YLL討論網

彼為容易啊~~

More accurately:

t=(x+y+z)/sqrt(3)
r=the distance between (x,y,z) & L: x=y=z
m: the angle of 圓柱坐標

then
x=t/sqrt(3) + r* sqrt(2/3)* cos(m)
y=t/sqrt(3) + r* sqrt(2/3)* cos(m+120')
z=t/sqrt(3) + r* sqrt(2/3)* cos(m-120')

圓柱坐標變換: change 直角坐標(x,y,z) to 圓柱坐標(t,r,m)
t=(x+y+z)/3
r=the distance between (x,y,z) & L: x=y=z
m: the angle of  圓柱坐標

then
x=t+ r* sqrt(2/3)* cos(m)
y=t+ r* sqrt(2/3)* cos(m+120')
z=t+ r* sqrt(2/3)* cos(m-120')

don't know AT ALL.......
(是圓柱坐標變換嗎？)

Meowth 寫到:三元對稱不等式, may try 圓柱座標變換

A=k-a
B=k-b
C=k-c

let x=a/k, y=b/k, z=c/k

1>= x,y,z >=0

let
x=t+r*sqrt(2/3)*cos(m)
y=t+r*sqrt(2/3)*cos(m+120')
z=t+r*sqrt(2/3)*cos(m-120')
1>=t>=0
r=d(L:   x=y=z,   (x,y,z))

f=Ab+Bc+Ca
=kk[x(1-y)+y(1-z)+z(1-x)]
=kk[(x+y+z)-xy-yz-zx]
=kk[3t- 3tt + rr/2]
=kk[3(1/4-(t-1/2)^2) +rr/2]

To Maximize f:
we should maximize r, that is we should choose the ridges of the cube.
(1) when 1/3>=t>=0
r=s*t
As t increased, 3(1/4-(t-1/2)^2) & rr all increasing.
so, f is maximized at t=1/3, where 3 points (0,0,1),(0,1,0)(1,0,0) get maximized f values. (f=kk)

(2) when 1>=t>=2/3
r=s*(1-t)
As t increased, 3(1/4-(t-1/2)^2) & rr all decreasing.
so, f is maximized at t=2/3, where 3 points (0,1,1),(1,1,0)(1,0,1) get maximized f values. (f=kk)

(3) when 2/3>=t >=1/3
we should maximize r, that is we should choose the ridges of the cube.
that are (1,0,q),(0,1,q),(1,q,0),(0,q,1),(q,1,0),(q,0,1).
==> f=kk

from (1)(2)(3), we get max(f)=kk, at (x,y,z)= (1,0,q),(0,1,q),(1,q,0),(0,q,1),(q,1,0),(q,0,1), that is, (a,b,c)=(k,0,qk),(0,k,qk,(k,qk0),(0,qk,k),(qk,k,0),(qk,0,k);  1>=q>=0.

---------
We can also get the minimum of f:

minimize 3t(1-t) & rr/2
==> t=0 or 1, r=0
==> (x,y,z)=(0,0,0) or (1,1,1)
==> (a,c,b)=(0,0,0) or (k,k,k)
==> min(f)=0
--------
Any body know what I write?

三長方形面積有限,不會因為擺位不同而增大

all values are not fixed, will the orientation of the rectangles change, then the total area will be larger?

The rectangles are not overlapping in the square

你認為那裡出問題

Sometime the figure may be misleading.

正方形面積=k²

都看不懂ㄋㄟ...

試放那題解

kevin 寫到:Meowth你的解法跟算幾不等式有關係嗎?
L.H.S?

無關算幾不等式吧

ok. 14天後給你答覆. (他放暑假去外婆家,等他回來)

Meowth你的解法跟算幾不等式有關係嗎?
L.H.S?

正確一點是高小,資質優秀的初小也會

可能會

改天問我姪子(小三) 看他會不會