# How to draw a perfect star?

How to draw a perfect star?

The perfect star fits into the perfect pentagon. The diagonals of a perfect pentagon describe the perfect star. The edge length of the pentagon is in proportion to its diagonal in the ratio of the golden mean. Two diagonals of the pentagon cross each other at their golden mean.
There are at least three methods for constructing the perfect five pointed star:
1. fitting the star into a given circle
2. drawing a star with a given arm length
3. drawing a star fitting into a pentagon with a given edge length.

1. a) Draw any circle
b) Draw the x and why axes of the circle Call the intersection of the vertical axis and the perimeter of the circle, point "A"
c) Construct a square in the upper right quadrant. point "A" will coincide with the upper left corner of this square.
d) Find the mid point of the base of the square.
e) Describe an arc in the radius equal to the distance from the mid point of the square to point "A". The arc is swung in the counter clockwise direction and intersects the horizontal axis at a point called "B"
f) Finally, describe an arc with its center at point "A" and with its radius equal to "A-B." The arc will intersect the circle at points "C" and "D." points "C" and "D" are two points of the star. Point "A" is a third point. Describing the arc in the radius of "A-B" with it's center at "B" will intersect the circle at the fourth point of the star. call the fourth point "E," Continue with a final arc equal to "A-B" and its center at "E."

2 and 3 also relate to the method of construction related to the "golden section."
I will describe those methods at another time.