Mechanical Pendulums vs Spirolaterals

In mechanics, in the area of dynamical system, a N-tuple pendulum is a set of N simple pendulums attached to each other. These N-tuple pendulums are physical systems that exibits rich dynamical behavior. For certain energies, are the motion of these mechanical pendulums often chaotic. You can influence the motion of the pendulums by holding your device in different positions. The equations of motions of these pendulums has been derived using the Sophia mechanical package. The different set of differential equations are solved using the 4:th order Runge-Kutta method for the time stepping. Within this application you can switch between these mechanical pendulums: - Double - Triple - Quadruple - Quintuple - Sextuple - Octuple - Symmtric Double - Simple 3-Dimensional The visualization of the pendulums can be viewed in either a Quartz view or in an OpenGL view.

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!