Re: A Common Sense about the Quadrature of A Circle

[Sonnet Nguyen <Sonnet.Nguyen@fuw.edu.pl>]

Dear friends, (to Mr AiViet et al)

On Fri, 20 Jun 1997, Aiviet Nguyen wrote:

>   Ne^'u na(m 91 mo+'i kha'm pha' ra ba`i na`y thi` kho^ng chu+`ng la.i 
> che'p tro^m cu?a cu. Tri' ua^?n ro^`i. Hy vo.ng kho^ng pha?i la` anh. 
> Co`n ne^'u lo+~ pha?i thi` ddu+ng bao gio+` ra u+'ng cu+? hie^.u tru+o+ng 
> nghe.

Hilbert cu~ng dda~ tu+`ng ma^'t nhie^`u tho`i gian cho ba`i na`y.
Ve^` lo+`i gia?i (1991) dda(ng trong ta.p chi' X (I have to check a title
of the Journal and date). 
Ba`i na`y kho^ng lie^n quan gi` dde^'n VN-se mathematicians and tranh
cu+? hie^.u tru+o+ng ca?.

>   Tru+o+'c he^'t ba`i Toa'n pha't bie^?u nhu+ anh Sonnet ma` cha(?ng 
> gio+'i ha.n phu+o+ng tie^.n thi` lo+`i gia?i cu?a Anh Minh la` ddu'ng la('m,
> hay la` pha' ddai thu`ng ga'nh nu+o+'c cu?a cu. Tri' Ua^?n la` ddu+o+.c.

Ba`i toa'n du+o+.c pha't bie^?u nhu+ dda~ ddu+o+.c pha't bie^?u la` 
tu+o+ng ddo^'i chua^?n.  (Nha('c la.i cho nhu+~ng ai chu+a nho+':
Co' the^? ca('t hi`nh tro`n tha`nh 1 so^' hu+~u ha.n ma?nh ro^`i ghe'p
la.i ddu+o+.c hi`nh vuo^ng hay kho^ng ?)

>   Nay to^i "chu+'ng minh" kho^ng the^? ca^`u phu+o+ng ddu+o+.c du+.a 
> tre^n mo^.t Lu+o+ng Tri: " DDi.nh Lua^.t Ba?o toa`n Lo^`i". Theo Common 
> Sense ma` no'i thi` khi anh ca('t the^' na`o thi` Cong Lo^`i va` Cong 
> lo~m cu~ng Trie^.t tie^u. DDu+o+`ng Tro`n co' Toa`n Cong Lo^`i ma` Hinh 
> Vuo^ng thi` kho^ng co' ti' na`o Cong ca?.( Q.E.D.)
>   Ta^'t nhie^n ca'c vi. Toa'n ho.c co' the^? ti`m kie^'m ra thua^.t Toa'n 
> vo^ ha.n na`o ddo' dde^? ly' lua^.n cu?a Lu+o+ng Tri tha`nh le^'u la'o.
> Nhu+ng theo to^i mo^.t thua^.t Toa'n ma` ca^`n dde^'n vo^ ha.n operation 
> thi` xem nhu+ ba`i Toa'n va^~n la` chu+a gia?i ddu+o+.c.
> Vi` va^.y Hu? ly' lua^.n to^i kho^ng hie^?u sao la.i co' kho^'i ke? to^'n 
> gia^'y mu+.c dde^? ti`m lo+`i gia?i hay dde^? chu+'ng minh ba`i na`y 
> kho^ng co' lo+`i gia?i nhi?
>   Xin mo+`i ti`m ra cho^~ sai cu?a Common Sense. Va`i ha`ng tho^ la^.u.

Ne^'u no'i ve^` vo^ ha.n operations, chi? ca^`n chi? ra 1 song a'nh
la` song.  Va^'n dde^` nhu+ va^.y thi` qua' ddo+n gia?n, for 10 year old
choolgirls!

Cha` ca^u ho?i ha('c bu'a tha^.t.
Thu+.c su+. ma` no'i va^'n dde^` o+? cho^~ the^' na`o la` cong lo^`i?
Cha('c la` anh ddi.nh nghi~a la`:
cong lo^`i la` convex set and his boundary does not cosist a line (?). 
Nguye^n ly' ba?o toa`n CONVEX thi` ddu'ng co`n ba?o toa`n cong CONVEX thi` 
(co' the^?) kho^ng ddu'ng.   I'll give you an contrexample.

Va^'n dde^` o+? cho^~ (ne^'u infor. to^i bie^'t la` ddu'ng) thi` to^`n
ta.i hu+~u ha.n operations,  thu+.c su+. la`m to^i ba`ng hoa`ng ca?
ngu+o+`i, ne^n vie^'t le^n cho mo.i ngu+o+`i suy nghi~ cho+i:
mo^.t be^n la` INTUITION co`n be^n kia la` PROOF.
regards,
SN