– Elizabeth (@cheesemonkeysf)

Reading the first reminded me a little bit of the section in Ed Frenkel’s book “Love and Math” where he describes the discrimination he faced in his college entrance interviews. One of the questions was to define a circle.

For the second piece, I’ve been thinking a little bit about how to help use any sort of manipulative to see / feel math better. Love the phrase “kinesthetically see the rotation.”

This was my attempt from last weekend to use our Zometool set to understand some 3D geometry and rotations a little better:

http://mikesmathpage.wordpress.com/2014/10/28/a-3d-geometry-project-for-kids-and-adults-inspired-by-kip-thorne/

Funny enough, Fawn Nguyen was involved in a sort of similar zometool activity at almost the same time:

http://mikesmathpage.wordpress.com/2014/10/28/when-my-evening-was-similar-to-fawn-nguyens-evening/

For the continued fraction activity – all I can say is YES!! I think continued fractions are great examples for kids. We’ve played with them several different ways and always seem to have a lot of fun. This was one of our projects relating to geometry and the square root of 2:

http://mikesmathpage.wordpress.com/2014/02/01/geometry-continued-fractions-and-the-square-root-of-2/

Some fun questions to ask about the 1 + 1/x = x equation in the blog is – why are there two solutions? What does the other solution represent?

Also, there’s a really great section in Jordan Ellenberg’s book “How not to be Wrong” about what he calls “algebraic intimidation.” Ellenberg’s idea does have some application here when you think about why this algebra works to simplify the continued fraction. We did a project where some very similar looking algebraic ideas fail here:

http://mikesmathpage.wordpress.com/2014/07/11/just-for-fun-some-infinite-sums/

The last piece on the perpendicular bisectors is really a beautiful activity – especially the last part where he says “In fact, the fact that they didn’t discover it on it’s own was so powerful when they ended up seeing it.” This statement probably isn’t true for all activities, but when it is, like for his activity, it really is powerful.

One of my favorite activities – just purely for the reaction when the kids see it – is here:

http://mikesmathpage.wordpress.com/2013/12/01/computer-math-and-the-chaos-game/