How to draw a perfect star?

How to draw a perfect star?

There are several ways to draw a perfect star with five points or six depending on your preference. A very easy way to do it is to draw an equilateral triangle. Now draw another triangle intersecting this triangle at its mid-points provided that the second triangle should be up side down or should resemble an inverted pyramid. This would give you a perfect star with six points if executed properly.

Another method by which you can obtain a five-point perfect star is to get it with the help of a protractor and a compass
. First draw a circle of the desired size with the compass. The size of the circle should coincide with the size of the star that you want. Then draw a smaller circle inside the previous one with the same centre point. It is better to make the smaller circle of about the half size of the first one. Next draw a line from the edge of the bigger circle to the center point. Use a protractor with the center point of the circle under the circle point of the protractor and mark every 72 degrees around the circle. Draw lines connecting the marked points with the centre point. Then connect the top of one of these lines with the line touching the inner circle and thus form a point. Connect these points until you get a perfect five point 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.