Today we celebrate another Permutation Day! I call days like today permutation days because the digits of the day and month can be rearranged to form the year.
Celebrate Permutation Day by mixing things up! Try doing things in a different order today. Just remember, for some operations, order definitely matters!
I like the way these ellipses are climbing up their circumscribing cylinder.
And this sculpture puts me in mind of how planes and cylinders intersect: if the plane is perpendicular to the central axis of the cylinder, the intersection is a circle. But if you start to tilt the plane, the circle grows into an ellipse.
While playing around building trains, it occurred to me that one link of curved track was a nice, everyday representation of 
I don’t usually celebrate Pi Day, but a variety of inspirations intersected at a fun project idea this time around.
Thanks to Math for America, I participated in a terrific workshop on Zometool earlier this year, led by George Hart. We built, explored, conjectured, proved, and collaborated around a lot of rich mathematical ideas. And this semester, Steven Strogatz is teaching a History of Math course at Cornell, and he has been generously sharing thoughts and resources online. As a result, I have been reading up on the derivations of the volume and surface area formulas for Platonic and Archimedean solids.
So when I recently re-watched James Tanton’s brilliant video “What is Pi for a Square?“, the idea hit me: for Pi Day, students could explore the value of “Pi” for various Zometool-constructible solids!
What makes James Tanton’s exploration so wonderful is that it highlights the invariance of Pi in circles (as circumference by diameter) while inviting students to play around with the notions of “diameter” “radius”, and “Pi” in regular polygons. We’ll be taking the question “What is Pi?” up a dimension, and thanks to Zometool, we have a tangible context for our conversations and calculations.
We’ll be exploring properties of polyhedra, calculating areas, volumes and ratios, arguing about definitions, and comparing the sphereness of various things. I’m looking forward to a great day of mathematics! And perhaps discovering what the value of “Pi” is for a rhombic triacontahedron.
Well, not really a sphere. But “Dual Snub Hexpropello Dodecahedron” didn’t fit in the title.
This sculpture is by Roland Gagneux. You can find out more about his work here.
This is another piece from the 2013 Bridges Mathematical Art Gallery.