Dividing A Circle Into Thirds

[Robert Bonomi]

It is -provably- *PRECISELY**CORRECT*.

strike a circle, radius OA ('O' is the center, 'A' is on the circle) strike an arc, of the same radius, centered at 'A', intersecting the circle at 'B'

_by_definition_, 0A, and 0B are the same length, each being a radius of the circle. AB was constructed as the same length as OA.

THEREFORE, 0AB is an *equilateral*triangle*. and all the angles are *precisely* 60 degrees.

Repeating the process around the circle will lead to _exactly_ *six* such equilateral triangles, which *precisely* fill the entire 360 degrees of the circle.

[Larry Blanchard]

Don't feel bad. I was going to complain as well, but I looked up the formula for the chord of a circle first :-).

[Phisherman]

Draw a circle with a compass. Set the compass on the edge of the circle and draw an arc to cross the circle. Reset the compass at one of the intersections and repeat. You'll get 6 equal sections of the circle. Easy.

[Jim Wilson]

Andy Dingley provided one (good) method of finding the center of a circle...

Here's a method I often use, which is a tad simpler:

Place the point of a compass (or dividers) on the original circle A somewhere, and make a new circle B. If you can, make circle B just a little bigger than A, but the size really isn't important.

Draw two more circles, C and D, the same size as B. Place C's center on one of the intersections of A & B. Place D's on the other. Note that C and D both will intersect A at B's center.

Now draw a line through the two intersections of B and C, and another line through the two intersections of B and D. The two lines intersect at the center of A.

This is much easier to do than to describe. Only takes a few seconds. When you see how the elements fall together, you will realize that you don't need whole circles. Short arcs in the appropriate places suffice.

Jim