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For the pentagon, this results in a polygon whose angles are all (360 − 108) / 2 = 126°. To find the number of sides this polygon has, the result is 360 / (180 − 126) = 6 2 ⁄ 3, which is not a whole number. Therefore, a pentagon cannot appear in any tiling made by regular polygons.
F 0 = 3, F 1 = 5, F 2 = 17, F 3 = 257, and F 4 = 65537 (sequence A019434 in the OEIS). Since there are 31 nonempty subsets of the five known Fermat primes, there are 31 known constructible polygons with an odd number of sides. The next twenty-eight Fermat numbers, F 5 through F 32, are known to be composite. [3] Thus a regular n-gon is ...
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.
There are known to be an infinitude of constructible regular polygons with an even number of sides (because if a regular n-gon is constructible, then so is a regular 2n-gon and hence a regular 4n-gon, 8n-gon, etc.). However, there are only 5 known Fermat primes, giving only 31 known constructible regular n-gons with an odd number of sides.
Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions, all of which can be edited dynamically later. Elements can be entered and modified using mouse and touch controls, or through an input bar. GeoGebra can store variables for numbers, vectors and points ...
A polygon is a shape that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. The interior of the polygon is sometimes called its body.
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