º º
December 26, 2004
1
1
1.1
. . . . 1
1.2
. . . . 2
1
1.1
1.1
× = l 2 × w 2
l 1 × w 1
l 2 + w 2 ≤ l 1 + w 1
l × w
x
lw + 2(l + w)x + πx 2 .
l w
x
l 1 × w 1
l 2 × w 2
ål 2 × w 2
l 1 × w 1
l 2 w 2 + 2(l 2 + w 2 )x + πx 2 ≤ l 1 w 1 + 2(l 1 + w 1 )x + πx 2
⇒ 2(l 1 + w 1 − l 2 − w 2 )x + l 1 w 1 − l 2 w 2 ≥ 0.
x ≥ 0
2(l 1 + w 1 − l 2 − w 2 ) ≥ 0 ⇒ l 1 + w 1 ≥ l 2 + w 2 ,
1
9
0
90
9
9
1
0
9
DZ9
9
0
1
1
Ì
1 2 .
l 1 + w 1
2
l 2 + w 2 2 .
≤
l 2 + w 2
2 ≤ l 1 + w 1
2 ⇒ l 2 + w 2 ≤ l 1 + w 1 .
1.2
Ú
1.2
1
!
1 Americam Mathematical Monthly, 94(1987), pp. 601 − 617
Wagon
ëA B C D
ABCD
A
B
X
P
P
P
ABCD
P
ABCD
"
P P
P P P
P
#−1, 0, 1
(1)
P
X, Y
#0
(2)
P
X, Y
(a)
P
#1
(b)
P
#−1
ü
4
DZ
DZ
Ð
0
0
P
DZP
ABCD
"P
#
2
4
$0
P
ABCD
P = A, B, C, D
P
# $0
A, B, C, D
# $0
A
#
0
B, C, D
#0
%
1.1
1.1
1.2
1.1
ë
1.3
O
A, B
O
&∠AOB = 90 ◦
(A
x
) 2 + (B
x
) 2 = 1.
'
(% ( ( )
( (
ABCD
BC = k > CD = 1
EF GH
HE EF < k.
1 k
E
F
G H
A
B C
D
1.2
R
n
R 1 , R 2 , · · · , R n
b
a
d
c cos(2π(x + y)) + i sin(2π(x + y))dxdy
= b
a cos(2πx) + i sin(2πx)dx
× d
c cos(2πy) + i sin(2πy)dy .
*
a − b
c − d
)
R
R cos(2π(x + y)) + i sin(2π(x + y))dxdy
= n
i=1
R 1
cos(2π(x + y)) + i sin(2π(x + y))dxdy.
R i
)0
