Скачать или смотреть Turn angles, continued fractions and approximate geometry | WildTrig: Intro to Rational Trigonometry

The natural unit of angle is not the degree, or the radian, or the grad. The natural unit assigns a value of 1 to the full turn around the circle, and we could call this unit turn angle a circ, following a suggestion by a viewer, Vincent Marciante.

In this video we explore how to evaluate arbitrary angles in terms of a unit circ, at least approximately, by employing an angular variant of the technology of continued fractions used to measure commensurability of linear segments.

Continued fractions arise from the Euclidean algorithm for finding greatest common divisors, and that idea applies just as well to angles as it does to segments. Nevertheless, there is a big difference between discussing commensurability of linear segments and circular arcs: while we can arbitrarily divide a given segment into equal pieces, the same is generally impossible for circular arcs.

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Here are the Insights into Mathematics Playlists:

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