Thursday, November 12, 2009

Fox 185

Red Fox: Hey Polar, check this out; a unique configuration of a circle and a square! Ain't it beautiful?
Polar Fox: Not bad! What'd you have to say about it?
Red Fox: Here I say all fractions are reachable by adding simple tangents and other similar connections.

Polar Fox: Hmmm! Is that not a too strong statement?
Red Fox: Well, imagine drawing new tangents and line segments between existing intersection points.
If you keep on doing that, soon those intersection points will numerically-explode. And you can compute any fraction similar to the answer.
Polar Fox: OK. There are infinitely-many integers but NONE satisfies: a-cube plus b-cube equals to c-cube. Do you have one such a, b, c?
Red Fox: I know Fermat says NO. And I see your point. But this is not the same thing. You can probably span the whole plane like this.

Polar Fox: Fine, give me an 11/19 then.
Red Fox: I got to work on that.

Tuesday, November 10, 2009

Fox 182

Does the above have any "haiku" value?
Probably not much :)