30 Jul

For definiteness, the unlabeled points do in fact trisect each of the sides of the triangle. Stumped? You can peek at the answer using the password “threedian”.

30 Jul

There is no excerpt because this is a protected post.

30 Jul

What are the next few terms in this sequence of smallish numbers? 1 1 1 3 1 3 1 1 3 1 1 3 1 1 3 1 1 1 3 2 1 1 3 2 1 3 1 1 3 1 1 1 3 2 1 1 3 2 1 1 3 ? ? ?… [Read more]

30 Jul

There is no excerpt because this is a protected post.

21 Oct

As one of their projects, students in my class this fall wrote about something they’ve seen that sparked mathematical questions and ideas for them. The series of posts below shows the results of their work. I hope you’ll enjoy seeing math through their eyes as much as I have.

24 Jul

I recently purchased a large number of styrofoam balls as supplies for an upcoming build (about which I will post later). The plans for that build required the diameter of the styrofoam balls, to pretty high accuracy. Although the balls were nominally 4 1/2 inches in diameter, I had noticed in a craft shop that… [Read more]

14 Apr

Hey, I have recently become problem editor for the undergraduate Math Horizons magazine of the Mathematical Association of America. So I’d love if you have problems/mathematical puzzles to submit to the column. The official submission blurb follows, and of course you will be credited in the Magazine. The Playground features problems for students at the… [Read more]

11 Apr

This post contains the details of the claim made in “More Spherical Construction” that you can determine the side length of a spherical square from the ratio between the lengths of its diagonals. We’ll do this on a sphere of radius one; everything scales by a factor of the radius for a general sphere. The… [Read more]

10 Apr

One might think that having produced prototypes of the Gengzhi Goblets, our work is just about done to produce sufficient quantity (roughly 300 of each) to serve as G4G13 giveaways. The question comes down to materials and expense. If the Gengzhi Goblets are actually to be used as measuring cups, then they need to be… [Read more]

10 Apr

This post contains the details of computing the height and radius of 1-cup and 1/4-cup Gengzhi Goblets.

10 Apr

The following shapes arose as a natural G4G13 giveaway: a regular 13-gon prism, a cup with octagonal cross sections whose octagon sides scaled with height as… [Read More]

10 Apr

So I had zeroed in on the proof of the Archimedean volume relationship as the source of my giveaway for G4G13. But how to create an interesting variation? The first thing to notice is that the function of h that appears in the proof in the cross-sectional area of of the cone, namely h², could… [Read more]