Art of Modern Earth - How Crop Circle Created - Step Two : Designing the Drawing - The Polygon

The next element of crop circle we need to know is the polygon. The most appearance of polygon used in early artists CC designs are equilateral triangle, square, the pentagon, five-pointed star (pentagram), the hexagon, six-pointed star (hexagram) and others.

Here is how to construct an equilateral triangle 

Constructing Equilatereal Triangle

In order to construct  an equilateral triangle, you need to draw 4 same diameter auxiliary  circles. And each circle has 2 constraint, i.e : center circle position (point1, 2, 3a and 3b) and the diameter. the step in constructing the triangle (this is the algorithm to draw perfect equilateral triangle):

• With center in point 1 draw a full circle with certain diameter 
• Pick one point in the circle 1 line as the center of  circle 2. This point named T1.
• With center in point T1, draw Circle 2 with the same diameter of circle 1. Circle 2 line will cut the circle 1 at point 3a and 3b. Use this two point to as the center of circle 3a and 3b
• Draw circle 3a with the same diameter of cirle 1. Circle 3a line will cut circle 1 in 2 point i.e, point T1 and another point named T2.
• Draw circle 3b with the same diameter of cirle 1. Circle 3b line will cut circle 1 in 2 point i.e, point T1 and another point named T3.
• Draw line to connect point T1, T2 and T3. Your equilateral triangle is ready

Well, that's such a long way to draw triangle...can we do it faster or short way?:

Yes we can. If we know precisely where point T1, T2 and T3 lies on drawing area,  we just have to follow the last step in drawing that equilateral triangle. And the question arise, how do we know those precise positions?...

Now lets move to another basic element. The hexagon and 6- pointed star (Hexagram).

Constructing Hexagon and Hexagram

To get 6 points in hexagon and hexagram, we have the procedure (algorithm) almost similar in getting 3 points in triangle we mention above. The difference between hexagon and hexagram only happen in connecting those 6 points. At the above pic, we will get the hexagon if we successively connect points  2-3a-4-E-5-3b. Meanwhile, to get hexagram we connect points 2-4-5 and then 3a-3b-E.

There is on basic polygon i want to mention here, but after googling in the internet, i found a good site to describe how to construct a Pentagon or Pentagram (Five Pointed Star). Here is the link:

http://home.hiwaay.net/~jalison/pent.html

Constructing Pentagram

• Draw line and mark points A and B. Draw circle with radius AB. Draw circle with radius BA. Construct square ABCD.
• Construct midpoint of AB at point E. Draw circle with radius ED. Mark points F and G where circle ED intersects the line.
• Draw circle with radius AF. Draw circle with radius BG. Mark the intersection points of the circles at points H, I and J.
• A, B, H, I and J form the points of a perfect geometric pentagram.

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