What mathematical constant relates to the ratios of line segments within a perfectly drawn pentagram?
The golden ratio, φ (approximately 1.618).
The construction of the pentagram, derived from connecting every second vertex of a regular pentagon, inherently generates deep mathematical relationships tied to the golden ratio, represented by the Greek letter phi ($\phi$). Specifically, when measuring the line segments created by the intersections within the pentagram, the ratio achieved when dividing the length of any longer segment by the length of the adjacent shorter segment is invariably equal to $\phi$, approximately 1.618. This intrinsic mathematical property is not coincidental; it is a fundamental consequence of how the star polygon is formed, linking this ancient symbol directly to one of the most famous irrational numbers in mathematics.
