Celestial Dances vs Spirolaterals

This app invites you to explore the relative motions of our solar system's planets, their moons, and several exoplanet systems. It is based on ideas presented in "A Little Book of Coincidence" by John Martineau. Are the amazing patterns created by these orbiting bodies just a coincidence, or is something more than that going on? Take a look and see what you think. Be sure to check out the special relationship between the Earth and Venus.

Spirolaterals allows you to explore geometric line designs based on applying a simple rule to a number sequence. Be warned though: spirolaterals can be very addictive! You can create your own spirolaterals by entering a number or text like your name. Or you can explore the gallery of 80 spirolaterals by tapping Surprise Me! Spirolaterals raise many interesting questions: Which ones repeat and why? What kinds of symmetry are present? What happens when you use a palindrome or when your numbers increase or decrease by the same amount? I have used Spirolaterals in my math classes for many years, and students always find them fascinating. They try their name or phone number. They try to create some particular pattern. This year some students spent hours trying to create a 4x4 grid! If you create an interesting spirolateral, email me and I may include it in the Surprise Me! gallery in a future version, with full credit to you!