## Thursday, October 13, 2011

### Apollonian Pumpkin Patches

Phyllis from All Things Beautiful asked if I could explain our Apollonian pumpkin patch a little bit better, so I will try - keeping in mind that my basic idea today was to get the boys drawing and coloring, not to teach them a math lesson.

To begin with, an Apollonian gasket is a fractal that starts out with three tangent circles being drawn inside another circle, so each circle is also tangent to the outside circle. Then the spaces left outside the three circles are filled in with sets of three tangent circles, and the spaces left by them are filled in with three tangent circles, with all the circles growing smaller, but continuing into infinity - or something like that. Below is a picture of an Apollonian gasket from Wikipedia.

It can be turned into a pumpkin patch, by adding lines in each circle, to suggest the ridges of pumpkins, and then coloring all the circles orange, until you get to the really tiny circles, that can be colored green, to suggest vines and leaves.

Our printer was refusing to load paper this morning, so we had to draw our pumpkin patches freehand, meaning they weren't at all mathematically correct, but still a lot of fun to draw and color.

Of course, if you haven't seen it yet, this would be a good time to check out ViHart's "Doodling in Math Class" video, too.

It's great to be a homeschooler.

Christy Killoran said...

I wish I had lessons like this in math, or even in art!

Natalie PlanetSmarty said...

You manage to find the coolest videos. I've never heard of Apollonian circles before, but it makes sense

Phyllis said...

Thank you so much! I see now what you are doing. This looks like great fun.

Unknown said...

Reminds me of the Tessellations I made in Geometry- another great way to link Art and Math together!

Anonymous said...

That video (and her others) is soooo awesome...thanks for sharing the link!

Ticia said...

I've never heard of those either, and I thought I was well versed in geometry/math ideas.......

Yelena said...

This was such an inspiring idea - turning the Apollonian gasket into a Halloween-themed coloring project. My son usually avoids coloring if he can, but this really worked!