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Thursday, July 10, 2014

Day 318 - Pythagorean blocks

Today we printed xoan's Pythagoras' 3-4-5! model from Thingiverse, which was one of the many entries to the Makerbot Academy Math Manipulatives Challenge, which called on modelers to design hands-on mathematical tools for K-12 classrooms. I love the simplicity of this model, and that it illustrates the Pythagorean Theorem so elegantly.


Thingiverse link: http://www.thingiverse.com/make:88124

Settings: MakerBot Replicator Mini on .3 layer height with raft but no support.

Technical notes, math flavor: Of course the entire point of this model is that you can also arrange it like this:


The point is that the triangle in the middle is a right triangle, and therefore the sum of the squares of the lengths of its legs is equal to the square of the length of its hypotenuse. In this case the triangle is what's known as a "3-4-5 triangle", because its legs are lengths 3 and 4 and its hypotenuse is length 5. The square on the left has side length 4 and area 4^2 = 16, while the square on the bottom has side length 3 and area 3^2 = 9. The sum of those areas is 9+16 = 25, which is equal to the area of the larger square, which is 5^2 = 25. That's how this model illustrates what the Pythagorean Theorem says about the 3-4-5 triangle, namely that 3^2 + 4^2 = 5^2.

We chose this model because it is a combination of basic mathematics and 3D printing, and Today (July 10) I had the honor of speaking about both of those things on the closing day of the Opening the Gate 2014 Summer Institute for Mathematics Faculty Professional Development, hosted by New Jersey City University and Hudson County Community College. For the first part of the morning we talked about STEM retention in calculus, through precalculus and algebra remediation; for the second part of the morning we demoed the MakerBot Mini and talked about using 3D printing as a tool for STEM recruitment. Here are some of the conference fellows enjoying the 3D prints: