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 a model that passed all of Shapeways’ tests! The link to its page is here. Here are […]
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 structure of the Rook’s graph. The Rook’s graph is a specific type of chessboard graph. […]
My first print! And using Fusion 360 to illustrate a sphere homotopy
I want to thank Shapeways so much for awarding me the Shapeways Education Grant to work on this project. This allows me to order my models from Shapeways completely free of charge! Doing so has been very exciting, but I’ll get to that more later. In this post, to demonstrate Fusion 360, I’ll show you how to build up the sphere we made in Mathematica last time, in the middle of the homotopy.
Getting Started – Using Mathematica to animate a homotopy
We decided a simple example to start off with would be the homotopy between a sphere with a hole in it and a point. You can think of this homotopy as if you were peeling an orange from the top, shrinking the peel as you go along until you are left with just the bottom point of the sphere. Difficult to imagine? To visualize it, I wrote up some Mathematica code.
An introduction to my 3D printing project: Zoetropes and homotopies
Our project will use 3D printing to create a series of models demonstrating homotopies, or continuous deformations, between two objects. These can sometimes be hard to visualize. The classic example is of the donut and the coffee mug. These are homotopy equivalent, that is, there exists a continuous deformation from one into the other.