# Ruler and Compass Construction of a Square with Doubled Area

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Mathematicians in ancient Greece showed that ruler and compass constructions could be used in a wide variety of geometrical operations. Some elementary examples are: drawing a line (or ray) through two points, drawing a circle (or arc) of arbitrary radius centered at a point, creating a point at the intersection of two nonparallel lines and drawing a perpendicular to a line at a given point. Three geometric constructions sought from antiquity are squaring a circle, doubling a cube and trisecting an arbitrary angle. These have since been shown to be impossible using only a ruler and compass.

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Contributed by: S. M. Blinder (August 2022)

Open content licensed under CC BY-NC-SA

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Reference

[1] K. Brakke. "Ruler and Compass Construction Doubling the Area of a Given Square." (Sep 30, 2021) facstaff.susqu.edu/brakke/rulerandcompass/20-doubledsquare.html.

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