### Perpetual motion

Popular Science's cover by Norman Rockwell, October 1920 - via commons
Like the research on the philosopher's stone, the mysterious alchemical material which should allow the transmutation of the elements, particularly of base metals into precious gold, there is the search for a tool that can generate perpetual motion, or a gear capable to move indefinitely without any need of power supply from the outside.
As we will see this research has well over a thousand years and continues today among people who genuinely (and a little naively!) looking to get what would be a considerable technological leap and scammers themselves. The best way to deal with all of these is to remember what Richard Feynman said some students who invited him to a demonstration for an engine running unless perpetual but rather long:
You have to ask yourself, 'Where is the power supply?'(1)
The magic wheel

His most important work is the Siddhanta-Shiromani, the Crown of treatises, a poem where, among others results, he comes to approximate the derivative for the sine function: $\frac{\text{d}}{\text{d} y} \sin y = \cos y$ He also made a demonstration of the Pythagorean theorem, and his path is crossed, as it can only in the tortuous paths of mathematics, with Pierre de Fermat, the amateur mathematician known to throw challenges to more titles colleagues, as in the case the best known Fermat's last theorem or for the following Diophantine equation: $61 x^2 + 1 = y^2$ The latter, proposed in 1657, was resolved in 18th century by Euler, unless we consider the solution discovery by Bhaskara II already 6 centuries before.