polygon, closed plane figure bounded by straight line segments as sides. A polygon is convex if any two points inside the polygon can be connected by a line segment that does not intersect any side. If a side is intersected, the polygon is called concave. In a regular polygon the sides are of equal length and meet at equal angles; all other polygons are not regular, although either their sides or their angles may be equal, as in the cases of the rhombus and the rectangle. The simplest regular polygons are the equilateral triangle triangle, in mathematics, plane figure bounded by three straight lines, the sides, which intersect at three points called the vertices. Any one of the sides may be considered the base of the triangle.
..... Click the link for more information. , the square square, closed plane figure bounded by four straight line segments of equal length and meeting at right angles. The points of intersection of the lines, or sides, are called vertices.
..... Click the link for more information. , the regular pentagon (of 5 sides), and the regular hexagon (of 6 sides). Although the Greeks had developed methods of constructing these four polygons using only a straightedge and compass, they were unable to do the same for the regular heptagon (of 7 sides). In the 19th cent. C. F. Gauss showed that a regular heptagon was impossible to construct in this way. He proved that a regular polygon is constructible with a straightedge and compass only when the number of sides p is a prime number (see number theory number theory, branch of mathematics concerned with the properties of the integers (the numbers 0, 1, −1, 2, −2, 3, −3, …). An important area in number theory is the analysis of prime numbers.
..... Click the link for more information. ) of the form p = 22n + 1 or a product of such primes. The first five regular polygons with a prime number of sides that can be constructed using a straightedge and compass have 3, 5, 17, 257, and 65,537 sides.
polygon
..... Click the link for more information. , the square square, closed plane figure bounded by four straight line segments of equal length and meeting at right angles. The points of intersection of the lines, or sides, are called vertices.
..... Click the link for more information. , the regular pentagon (of 5 sides), and the regular hexagon (of 6 sides). Although the Greeks had developed methods of constructing these four polygons using only a straightedge and compass, they were unable to do the same for the regular heptagon (of 7 sides). In the 19th cent. C. F. Gauss showed that a regular heptagon was impossible to construct in this way. He proved that a regular polygon is constructible with a straightedge and compass only when the number of sides p is a prime number (see number theory number theory, branch of mathematics concerned with the properties of the integers (the numbers 0, 1, −1, 2, −2, 3, −3, …). An important area in number theory is the analysis of prime numbers.
..... Click the link for more information. ) of the form p = 22n + 1 or a product of such primes. The first five regular polygons with a prime number of sides that can be constructed using a straightedge and compass have 3, 5, 17, 257, and 65,537 sides.
polygon
In geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides). If none of the sides, when extended, intersects the polygon, it is a convex polygon; otherwise it is concave. A polygon with all sides equal is equilateral. One with all interior angles equal is equiangular. Any polygon that is both equilateral and equiangular is a regular polygon (e.g., equilateral triangle, square).
polygon
In computer graphics, a multi-sided object that can be filled with color or moved around as a single entity. See triangle.
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polygon
a closed plane figure bounded by three or more straight sides that meet in pairs in the same number of vertices, and do not intersect other than at these vertices. The sum of the interior angles is (n--2) × 180° for n sides; the sum of the exterior angles is 360°. A regular polygon has all its sides and angles equal. Specific polygons are named according to the number of sides, such as triangle, pentagon, etc.
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