Mental Nuts-- Can You Crack 'em?

[BigV]

Originally Posted by infinite monkey

Parallel planes never intersect. Geometry.




What if you laid out the circumference of the path of the squirrel and the circumference of the path of the hunter into straight lines?

Parallel lines.

Parallel planes don't intersect, true. that's a geometrical fact. Ok, but it has nothing to do with circles. Maybe there's more there, but by itself, it's ... nothing.

circumference is the distance around something, usually a circle and that applies here. It's a distance. We don't know what either distance is for the squirrel or for the hunter, except because we know how a circumference is defined, we know that the circumference of the path of the hunter is greater than the circumference of the path of the squirrel, since the radius, the distance from the center to the edge, is greater for the hunter than for the squirrel. The radius in this mental nut is the center of the tree, the point about which each "goes around".

So, we have circumferences. One's bigger than the other. But distances are scalar values, they have a quantity only. They're not vector quantities which have direction. If you measure the distance around something, its circumference, it's a value, and it has that same value regardless of direction. Actually, direction is meaningless in the context of a circumference.

So, I'm still stuck, there's no such thing as a parallel circumference, even ones that have been unwound into straight line segments.

Please continue.

footfootfoot, if you can quench my thirst, I'd be much obliged. If you can't, just toss out another nut, willya?