Báo cáo môn lịch sử toán về chủ đề Toán cổ Trung Quốc

b¸o c¸o m«n
lÞch sö to¸n Häc
Chñ ®Ò: To¸n häc cæ Trung Quèc
Giáo viên hướng dẫn: TS. Trần Hồng Nga
Lớp: ĐHSP Toán K55
Nhóm thực hiện:
M&C L&C
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
Phn 1: 
Phn 2:
 !"#$%&
'()*+, ("/*01-2 ,$
3*4$5$6&
37-08 -90#:&;
3< =*0'()&;
3>,?*4$&;
3*@*A,0#B&;
CD*0".E !F2"@ GD-*H$-,"2907*!I-J
Phn 3:KL
Phn 4: MNOPQPRS
TU
V=π
*@*) 0#:
,A* ,W-,(
Phần 5:CX
Ti liu tham kho;
Lời nói đầu
Y
rung Qu=c là qu=c gia
nZm [ phía B\c c]a !^t

n7c ta, thu%c khu v_c
gió mùa, khí hBu !a
d/ng t> ^m !4n khô do !^t
n7c r%ng l7n, !Fa hình
ph`c t/p, !% cao chênh
l)ch l7n. Dân s= Trung
Qu=c tính !4n nay !ã hn
1.34 ta ngbi (tính !4n
4/2011), vcn hoá chFu
@nh h[ng sâu s\c t> các
t t[ng !/o PhBt – tôn
giáo chính th`c [ !^t
n7c này. Trung
Qu=c t> lâu !Ic bi4t
!4n là m%t trong nh+ng n7c có nHn vcn hoá !d s% và lâu !bi nh^t th4 gi7i
và là m%t cái nôi c]a nHn vcn minh nhân lo/i. Vì th4 Trung Qu=c có !óng
góp r^t l7n trong s_ phát trien khoa hfc nhân lo/i.
Kho@ng 3000 ncm tr7c công nguyên ngbi Trung Hoa !ã bi4t dùng
quy (compa) và c] (êke) !e vg các hình hình hfc. Hf !ã dùng h) !4m thBp
phân, vH ký hi)u tIng hình và s=, vH phép tính toán v7i các s= l7n. NHn
toán hfc ch Trung Qu=c !ã !/t !Ic nh+ng thành t_u khá cao. S_ phát
trien toán hfc ch xa [ Trung Qu=c có b@n s\c riêng bi)t. Ch' ti4c là
nh+ng tài li)u vH toán hfc ch Trung Qu=c lu l/i r^t ít ii và t@n m/n.
Chúng ta nghiên c`u lFch sj toán hfc c]a Trung Qu=c ch] y4u qua các
cu=n sách: Chu Bk toán kinh, Cju chng toán thuBt và Tôn tj toán kinh.

1. Chu Bễ toán kinh:
b*#$",!6Wjlm)!4A0B  <0>#^0W7Ab*<n.!6E$^0
*)-$=$ok0".2*p0#"W !6-11*!45$,*)AGH <W=pGH5$,)
*+,-/0#"A%00,A* G$9

b*q9.p!6-1-$=j$-0".0$B0p0#"W Dn!61*!42,*
-coB-Yp-coB-p 0#:oB-p!6-1-@2.**)AW=<ApW=l
b*,A?\-0#*H$-1A%0D0".f-h*0*4(DhC$*p9!60:A#,
W=*E^ E'pJY;p!<n(DA%0-"W=-_-2:-8E W"G7*04*7*d*!1
q<n(D-$=W 0".-h^0-],#$T$=-$noFr]n"D!=0W 
GD"042a0`-1b*!6o*sW"/(/*V 0".-],$k-1-
#Z+2*40`-0#"W -10>0b*I$p0`-(D2"@0>042aC3
!4042a0`T$,-$=W Dn0,0^n0#:!%0".f-2.-,"-],b*
-h#$T$=-
>042aC3pb*0#$T$=-!6o*40lt-"A ,u5$n&vGDs2wu-]&v
!eGg :f-#sA%0W=!d=A!b*042a0`C3-1Gg+
::f-lt5$nGD-]
#$T$=--h!6!11 *H$0D*(*)$GH)!4A0B  <GH28*)$0I
: W=pGH080".G7* W=(7x/pW=;yYz!I-G*40W,$u0> @*
5$,0#.*v
 *0I:0B  <0w"GF0#8-'!eo*e$l*kW=p29lt0#"
080". 08!I-0_-*)0#soD08Q042'0`3p{|-!Fu0`-
{|-jv!6!F},qb0#~(D:0>*+,#,!H$oZ,$
$ k 0". 2*0#: oDn l7*l/!=*
0"/*%*l$-]n4$o,"dAA%0W=G^!HGH
0*s  Gcp A%0  W= 08  -^0 -],  0,A  *  G$9
u00_!F(8*0,"vpA%0W=08-^0-],
<W=
#"$k0".2*-1-•0#:oDn!=*
0"/*-],A%0GF"D0jG7*5$,I0
T$,I00<$G7*GF"D0j#Z08-^0
W=(Dl":0#~GD:G$9AD-1:
G$90I0#-"!^0GD:0#:0I0#
-"0#b*#"W Dn-1:GgA*f,-"
!F(8*0,"q<n(D-`A*-h^0-],<

