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Can you square a circle using straightedge and compass? | Constructible numbers
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#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.
Straightedge and compass construction
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.
Straightedge and compass construction
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