## Thursday, August 9, 2012

### Smart kitty - but what is this move called?

Bartleby exhibited some smart hunting strategies yesterday that I remember hearing about before, but I forgot the name for it. Does anybody know what this is called? I feel like I learned it in some math class.

The idea is, I'm standing in the center of the circle swinging a toy on a string (the red circle) around in a circle. Bartleby is the black circle. Sometimes he would just run around the circle after the toy, but often he would anticipate where the toy was heading (sometimes well ahead of where it was) and dart straight across the circle by my legs to get it. He was pretty good at anticipating this and got it most of the time. In fact the times he chose to use this strategy and when he didn't probably had more to do with whether I was keeping it going at a constant speed than anything else.

But what is this solution called? Does anyone remember?

1. Ya, I guess that's more or less the idea.

But I thought there was some math problem relating the speed of the red circle and the chord between the black circle and the red circle to determine the angle of the chord that the cat should run to catch up with it.

I've been googling it but I can't seem to find it.

2. I'm not a big math guy, but the only thing that comes to mind is possibly parametric equations, or parametricized curves.

3. ^^ Parameterized curves.

Man, my spelling is crap today.

2. Perhaps of interest:

Chases and Escapes:
The Mathematics of Pursuit and Evasion
Paul J. Nahin
http://press.princeton.edu/titles/8371.html

Also http://mathworld.wolfram.com/PursuitCurve.html

1. We'll see what Daniel says, but I think that you might have nailed it. I was close, just not specific enough (pursuit curves are formed using parametric equations). Like I said, I'm not a big math guy. With practice I can do it, it just doesn't interest me that much.

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