Exploring introductory trig using 3d printing

My younger son is studying trig right now and I thought it would be fun for him to play around with some 3d curves made with trig functions.

I showed him how to use Mathematica’s ParametricPlot3D[] function and then just let him make some shapes on his own. He settled on a curve that looked like this:

OwenPic

Here’s the code just in case it is not legible in the video:

OwenCode

After he made the curve we printed it – it was really fun to see him working on the print when it was finished. I wish the picture was better!

3d Printing

When everything was finished I asked him to tell me about the curve. I’d not seen the code before and didn’t know there was a stray Cos[x] in it. Talking about that piece of the code led to a great conversation about elementary trig functions (totally by accident!):

Finally, I had him talk about the 3d printed shape:

I really enjoyed this project today – it is fun to use 3d printing to explore so many different areas of math.

Sharing Ricky Reusser’s ‘Periodic Planar Three-Body Orbits” program with my son

I saw an really neat idea in a tweet from Nalini Joshi yesterday:

A direct link to Ricky Reusser’s incredible 3-body problem visualization is here:

Ricky Reusser’s amazing 3-body problem visualization

For today’s math project I asked my son to play around with the program and pick three examples that he found interesting. The discussion of those three examples is below.

Here’s the first one, with a short discussion of three body problem at the start:

Next up was an orbit shaped almost like an infinity symbol:

Finally, an orbit that it completely amazing – I almost can’t believe a shape like this is possible!