("/*GH!F(8*0,"u:Jv

2. Cửu chương toán thuật:
V Dn!I-G*40(/**H$(rpGDA•*(r
!H$-1ohW$0wAl" D0".f-@fC
u042'0`vp€$$nu042'0`Vvp#
€u042'0`3Vvp€8$r"u042'0`
3v•w"€$$n0:0 *@-],j$-0".
0$B0(D#rV,uA^0cAYv>042'0`3
!4042'0`Cpj$-0".0$B0!I-lt(DA
W *."2",GD0#[0D0  ‚A2*!*e-],0".
f--h#$T$=-j$-0".0$B0-ƒ(D-$=
0>!*e!%-!."-"b*!"#$%pDE<nl_pD
0*sGcpb*0$0$4pGG•-],#$T$=-E,2*,
  ‚ADn0#:oDn#bA#DGD-108-^0#B 2$9
10^0-@Y;oD*poD*0".D"-ƒs$*@0*40GD(b**@*V,$A•*1AoD*0".
-1s$0$B008$B008DndA 5$n0\--$"|-   080_-*)
lrlr0#s+W=(*)$-m0e
,6n(705$,%*l$-],Cửu chương toán thuật
Chương I:f*(Du !*Hvs$5$n0\-08l*)08-
A%0W=: xp2e-@:0#~p-1   08W=f-GH <W=qGF!"
l*)08-(DA%0:-+B0G7* -/lD*GD;o7-uA•*o7-2"@
-Av„*)08-:G$9p:-+B0!I-08"D0"D-8E *08l*)
08-:0#~p:5$/0p:GD2cb*0,(^n

=
π
„*)08-:G*s <
!I--"*l*)08-:0,-1!.n(70#tG7*!.n:G*s <p!.niGD
-*H$-,"!H$oZ-*H$-,"-],G*s <

Chương IIf*(D ! "#$ %! #7-400#:oDn
A%0o@-$‚!e!h*0>("/*01-DnW,("/*01-2 V,$!1(DoD*0".
("/*pA•*("/*0$<0w"A%00$B00".#*sp @. 0$0$40b*E,[#$
T$=-Q!<nb*0,0^n+2*40`-0".GH5$n0\-0,AE$^0u5$n0\-ADb
!12*o*40,**.0#F0`D"!1-],,*!/*(I0'()GDA%0*.0#Fo^02:-],
!/*(IDn0:0:A!I-*.0#F0`-],!/*(I2*,vGD-*,0'()G7*W=
$ns,n <
 Chương III:f*(D #&'( uW$n <vdA+oD*0".
-*,0'()p-*,0'()I-p-ƒ5$n0\-0,AE$^0!GD2 
Chương IV:f*(D)*+-1 5$n0\-2,*-coB-,*GDoB-o,p
G*40l7*l/E !F-/:-+B0o*40l*)08-GD-/2*,pE !F-/
:G$90w"l*)08-pE !F-/:(B  0w"0e08-pE !F
!b28:0#~p:-r$

Chương V:%*l$(D,- #. !  /#0!"0e08-p28-07-
-r0*402*E<nl_0b0Dp!D"D"=p!\ !s!B pE<n ."!D*p•G7*:
0t2 ,$p0#"!1-1-90`-080e08-+2=*2 ,$
Chương VI:f*(D12#&uT$<0<$vdAA%0("/0oD*0".08
W=(I01- @*-$-^ -" $n)0w"+!*H$2*)Dn-D `-0/ 
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 VŠL’uyL,’Yo’-v
3BnW=VoZyL,’Yo’-#d*0sAo70A%0o%*W=-],L
q1(D5$n0\-D8!*eAo*&T$n0\-0#s!I-01A0\00#"o=-<$

