By Parts Table Method and Strange Sums

Today, I will be writing about calculus. How many of you have heard of the table method for integration by parts? Not many, if my tutees at the Science and Math Learning Center are any indication. If it sounds unfamiliar, then … Continue reading

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On the Book Embeddings of the Rook’s Graph and the Shrikhande Graph

I’ve already 3D printed one book embedding, which was of , the complete graph on vertices, which looks like this: Just so we’re all on the same page, let me define a book embedding again. An n-page book embedding of a graph … Continue reading

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Crossless Edge-Colorings

Introduction This post is an exploration of something I brought up in my last post: in order to nicely design the Shrikhande for 3D printing, I decided to draw it up (using Tikz) and use color to denote the orientation of … Continue reading

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An interesting puzzle and a fun solution

I was told this puzzle while at MathFest in Columbus, Ohio, and it has been stuck in my head ever since. Here it is: List the numbers from 1 up to 100. 1, 2,…, 99, 100 Choose two at random, say … Continue reading

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