n*********3
发帖数: 534 | 1 Given a wall and a rope, the wall is longer than the rope.
What is the shape surrounded by the rope using the wall as one side that
would give the maximum area.
Is it necessary that it is a half circle? any way to prove it?
See, if the shape is to be of a rectangle or square, the answer is not a
square, but a rectangle of certain ratio of its sides. | n*********3
发帖数: 534 | | l******r
发帖数: 18699 | 3 以墙做镜面反射，然后得到区域其周长两倍于绳长（固定）。根据wellknownresult：
固定周长圆面积最大，从而得到半圆面积最大。
【在 n*********3 的大作中提到】
: Given a wall and a rope, the wall is longer than the rope.
: What is the shape surrounded by the rope using the wall as one side that
: would give the maximum area.
: Is it necessary that it is a half circle? any way to prove it?
: See, if the shape is to be of a rectangle or square, the answer is not a
: square, but a rectangle of certain ratio of its sides.
| n*********3
发帖数: 534 | 4 Thanks,
looks like it is right.
that is really clever.
Thanks, | n*********3
发帖数: 534 | 5 Given a wall and a rope, the wall is longer than the rope.
What is the shape surrounded by the rope using the wall as one side that
would give the maximum area.
Is it necessary that it is a half circle? any way to prove it?
See, if the shape is to be of a rectangle or square, the answer is not a
square, but a rectangle of certain ratio of its sides. | n*********3
发帖数: 534 | | l******r
发帖数: 18699 | 7 以墙做镜面反射，然后得到区域其周长两倍于绳长（固定）。根据wellknownresult：
固定周长圆面积最大，从而得到半圆面积最大。
【在 n*********3 的大作中提到】
: Given a wall and a rope, the wall is longer than the rope.
: What is the shape surrounded by the rope using the wall as one side that
: would give the maximum area.
: Is it necessary that it is a half circle? any way to prove it?
: See, if the shape is to be of a rectangle or square, the answer is not a
: square, but a rectangle of certain ratio of its sides.
| n*********3
发帖数: 534 | 8 Thanks,
looks like it is right.
that is really clever.
Thanks, | n*********3
发帖数: 534 | 9 I suddenly realize that Gauss's famous act of solving in a short time,
perhaps
less than a minute, the following problem
1+2+3+...+100=
is quite similar to Lookacar's solution below.
Both of them use symmetry to apply to math.
Maybe Lookacar is a genius.
Is he still fighting with those trivial matters?
【在 l******r 的大作中提到】
: 以墙做镜面反射，然后得到区域其周长两倍于绳长（固定）。根据wellknownresult：
: 固定周长圆面积最大，从而得到半圆面积最大。
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