Re: [math/phys] Equilibrium & Opt., a question for Vu~

[Vu Quoc HUNG <hung@vsb.cz>]

Toi vua ddo.c loi giai ve ba`i toan tim ddiem co' tong khoang ca'ch to'i 
3 ddinh cua 3 giac ABC la` nho? nhat cua Vu~, sa('p ddi ngu? nhu+ng ha~y 
co`n ba(n khoan va`i ddieu vi` lo+`i gia?i bat ngo+` va` qua' hay:

On Mon, 7 Apr 1997 vnsa-l@csd.uwm.edu wrote:

> Date: Mon, 07 Apr 1997 14:50:35 +0200
> From: Minh Vu Huynh <huynm000@goofy.zdv.Uni-Mainz.de>
> Subject: [Math/Phys.] Equilibrium & Optimality
> 
> La^'y ba so+.i da^y da`i nhu+ nhau nu't va`o ta.i mo^.t ddie^?m, buo^.c va`o
> mo^~i dda^`u da^y 1 tro.ng lu+o+ng gio^'ng nhau ro^`i ke'o
> ca'c so+.i da^y na`y qua ca'c ddi?nh cu?a tam gia'c ABC.
> 
> Na(ng lu+o+.ng cu?a he^. tho^'ng na`y ti? le^. thua^.n vo+'i to^?ng
> MA+MB+MC. Vi` va^.y ddie^?m M pha?i ti`m la` ddie^?m ma` na(ng lu+o+.ng
> dda.t cu+.c tie^?u. Mo^.t he^. tho^'ng trong ca^n ba(`ng (Equilibrium)
> co' na(ng lu+o+.ng i't nha^'t. Bo+?i va^.y ddie^?m M la` ddie^?m ta.i ddo'
> ca'c lu+.c ke'o ca^n ba(`ng nhau. Tu+` ddo' suy ra M la` ddie^?m tho?a ma~n
  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ !?
> 	<AMB = <BMC = <CMA =120 ddo^.
        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ?!
ddong y' la` ddiem M la` ddiem ma` he. thong co' nang luong cu+.c tieu 
va` dda.t tra.ng thai' ca^n ba(`ng, tuy nhien neu tu+ ddo' ma` suy ra 
ca'c lu+.c ke'o (tai. ddiem M) ca^n bang nhau (that's true) roi ngay sau 
ddo' suy ra 3 go'c ta.i ddiem M = 120 co' chi'nh xa'c k0 ? Vo+'i truong 
ho+.p tu+' gia'c (ca'c go'c ta.i ddiem M = 90 ddo^.) k0 hieu CM na`y co`n 
ap' du.ng dduoc k0.

La^u roi co' 1 ba'c na`o ddo' ho?i ca'ch CM la` hi`nh tro`n la` hi`nh co'
dien ti'ch lo+'n nha^'t trong ca'c hi`nh co' chu vi ba`ng nhau, to^i nho+'
la` co' lo+`i gia?i ba(`ng ca'ch su+? du.ng na(ng lu+o_ng (su+'c ca(ng) be^`
ma(.t, xong la^u ro^`i k0 nho+', ba'c na`o nho+' thi` chi? ba?o giu`m. 

> 
> Ho^`i ddo' to^i ra^'t me^ lo+`i gia?i na`y bo+?i no' cho phe'p to^?ng qua't
> ho'a cho dda gia'c, hoa(.c min cu?a to^?ng a_1*MA_1+...+a_n*MA_n
> 
> Trong Kinh te^' mo^n to^i ho.c ba^y gio+` kha'i nie^.m Equilibrium va` ly'
> thuye^'t ve^` no' tu+o+ng ddo^'i quan tro.ng . Thu+o+`ng ga('n lie^`n vo+'i
> Equilibrium la` 1 tra.ng tha'i cu+.c tri. (vi' du. optimale allocation,
> optimale Welfare - Pareto efficient).
> 
> Ca'c ba'c ngihie^n cu+'u toa'n va` ly' co' the^? cho to^i lessons ve^`
> Equilibrium trong Math va Phys. (for dummies only!) ddu+o+.c kho^ng.
> What is equilibrium in math/phys sense? Which energie is in equilibrium
> minimal (What's the intuition for that) ? What is energie? 
> 
> Ca'm o+n ca'c ba'c tru+o+'c,
> 
> Vu~
>