Relationship To Constructible Polygons
An n-sided regular polygon can be constructed with compass and straightedge if and only if n is the product of a power of 2 and distinct Fermat primes. In other words, if and only if n is of the form n = 2kp1p2…ps, where k is a nonnegative integer and the pi are distinct Fermat primes.
A positive integer n is of the above form if and only if its totient φ(n) is a power of 2.
Read more about this topic: Fermat Number
Famous quotes containing the words relationship to and/or relationship:
“Women, because of their colonial relationship to men, have to fight for their own independence. This fight for our own independence will lead to the growth and development of the revolutionary movement in this country. Only the independent woman can be truly effective in the larger revolutionary struggle.”
—Women’s Liberation Workshop, Students for a Democratic Society, Radical political/social activist organization. “Liberation of Women,” in New Left Notes (July 10, 1967)
“Every relationship that does not raise us up pulls us down, and vice versa; this is why men usually sink down somewhat when they take wives while women are usually somewhat raised up. Overly spiritual men require marriage every bit as much as they resist it as bitter medicine.”
—Friedrich Nietzsche (1844–1900)