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> The reason it won't converge is that a very large number of the points will ALWAYS lie off of the line. No they won't. It moves zero distance horizontally an
by neilk 16y ago
> The reason it won't converge is that a very large number of the points will ALWAYS lie off of the line.
No they won't. It moves zero distance horizontally and zero distance vertically. All the points of the infinitely zigzagging line are on the hypotenuse.
Of course, now we're back to Zeno; if it's not moving off the line, and it only makes progress when it's off the line, how can it get anywhere?
- RiderOfGiraffes 16y agoFor every fractally-type enclosing shape, yes they will. And when you talk about the limit, then you have a circle. You can't talk about moving "zero distance horizontally and zero distance vertically" becuase then, as you rightly say, we're back to Zeno. You don't have an infinitely zigzagging line. That way of trying to think about things is a dead end, and unhelpful. Better answers are given elsewhere in this thread.