Funghini

The function

2 x y / (x^2+y^2) 

is discontinuous at (x,y)=(0,0). The graph is a surface of fixed height along each line through the origin - a very hard concept to wrap the mind around. This creates the fold at the middle. Note in the print below that there are four fixed height lines on it in a different color to emphasize this strange fact. The title of this post reflects the fact that the graph looks very much like a specialty pasta, though I am not completely sure Funghini is the right term.

Calling it a Semester on Multivariable Calculus

This is it for the multivariable calculus 3D print labs. Some students got quite poetic on their final print with names like "Skating Rink," "Guitar Pick," "The Snowcone," and "The Abyss" (The Abyss is not depicted here). Students are mostly enthusiastic about being able to apply the math they are learning (hundreds of years old) to a technology which is less than five years old. The class prints will remain in the department's display case until it runs out of room. 

Mandatory DIY

The downside of 3D printers is that there aren't any repair shops. When it breaks, a mathematician does hardware.

Level Sets

The level sets of a three-variable function - another class project.

Mathematical 3D Printing talk

Today I gave a talk about my 3D printing:

Mathematical 3D Printing 

The event was organized by the GMU AWM chapter. Here is a souvenir I made for it:

Visitors and Polyhedra

Today I gave a talk for a few high school students and teachers visiting GMU from a local high school. I wanted to explain how every 3D model is stored as a polyhedron. For example, the simple heart

is stored as an object

consisting of a large number of  vertices  

a large number of edges

 

and a large number of  faces

In particular, even the simple heart has 7852 vertices and 15700 faces!

Young Makers

I've had a nice time in the last couple weeks being able to work with two young makers, who both seemed very positive about the experience. In both cases, they used the iPhone App 123D Sculpt+, with no instructions at all, and created fun models. The first one is a toadstool by a third grader. The colors were by request.

This second one is the Enterprise by a 6th grader, who was doing a school project on 3D printing. This was the first version, but I reprinted it larger in the requested color of white. Unfortunately I did not take a photo of the larger white version.

It was great fun, and I hope to have the chance to try this again another time. With third graders, I cannot imagine doing anything more mathematical, but with a 6th grader, I believe simple OpenSCAD coding is within reach. It would be a good way to reinforce the concepts of translation and scaling that are being taught in the 6th grade math class.