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The Magic Cafe Forum Index » » Puzzle me this... » » Yin-Yang Challenge (1 Likes) Printer Friendly Version

Scott Cram
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Inner circle
2678 Posts

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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.
wulfiesmith
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Inner circle
Beverley, UK
1339 Posts

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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)
EdgarWilde
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Regular user
127 Posts

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Surely any diameter would work? Of have I misunderstood the question?
Rayman
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Brooklyn
82 Posts

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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??
leonard
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Regular user
North Carolina
151 Posts

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Quote:
On Jun 12, 2024, EdgarWilde wrote:
Surely any diameter would work? Of have I misunderstood the question?


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.
leonard
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North Carolina
151 Posts

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Quote:
On Sep 9, 2024, Rayman wrote:
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 believe that the problem statement indicates these radii as 1/6 of a unit.
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