Squaring of Circle | Ellipse | Rectangle | Polygon || Square Multiplication

Cubing of Sphere | Ellipsoid | Cuboid || Cube Multiplication

Squaring the Polygon - Calculator

Name: Squaring the Polygon - Calculator
Author: Jürgen Kummer

Calculator for the edge lengths of a square and of a polygon, if both have the same area. Please enter the number of vertices of the regular polygon (at least 3) and one further value, the other values will be calculated. For the formulas of the regular polygon, see the regular n-gon calculator.

	Square	Polygon
Vertices:	4
Edge length:
Perimeter:
Area:

Round to decimal places.

The unit is the same for length and perimeter. The area has this unit squared. For example, length in centimeters, area in square centimeters.

Example: Equilateral triangle, square and regular pentagon with the same area. The edge length of the triangle is 213 pixels, of the square it is 140 and of the pentagon it is 107 pixels. There are a total of 19600 pixels for each. A pixel is already a unit of area, so it is not squared.

Constructible lengths are those that can be expressed either as a rational number, as a square root, or as a finite chain of square roots. According to the power-of-two rule, a length is constructible if and only if it lies in a so-called field extension of degree 2^n over the rational numbers. This means that, algebraically speaking, every step with a compass or straightedge corresponds to a linear or quadratic equation. Since solving such equations always leads to square roots or combinations thereof, higher roots like the cube or fifth root remain inaccessible to these tools, unless the exponent is itself a power of two.
A limiting case of constructibility is found in regular polygons. While the heptagon cannot be constructed with compass and straightedge because it leads to a cubic equation, Carl Friedrich Gauss discovered in 1796 that the seventeen-gon is constructible. This is because 17 is a Fermat prime, and the construction can be completely reduced to a chain of square roots.

Last updated on 01/22/2026. Author: Jürgen Kummer

© Jumk.de Webprojects | Online Calculators | Imprint & Privacy | German: Quadratur des Kreises - Rechner

↑ nach oben ↑