This week I’ve been doing a fun 3d printing project with my younger son who is learning trig (from Art of Problem Solving’s Prealgebra book). We have used 3d printing to explore 2d geometry before – see some of the projects here, for example:

This week I had my son create, code, and then print some simple 2d shapes – the project combines ideas from trig, geometry, and algebra.

Here’s his description of the first shape -> a 3-4-5 triangle:

Here’s the 2nd shape – a 7-6-3 triangle. Creating this shape shows how ideas from introductory trigonometry come into play:

Finally, here’s a regular pentagon that we made yesterday. Unfortunately we made a mistake in the code for the print – mixing up a Sin() and a Cos(), but here is explanation of how to make the shape is correct:

I’d forgotten how useful 3d printing can be as a tool to explore 2d geometry – this week was a happy reminder of how fun those activities can be!

One thought on “Exploring trig and 2d geometry with 3d printing”

That was fun to watch. It made me think about a series of problems Diego Rattagi posted showing how the pentagon (and other regular polygons) all intersect with parabolas very neatly. Anyway: I kept one of them here: https://blog.mathoffthegrid.com/2019/07/pentagon-quadrature-of-parabola.html. They are also good for playing with the embedded golden ratio. in 18-7-90 and 36-54-90’s.

That was fun to watch. It made me think about a series of problems Diego Rattagi posted showing how the pentagon (and other regular polygons) all intersect with parabolas very neatly. Anyway: I kept one of them here: https://blog.mathoffthegrid.com/2019/07/pentagon-quadrature-of-parabola.html. They are also good for playing with the embedded golden ratio. in 18-7-90 and 36-54-90’s.