Constructing Regular Polygons
Some regular polygons (e.g. a pentagon) are easy to construct with straightedge and compass; others are not. This led to the question: Is it possible to construct all regular polygons with straightedge and compass?
Carl Friedrich Gauss in 1796 showed that a regular n-sided polygon can be constructed with straightedge and compass if the odd prime factors of n are distinct Fermat primes. Gauss conjectured that this condition was also necessary, but he offered no proof of this fact, which was provided by Pierre Wantzel in 1837.
Read more about this topic: Compass And Straightedge Constructions
Famous quotes containing the words constructing and/or regular:
“The very hope of experimental philosophy, its expectation of constructing the sciences into a true philosophy of nature, is based on induction, or, if you please, the a priori presumption, that physical causation is universal; that the constitution of nature is written in its actual manifestations, and needs only to be deciphered by experimental and inductive research; that it is not a latent invisible writing, to be brought out by the magic of mental anticipation or metaphysical mediation.”
—Chauncey Wright (1830–1875)
“[I]n our country economy, letter writing is an hors d’oeuvre. It is no part of the regular routine of the day.”
—Thomas Jefferson (1743–1826)