Bay Area Mathematical Olympiad

MoMath program resources

The single best resource for Tracks of Galileo is the wonderful video interview that 3Blue1Brown made with Momath’s own Steve Strogatz.
I strongly recommend that you play with the free grapher Desmos.
My Geogebra files
- that demonstrated Mark Levi’s proof of the cycloid equation is here.
- that shows the forces on the catenary
- that develops the differential equation for the square-wheeled trike surface
- that explains the derivatives of sine and cosine with just geometry
To use Processing, go to the Processing website to download their software. Then when you click on the links below, you can copy and paste my code into your own Processing sketches to run and modify my code.
- Here is my brachistochrone processing file.
- A simulation of a simple gravity-obeying shooter.
- My simulation of Motionscape
I have made my “sandbox” in CoCalc (Sage) public. Here is the link. Get your own account by going to Cocalc.com, and then you can copy my file and modify it. When you go to the link, you get the latest version that I have made.

Blooms
- There are a number of nice videos about phyllotaxis and the golden ratio. Vi Hart has a nice 3-part series. Search for “Doodling in Math: Spirals, Fibonacci, and Being a Plant” and don’t forget to find all three parts. This website includes an applet that shows how different turn angles produce different plant growths.
- There are many videos about John Edmark’s work, several made by the Exploratorium museum in San Francisco, for example, this website. The Vimeo video that I shared is here.
- Here are several Processing files: simple strobe, phyllotaxis, and lame bloom simulation. To use the lame bloom simulation properly, you will also need to alter the code where it loads the three images (in the setup() function). You will need to save them and change the location depending on the file structure of your computer. Here are the files to download: my simple phyllotaxis spiral, Edmark’s jigsaw puzzle, and one of Edmark’s blooms.
Penrose tiles There is a huge literature out there, but the best start is Martin Gardner’s essays which can be found in chapters 1 and 2 of his book, Penrose Tiles to Trapdoor Ciphers. This is an excellent site (make sure to find all the pages, not just the introduction), and try this website for constructing your own random tilings.

For more information, please contact Paul Zeitz, zeitzp (at) usfca . edu