# When Life Hands You Lemons, Make Fibonacci Lemonade

I’m so glad I found Andrea Hawksley’s blog earlier this year! Hawksley is a software developer, mathematical artist, co-founder of the Octahedral Group, an organization of Bay Area mathematical artists. She works on the eleVR project, where she helps make 3-D VR videos for viewing on a spherical viewer. (They have a blog, too. I haven’t browsed it much yet, but it deals with the geometry and neuroscience of creating VR videos. Cool!)

Hawksley posts about recreational math and the mathematical art she and others make. I am indebted to her for posting a template and instructions for making a 6-card ball with pyritohedral symmetry group out of playing cards. I made one while my students were taking their final exam last semester. Here’s my finished product:

A 6-card ball I made using Andrea Hawksley’s template and instructions. Image: Evelyn Lamb.

The ball was her gift to attendees of the Gathering 4 Gardner conference, which she posted about here. If you’re like me, you’ll be swooning at the hair tie creations and the G4G gifts from other participants. You’ll also swoon over her other posts about mathematical art, particularly her “topological” origami.

Unukalhai, an origami sculpture in Andrea Hawksley’s Star Polyhedra series. Image: Andrea Hawksley.

Two of my favorites are her posts on non-Euclidean chess. What happens if we design “chutes” between random squares on the board? Could we handicap better players to make more interesting games? How does a bishop move if we tile our hyperbolic chessboard with squares that meet six to a vertex? How does a rook move on a hyperbolic chessboard tiled with pentagons that meet four to a vertex? It’s interesting to think about the ways that the game would be different with these different choices. I’d love for someone to write a program that plays chess on these boards to figure out how the strategy changes as we change the board.

Finally, one of Hawksley’s most recent posts is on making Fibonacci lemonade, a layered drink that gets sweeter as you go down the glass, with lemon to sugar ratio gradually approximating the Golden ratio. As she writes, “This drink may be the world’s first tastable example of the relationship between the Fibonacci sequence and the golden ratio!” It’s not bad to look at, either.