Irrational Gears by OSKAR

Hi Non-Twisty Puzzles fans,

Irrational Gears is a gearing system with a gear ratio equal to the golden ratio, that is 1:1.6180339887.... Gear systems are supposed to have a rational gear ratio, that is one can be expressed as a/b, where a and b are both integers. The golden ratio is an irrational number that cannot be expressed this way. The golden ratio is known as the most irrational number.

This gear system was designed by expressing the golden ratio as 6.47213617... : 10.47213617... . This is close to 6.5:10.5=13:21, a well-known approximation of the golden ratio. The teeth are wrapped around two cylinders, one of which slides over a square bar. At a full rotation of the small gear, the large gear has made 0.6180339887... part of a full rotation. The angle (1-0.6180339887... x 360 = 137.507764068... degrees. is also known as the golden angle, found in many places in nature.

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Enjoy!

Oskar