0-],#:q/*3˜!b*D{*W,$!<n

,A<!dD0^00B n ƒ0mA,*",0#^ ^0-*

^00j!"DG*s-8o.$n)0
#>o (*ƒ0*)!\-0#*
三  人  同  行  七  十  嬉 
五  樹  梅  花  廿  一  枝 
七  子  桃  園  秋  半  月 
共 除 百 零 五 定 為 其
„F-
,b*-t!*80o‚nA*
cA-†*A,*",cAA=0-D
‚n6E$AGrnG>,j,0.
#>0#cA(*cAo*40W=0D
 . *@*oD*0".!dl!I-"D0*)G7*rj$*H$u04
2aCv *@*+oD*0".04p[-<$•$pA6*!4042aCC,"?
EA7* .0*)!I-uzLv
<1=#>(#"oD*0".D8!*eAo*&p"D*W=ppy-1
0elto%W=D"+,29Ž
Trả lời:10eltW=Ypp!e083:Ypp(D+W=$ns0=
-t,$0>!9*A%0pl"!15$,W=Dn-10e0:A!I-W=00_
yLpYppL!1(DpYYpYGD;;
[*G:(Do%*-$-],GDp-*,-"Yl
YY(Do%*-$-],YGDp-*,-"l
Y(Do%*-$-],YGDp-*,-"l
;;(Do%*-$i^0-],Ypp
Y
4. Những thành tựu toán học khác ở Cổ Trung Quốc
• Số π

w"7080".pb*#$T$=-!6o*40*.0#FW=™Dn-D
-8E 42ap€$<A08!I-™špy42aVp
#"D0:A!I-™š
L
KWjlm-90`--],9-"W= *!e
080e08-:-r$30w"!b28„
3Š „

’ „

Š „

hV$*uL‘LvKW*#,0/**4,u0`-,A*0'
*,9Dn,nvcA;W,$-9$nsp(‡-!190$h*GDo\0!r$
*s-`$0#FW=*
?0>@A<B7 /#0 C/
#7-hC$*pD0".f-#$T$=-€$$n!HE$^0 08W=
*oZ -\0•0#~pGD908!I-07*W=W,$l^$ ‚n#s-W[-],
0*H<phC$*A*)0AD**s-`$GD080".07*yW=!6-"™,**.
0#F08-I (D
y
YY
GD



q. W=-],hC$*-ƒ*=2405$@-], D0".f-7-
"D*p!<n(D!*H$!6 !<nA%0:cAqe*7W_!11 Dnp
A%0W=D0".f-7-"D*2*4Ff*W=*(Dh
b*#$T$=--ƒWjlmo*e$!d0hI  `--~f*(D :

G$90r2:&p!I-A90@0#" 0b*2:-h!/*GD!I-"D-'o[*„
$nuYz?JzvKWjlm!,* !H$LyY-/%*0*4 :0#~GD!608
!I-™šJ
• Giải hệ phương trình
#"-j$-0".0$B0b*#$T$=-!6*@* 0#:oB-
,*G7*  . ADff*(D0*s0=&Q042a3p3*4$9!6
lt  . !1!e*@* 0#:oB-o,3D"042aCp$4*)0
!6oZ  . 0*s0=p0:A!I-*)A+$0a-], 0#:oB-
#" 0#:y;E

‘Y;LE
 
’yYJE
Y
’J;LE‘;JYYŠLp$
4*)0!6-f r$ns-],*)A(Dz#d*0,n04EŠn’zGD!I-
y;n

‘yJYn

’Jn
Y
’yLJYn‘LL’LV,$!1!e!,)W=-],‚
W=oB--,"^0GH!GFp90,n04
y;
D
; =
GDE !F0#" 0#:
A7*•Šzp0>!1240($B


Y
y;
z
==;
GD

Y
z=5

 . *s0=&!I-*@*08--*0*400#"0  ‚AV=0-j$
-&-],rj$*H$_--^0-],  . Dn0!G7*
 . "1-w!I- .0A*[-<$•$!r$042aCCucAzJv
• Tam giác pascal
$4*)0uYzL‘Lv-ƒ0:A#, *
ADW,$Dn,W-,(A7*0:A#,GDb*!b*pG:
0*4$ 090* s !6  f* W,*(D  ,A *
,W-,(&u:osv$4*)0(D*."W0".
f-0#"*H$cAp-10eEwA9(Db*
E<nl_sDq/*W=-],#$T$=-
#"0  ‚A-],9pb*0,-ƒ!60:A
0^n+-90`-(^n0h -^ W=W,$
( )
Y

Y
+
=++++


( )( )

;
Y
Y
YYYY
++
=++++


( )( ) ( )( )( )( )
YL
Y
;
Y
zLLz
Y
++++
=
++
+++++

5. Nhận xét
 :-$p#^021!.*.+!11 -],b*#$",GD"2"
0D0".f--],<("/*0>0b*-h!/*-"!4042aC3pC3$n*s
7080".oZ0$B008(DA-"H0".f-h#$T$=-
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