Category Archives: MathematicalADD

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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The Picture Post

This post will consist almost entirely of pictures of the objects created during the past year while using my Shapeways Education Grant. Check out my summary post for more words… The 3 by 3 Rook’s Graph The 4 by 4 Rook’s Graph … Continue reading

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3D Printing Graphs, Knots, and…Books?

It’s just about at that point where I am hit with nostalgia of the past year and excitement for the coming year. This time around, however, that excitement is accompanied by sadness – I will be graduating from James Madison … 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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The Perko Praxinoscope and the Shrikhande Graph

As I mentioned in my previous update, I fixed the design for the Perko knots on the pegs, and made a decision on designing the Shrikhande graph so that it looked like the Rook’s graph. Well I sent them off … 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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Quick Update on the 3D Printing Project

As the title suggests, this is just a quick update on the 3D printing project I’ve been doing this year. First, after multiple failed attempts to print the Perko knots attached to pegs for the praxinoscope, I have finally created … Continue reading

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Visualizing the difference between the 4×4 Rook’s graph and the Shrikhande graph

In the summer of 2015, I did a research project characterizing the critical groups of the Rook’s graph and its complement. I won’t be talking much about that specific project here – instead, I just want to look at the … Continue reading

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JMM and an Update

This post is just a quick update on the 3D printing project (with a few pictures from JMM, the Joint Mathematics Meetings) and some plans for the future! At this past JMM in Atlanta, Georgia, I gave an invited talk … Continue reading

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