Below is a diagram of a pentagram drawn into a true hexagram. Each of the six lines that form the hexagram are three inches long and each of the short segments of the hexagram are one inch long.
One is also the square root of one and three is the square root of nine. The distance between the adjacent outer points of the hexagram is 1.732 inches (AB, AC, BD, etc.) 1.732 is the square root of three. HD and all of the other segments that are comprised two of the short segments of the hexagram are two inches long. The distance HE is also two inches long. Two is the square root of four. The two diagonal lines of the pentagram (AE and BE) are 2.646 inches long. 2.646 is the square root of seven. The horizontal line of the pentagram (CD) is 3.464 inches long. 3.464 is the square root of 12.
The segment FH in the hexagram is bisected at G by the line AE of the pentagram. The proportion FG : GH is 1 : 2. The proportions of the segments in the entire line CB are as follows:
CF : FG : GH : HB = 3 : 1 : 2 : 3
The proportions of the line AE as bisected by the lines of the hexagram and the pentagram are as follows:
AG : GJ : JE : = 5 : 4 : 6
The proportions of the line CD as bisected by the lines of the hexagram and the pentagram are as follows:
CI : IJ : JK: KL : LD = 5 : 3 : 4 : 3 : 5
In the diagram below, points J and K from the diagram above are the centers and the segment JK is the radius of two circles, forming a vesica pisces that is perfectly inscribed by the four diagonal lines of the hexagram.
