

In playgrounds, the tippe top is often called a "magic top" because it flips itself over, turning upside down. Its counterintuitive behavior is subtle...



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Among the unusual objects that inspire both wonder and scientific curiosity, few are more astonishing than the rattleback. When spun, it has the remarkable ability to reverse its direction of rotation "by itself."

Some mathematical results are so vivid, so “concrete,” that they lend themselves beautifully to physical experiments. With a little ingenuity, they can even be “proved” physically! This is true of the Pythagorean theorem, the law of cosines and, indeed, triangle geometry as a whole.

Mathematics, and geometry in particular, is an essential component of that most technical of fields: robotics. The concept of space, which the mathematician Henri Poincaré (1854–1912) explored in depth, lies at the heart of the robotics engineer's work.

The cycloidal pendulum has three key properties: it is isochronous, tautochronous and brachistochronous. Behind these learned names lie fundamental properties—so fundamental, in fact, that we owe nothing less than the birth of clockmaking to the pendulum!
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