Equilateral pentagon Equilateral pentagon In geometry an equilateral pentagon is a polygon with five sides of equal length. Its five internal angles, in turn, can take a range of sets of values, thus permitting it to form a family of pentagons. The requirement is that all angles must add up to 540 degrees and must be between 0 and 360 degrees but not equal to 180 degrees. In contrast, the regular pentagon is unique, because it is equilateral and moreover it is equiangular (its five angles are equal; the measure is 108 degrees). Four intersecting equal circles arranged in a closed chain
Pentagon theorem and the left-hand triangle as: The side "s" is therefore: a well-established result. Consequently, this construction of the pentagon is valid. "See main article": Carlyle circle The Carlyle circle was invented as a geometric method to find the roots of a quadratic equation. This methodology leads to a procedure for constructing a regular pentagon. The steps are as follows: Steps 6–8 are equivalent to the following version, shown in the animation: This follows quickly from the knowledge that twice the sine of 18 degrees is the reciprocal golden ratio, which we know geometrically from the triangle with angles of