Monday, July 13, 2015

Balancing nunchucks

Waiting in the car for a ferry the other day, I found I had two long nails and a little magnet for some reason, and came up with this balanced configuration:


At first I thought it was funny that there was less than 1 nail to the left of the balance point, and more than one to the right, but then I recalled this old lever formula:

Can we figure out how far down the nail the balancing point is?  Call it x, and let’s say each nail has a length of 1 and mass of 1…


Saturday, April 18, 2015

First grade fractals

I visited my son’s first grade class the other day, and brought along a branch I found in our yard debris pile.  The kids didn’t take long to realize the big branch was made from smaller branches, which were made from still smaller branches.  After establishing that a self-similar shape like that is known as a fractal, we set about making our own using a template I made. (The template has two equilateral triangles with vertices and midpoints marked, just to get everyone started)
sierpinski fractal activity
For this “Sierpinski gasket” fractal activity, I wanted them to follow these steps:

1. connect the midpoints of a white triangle’s sides
2. color the triangle you created in step 1.
3. Go to step 1.
sierpinski fractal activity

At the end we taped their triangles together in progressively larger groups of three.  Judging by the results, not everyone grasped the iterative process, but they seemed to have fun with the idea, which is arguably more important.

Friday, March 13, 2015

Proof by Pancake

The most epic of Pi Days occurs tomorrow, 3.14.15…

While round pancakes are somewhat rare in our house, the kids and I decided to make an exception and do some flapjack math to celebrate the occasion.

Tuesday, February 24, 2015

Friday, February 13, 2015


I like how these two spirals create a series of nested hearts.  My daughter helped me add a dog, a cat, and a princess to the image.  Here’s the template I made if you want to try doing your own.

Monday, September 8, 2014

Pancake Spirograph

I’ve been working on making spirographic pancakes lately – Spirocakes.  Here’s the latest iteration of the “Pangraph,” a ring gear that fits over the frying pan and acts just like the old Spirograph toy:

It’s time-consuming to cut out the gears, so I didn’t want to just make random ones.  It was fun to work out which gears would make the most interesting patterns and be compatible with both the 35- and 36-tooth ring gears.

I even got to make use of the program I wrote 10 years ago to draw these patterns (technically called hypotrochoids and epitrochoids), to see what kinds of patterns I could expect to see with different gear sizes.

1-Fullscreen capture 982014 105959 AM

Friday, August 8, 2014

Graphs in the sand

I noticed this “flying ring” toy making a nice sine wave as the wind rolled it along the beach this evening. 
sine wave in the sand

It reminded me of how the wind sometimes blows plants growing in sand, causing them to trace circles.