Tuesday, March 10, 2015

Dividing a Circle into Five with a Compass and Straight Edge

Many ancient designs were constructed by dividing circles into either eight or six parts as the procedures for circle division using only a compass and straight edge are relatively straight forward. After becoming familiar with these two procedures, I wondered if it was possible to divide a circle into five parts with only a compass and straight edge. It turns out it is and this video tutorial is easy to follow.

There are a few more steps required for dividing a circle into five parts, but the procedure was easy enough for my seven year old to follow after spending several weeks creating circles divided into six and eight parts.

After creating a circle containing a diameter with a perpendicular bisector, a circle with the diameter of the large circle's radius is drawn centered at the radius midpoint as shown in the sketch above. Then the circle midpoint is connected to the point where the adjacent radius crosses the circumference. Finally, an arc with the radius of the distance from the circumference/radius crossing point to the circumference of the small circle is drawn. The distance between points where the arc crosses the circle circumference can be used to create five evenly spaced tick marks on the circumference of the circle. (The video is easier to understand.)

Once a circle is divided into five, the angles can be easily bisected to create ten sections. We divided our circles into ten and then created our own mandalas.






If you enjoy mandala math art, please visit my Math Page for more ideas.



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