c*****t
发帖数: 1879 | 1 Then, for case n = 1, X = A, Y = B. XY || AB.
For n >= 2 (real numbers >= 2 as well)
1. We draw a segment of length 1/n, making it parallel to AB.
2. Align one end X to be aligned with A, the other end pointing
toward B.
3. slide along the curve from A to B.
4. There must be at a point when the Y end touches the curve as
well.
To prove 4. we can draw the curve shifted the distance 1/n toward
B. Because n >= 2, 1/n <= 0.5.
Define a cave as part of the curve that is start with | c**********t
发帖数: 80 | 2 This was discussed days ago. It is incorrect, since it does not need
n to be integer. See part 2 of the question (say in post 638). only when n is
an integer can this be hopefully proved.
【在 c*****t 的大作中提到】
: Then, for case n = 1, X = A, Y = B. XY || AB.
: For n >= 2 (real numbers >= 2 as well)
: 1. We draw a segment of length 1/n, making it parallel to AB.
: 2. Align one end X to be aligned with A, the other end pointing
: toward B.
: 3. slide along the curve from A to B.
: 4. There must be at a point when the Y end touches the curve as
: well.
: To prove 4. we can draw the curve shifted the distance 1/n toward
: B. Because n >= 2, 1/n <= 0.5.
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