Some extensions of Matt Enlow’s tweet

Saw a neat tweet from Matt Enlow yesterday:

In each diagram, the green region(s) & blue region(s) have = area. Perhaps Geometry Ss could try to make their own? pic.twitter.com/miuVBbkgl6

— Matt Enlow (@CmonMattTHINK) August 23, 2016

The pictures on the bottom row reminded me of two fun projects that we’ve done.

This old Numberphile video featuring Harvard’s Barry Mazur discusses shapes similar to the bottom left picture:

 

 

Here’s the project that we did with that video:

Using Numberphile’s “Blob Pythagorean Theorem” video in a lesson

The picture on the bottom right reminds me of a really neat geometry problem that I heard MIT’s Bjorn Poonen discussing. The problem starts with the circle inscribed in the center of the picture below and then ask some questions about higher dimensional versions of the same situaiton:

 

Here are my blog posts about that problem:

A Strange Problem I overheard Bjorn Poonen discussing

Bjorn Poonen’s n-dimensional sphere problem with kids

A fun surprise in Bjorn Poonen’s n-dimensional sphere problem

Finally, Enlow actually provided a fun extension of his tweet, too! This is a great geometry problem!

Sometimes questions practically pose themselves. #sangaku pic.twitter.com/9qUijNBJud

— Matt Enlow (@CmonMattTHINK) August 24, 2016