Скачать или смотреть Can you square a circle using straightedge and compass? | Constructible numbers

#mathematics #geometry #algebra
A real number r is constructible if starting from a line segment of unit length,
a line segment of length |r| can be constructed with a compass and straightedge in a finite number of steps. The study of constructible numbers is elegantly linked to 4 famous problems in Euclidean geometry: (1) Doubling the cube (2) Trisecting the angle (3) Squaring the circle (4) Constructing regular polygons. The set of constructible numbers form a proper subfield of the real numbers, and field theory tools can be used to understand its structure. We will use one such fact to tackle the above 4 problems.

Compass equivalence theorem: https://en.wikipedia.org/wiki/Compass...

Straightedge and compass construction