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A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden.
Four 15-sided Reinhardt polygons, formed from four different Reuleaux polygons with 9, 3, 5, and 15 sides. A regular Reuleaux polygon has sides of equal length. More generally, when a Reuleaux polygon has sides that can be split into arcs of equal length, the convex hull of the arc endpoints is a Reinhardt polygon. These polygons are optimal in ...
An equidiagonal kite that maximizes the ratio of perimeter to diameter, inscribed in a Reuleaux triangle. Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite that can be inscribed into a Reuleaux triangle. [22]
By Barbier's theorem, the body's perimeter is exactly π times its width, but its area depends on its shape, with the Reuleaux triangle having the smallest possible area for its width and the circle the largest. Every superset of a body of constant width includes pairs of points that are farther apart than the width, and every curve of constant ...
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
These Reuleaux polygons have constant width, and all have the same width; therefore by Barbier's theorem they also have equal perimeters. In geometry, Barbier's theorem states that every curve of constant width has perimeter π times its width, regardless of its precise shape. [1] This theorem was first published by Joseph-Émile Barbier in ...
The mean width of a convex polygon is equal to its perimeter divided by . So its width is the diameter of a circle with the same perimeter as the polygon. [5] Every polygon inscribed in a circle (such that all vertices of the polygon touch the circle), if not self-intersecting, is convex. However, not every convex polygon can be inscribed in a ...
The apothem a can be used to find the area of any regular n-sided polygon of side length s according to the following formula, which also states that the area is equal to the apothem multiplied by half the perimeter since ns = p.