Search results
Results from the WOW.Com Content Network
With a construction system that can trisect angles, such as mathematical origami, more numbers of sides are possible, using Pierpont primes in place of Fermat primes, including -gons for equal to 7, 13, 14, 17, 19, etc. [6] Geometric Origami provides explicit folding instructions for 15 different regular polygons, including those with 3, 5, 6 ...
A regular polygon with n sides can be constructed with ruler, compass, and angle trisector if and only if =, where r, s, k ≥ 0 and where the p i are distinct Pierpont primes greater than 3 (primes of the form +). [8]: Thm. 2 These polygons are exactly the regular polygons that can be constructed with Conic section, and the regular polygons ...
Publication by C. F. Gauss in Intelligenzblatt der allgemeinen Literatur-Zeitung. As 17 is a Fermat prime, the regular heptadecagon is a constructible polygon (that is, one that can be constructed using a compass and unmarked straightedge): this was shown by Carl Friedrich Gauss in 1796 at the age of 19. [1]
A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.
In geometry, a pentagon (from Greek πέντε (pente) 'five' and γωνία (gonia) 'angle' [1]) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting regular pentagon (or star pentagon) is called a pentagram.
Any straight-sided digon is regular even though it is degenerate, because its two edges are the same length and its two angles are equal (both being zero degrees). As such, the regular digon is a constructible polygon. [3] Some definitions of a polygon do not consider the digon to be a proper polygon because of its degeneracy in the Euclidean ...
The interior angles of regular star polygons were first studied by Poinsot, in the same paper in which he describes the four regular star polyhedra: for a regular -gon (a p-gon with central density q), each interior angle is () radians or () degrees. [3] Exterior angle – The exterior angle is the supplementary angle to the interior angle.
Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms. [3] In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi.