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发帖数: 80 | 1 This proof is based upon melo's idea, and hopefully it is correct.
Let A be (0, 0) and B be (0, 1) on the X-Y plane. If we trace the curve
joining A and B
at a uniform speed, the curve can be represented as a vector-valued time
function
(x(t), y(t)). Without loss of generality, assume point (x(0), y(0)) be A, and
point (x(1), y(1)) be B. That is, it takes one second to trace the curve from
point A to B.
The uniform speed assumption and the fact that curve is continuous imply x(t)
and y(t) are bo |
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