Technique for Construction of a Regular Pentagon and Golden star : using a Golden Rectangle and Triangle

Abstract

Geometry is principally constructed by only compass and straightedge (i.e. ruler). In addition, Gauss, who is 1 of the top three world-class mathematicians, has discovered the theory of the construction of a regular polygon that has an amount of the edge in prime number. This regular polygon can be built when the amount of edge is f(n) = , where n is number in the arithmetic order starting from 0 and added one by one. For example, n = 0 is a construction of equilateral triangle, while n = 1 and n = 2 are construction of regular pentagon and hexagon, respectively.

            This article emphasisonly an alternative technique for the construction of a regular pentagon, which differs from the traditional construction explained in some treatises. Starting from, building up the golden rectangle and using a golden ratio of 1.618:1. The base of the golden triangle will be built from the wide side of the golden rectangle. Then 36° top corner of the golden triangle will be used to construct 108° interior corner of a regular pentagon, which the length of an edge is equal to the width of the golden rectangle resulting in an overlapping golden star created. This technique will easily encourage remembrance of the construction process, and an understanding of the length of an edge and interior corner of the regular pentagon.