Here's a challenging geometry puzzle for you. Here's a picture of the traditional Yin-Yang symbol. What is the equation of the line that goes through this symbol so each side of the line contain exactly equal amounts of black & white?

The outside is a unit circle (radius = 1 unit).

The arcs sweeping from the edge of the circle to the center, of course, have a radius of 1/2 of a unit.

The dots in the opposite-color field have a radius of 1/6 of a unit.

Hi Scott,
I know ... this is an old thread. But I have just "discovered" it.

I bought "Day One" from you many years ago.
It is a product of pure genius.
Consequently, I have the greatest respect for you.

Which is why this thread must go answered; well, so to speak.
Having said that, I have no idea what the answer is.

It is suffice to say ... you lead and we follow.

regards,
wulfiesmith (UK)

Surely any diameter would work? Of have I misunderstood the question?

I'm having difficulty finding the radius of the small, inner circles. If I can find that, I believe it's solvable using integration/calculus. What am I doing wrong here? Throw me a bone??

I think that each side of "any diameter" will have "inverse" areas of black and white. That is, what is black on one side will be white on the other side.

I believe that the problem statement indicates these radii as 1/6 of a unit.