How to Trisect a Circle With a Compass

An equilateral hexagon is the key to trisecting a circle.
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In classical geometry, it's easy to bisect most anything; segments, angles and circles can all be easily divided into two equal parts with only a compass and straight edge. Trisecting, however, can be trickier. In fact, it is mathematically impossible to divide an arbitrary angle into three equal parts by the rules of classical geometry. Fortunately, trisecting a circle is a very different and much easier problem.

    Draw a straight line though the center of the circle. Label the center of the circle "C" and the points where the diameter crosses the arc of the circle "A" and "B."

    Place the point of the compass at point B and the marking tip at C, setting the radius of the compass to be equal to the radius of the circle. Draw an arc with this radius centered on B and intersecting the circle on both sides. Mark the points of intersection "D" and "E."

    Draw a straight line from C to D and one from C to E. Lines CA, CD and CE divide the circle into three equal sections, because points D and E are each exactly 1/6 of the circle away from B, which is exactly 1/2 of the circle away from A.


About the Author

Tom Kantain has been writing and editing in various forms for over 20 years. He has written a regular magazine column on the philosophy of games. Kantain holds a Master of Arts in philosophy as well as a Bachelor of Laws.

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