Trivia

Subject:
Re: Spiral solution
Response To:
Re: Spiral solution ()

Alex Y
I agree that when the duck is at R/4 from the enter, with the cat opposite, he can sprint to the edge and escape.

But i just can't see the spiral with the duck keeping the cat on his 6.

I think that as long as the duck is within R/4 from the center, he is able to move closer to the edge while keeping the cat directly across the pond from him. The duck's velocity vector at any point has a circular component equal to the cat's angular velocity plus a component away from the center. As the duck reaches R/4 (or gets arbitrarily close to it) just before his dash to shore, the cat will be at his 3 or 9, not his 6.

It seems to me (and I say this with very little confidence) that keeping the cat on his 6 would end up in a stable situation with the duck at R/4 and the cat only 90* behind him, easily catching him when he sprinted to shore.

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