Concept
Constructible polygon
Related concepts (28)
257-gon
In Geometry, 257-gon, also known broadly as the Dihectapentacontakaiheptagon, is a polygon with 257 sides. The sum of the interior angles of any non-self-intersecting 257-gon is 45,900°. The area of a regular 257-gon is (with t = edge length) A whole regular 257-gon is not visually discernible from a circle, and its perimeter differs from that of the circumscribed circle by about 24 parts per million. The regular 257-gon (one with all sides equal and all angles equal) is of interest for being a constructible polygon: that is, it can be constructed using a compass and an unmarked straightedge.
Tetradecagon
In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon. A regular tetradecagon has Schläfli symbol {14} and can be constructed as a quasiregular truncated heptagon, t{7}, which alternates two types of edges. The area of a regular tetradecagon of side length a is given by As 14 = 2 × 7, a regular tetradecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis with use of the angle trisector, or with a marked ruler, as shown in the following two examples.
Tridecagon
In geometry, a tridecagon or triskaidecagon or 13-gon is a thirteen-sided polygon. A regular tridecagon is represented by Schläfli symbol {13}. The measure of each internal angle of a regular tridecagon is approximately 152.308 degrees, and the area with side length a is given by As 13 is a Pierpont prime but not a Fermat prime, the regular tridecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis, or an angle trisector.
Octadecagon
In geometry, an octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon. A regular octadecagon has a Schläfli symbol {18} and can be constructed as a quasiregular truncated enneagon, t{9}, which alternates two types of edges. As 18 = 2 × 32, a regular octadecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis, or an angle trisection with a tomahawk. The following approximate construction is very similar to that of the enneagon, as an octadecagon can be constructed as a truncated enneagon.
Exact trigonometric values
In mathematics, the values of the trigonometric functions can be expressed approximately, as in , or exactly, as in . While trigonometric tables contain many approximate values, the exact values for certain angles can be expressed by a combination of arithmetic operations and square roots. The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 90°.
Icositetragon
In geometry, an icositetragon (or icosikaitetragon) or 24-gon is a twenty-four-sided polygon. The sum of any icositetragon's interior angles is 3960 degrees. The regular icositetragon is represented by Schläfli symbol {24} and can also be constructed as a truncated dodecagon, t{12}, or a twice-truncated hexagon, tt{6}, or thrice-truncated triangle, ttt{3}. One interior angle in a regular icositetragon is 165°, meaning that one exterior angle would be 15°.
Icositrigon
In geometry, an icositrigon (or icosikaitrigon) or 23-gon is a 23-sided polygon. The icositrigon has the distinction of being the smallest regular polygon that is not neusis constructible. A regular icositrigon is represented by Schläfli symbol {23}. A regular icositrigon has internal angles of degrees, with an area of where is side length and is the inradius, or apothem. The regular icositrigon is not constructible with a compass and straightedge or angle trisection, on account of the number 23 being neither a Fermat nor Pierpont prime.
Triacontagon
In geometry, a triacontagon or 30-gon is a thirty-sided polygon. The sum of any triacontagon's interior angles is 5040 degrees. The regular triacontagon is a constructible polygon, by an edge-bisection of a regular pentadecagon, and can also be constructed as a truncated pentadecagon, t{15}. A truncated triacontagon, t{30}, is a hexacontagon, {60}. One interior angle in a regular triacontagon is 168 degrees, meaning that one exterior angle would be 12°.