## Yin Yang |

USE VERY LIGHT PENCIL MARKS FOR YOUR DRAWINGS, because you will erase many of them.

**Contruction:**

1. Draw an equilateral triangle. A nice length for the edge is 3 inches. Around each vertex draw a circle with radius half the length of the edge (so here, for example, your circle will have a 1.5 inch radius). Be sure to draw your triangle far enough from the border of your paper so that you can draw the circle.

To draw the equilateral triangle, you may use a ruler to draw the first edge, and then measure the edge and set your compass to that radius. | Put the point of your compass on one end of the edge and swing an arc. Do the same thing on the other end of the edge. Where the two arcs meet is the third vertex of your triangle. | Finish drawing the triangle. |

2. Next, draw three circles. Set the radius of your compass at 1/2 the length of your triangle's edge. Draw the three circles, each with a center on a vertex of the triangle. If you do it correctly, each circle will just touch (be tangent to) the other two circles. This shape is called a trefoil.

3. The next step is to circumscribe a big circle around the three circles. To do this, find where the center of the circle will be. You can find the center by constructing two lines drawn from the midpoint of a side of the equilateral triangle to its opposite vertex. Where these lines meet is the center of the "big" circle. When you draw it, it should just touch the three small circles.

4. If you want your yin yang to have 3 little circles in it, draw them. Set your compass to a small radius, and put the point at each vertex of the triangle. Draw a circle.

5. Can you see the yin yang emerging? All you need to do now is erase the excess lines.

You can draw a yin yang with four parts, or with n parts. Below is a four-part yin yang made by Pollyjean Anderson, a preservice teacher taking Math 112. For it, you start with four congruent circles at the vertices of a square rather than a triangle.