Tìm hiểu về công cụ maple xây dựng ứng dụng giải các bài toán hình học giải tích không gian

BG GIAO DUC vA DAo TAO TRU'ONG DHDL NGOAI NGU - TIN HOC TP.HCM KHOA CONG NGHt THONG TIN " , - : .- KHOA LUAN TOT NGHIEP • • " TIM HIEUVE CONG CU MAPLE & XAY DUNG UNG DUNG GIAI • • CACBAITOAN , ?,,, HINH HOC GIAI TICH KHONG GIAN • -' I ' I GIAo VI EN HUaNG DAN: TS DO VAN NHON SINH VIEN THUC HIEN: NGUYEN TAN HONG H~NH NGUYEN DINH HuNG TP.HO CHi MINH - 2004 M1)C L1)C Chuang : Giai thi~u dS tai Trang Chuang 2: M6 ta c6ng C\JMaple 2.1.T6 Chll'Ctrong Maple 2.2.Nhfrng (rng d\Jng to{m hccua Maple 2.3.L?p trinh va luu tru Maple 2A.He> trq Maple vai DS tai 2.5.Danh gia Maple Chuang 3: M6 hinh cac bai toan hinh hcgiai tich 3.1 M6 hinh cac bai toan Hinh HcGiai Tich ~ gl.al , cac , b'al to an , V.1~c 3.3 Vi d\l , mt ~ b"al toan , S a di-0 qua" trm h glal • 23 25 27 28 Chuang 4: T6 chilc luu trfr tri thll'c,lu?t suy diSn va BiSu diSn bai toan 4.1.T6 Chll'Ctri thilc 4.2.BiSu diSn bai toan 4.3 Vi d\l minh ha 30 37 45 Chuang 5: Phuang phap suy diSn va thu?t giai 5.1.Phuang phap suy diSn 5.2 Cac th U?t toan 50 51 Chuang 6: Danh gia - Huang phat triSn 63 Ph\l l\lc Tai li~u tham khao 'y 14 17 22 LOINOIDAu Nhu chung ta da: biSt, To{m hQc gifr vai tro tien phong cUQccach nwng khoa hQc cong ngh~ d6ng thai Toan hQc cung chinh hl nSn tang cua nSn tri thu'c nhan lo~li.Nh~n thu'c duQ'c diSu cling vai sv phat triSn m~mh me cua tin hQc, d~c bi~t lInh vvc cong ngh~ ph~n mSm, da: co nhiSu ph~n mSm toan hQc dai, cang phat huy m~mh me va g~n gUi vai nguai su dt,mg no, diSn hinh la MAPLE Vai Maple, toan hQc thvc sv tra cong C1,1cho mQi nguai lInh vvc giang de;tyva nghien cuu Day la ph~n mSm co kha nang tlnh toan Symbolic Cvc ky me;tnhcling vai mQt thu vi~n kh6ng 16 chua vo s6 cac ham tlnh toano VS l~p trinh, Maple co nhfrng diSm me;tnhvS t6 chu'c c~u truc dfr li~u trli'u tUQ'ngso vai cac Ngon Ngu' l~p trinh thong thuang khac la dan gian va d~ su' d1,1ng Ben ce;tnhdo, nhu'ng cong nghien cuu tin hQc va khoa hQc may tlnh, d~c bi~t la huang Tri Tu~ Nhan T~o da: va dang duQ'c ap d1,1ngthanh cong vao nhiSu lInh Vl,l'C,nhu vi~c giai cac bili toim theo each suy diin eila ngU'ai dang mQt phat triSn va hoan thi~n han Vai dS tai "Tim hiJu v~ cling c~ Maple, xay d(l'ng u-ng d~ng giiii cae bili loan Hinh H(Jc Giiii Tich Khong Gian chi~u", dva tren ph~n mSm Maple dS tim hiSu, nghien cu'u, biSu di~n logic va cai d~t lu~t suy di~n nh~m dua ung d1,1ngco kha nang giai tv dQng cac bai toan hinh hQc khong gIan Vi thai gian he;tnchS, chung toi khong thS tranh kh6i nhfrng sai sot, khiSm khuySt qua trinh thvc hi~n dS tai nay.Vi v~y, chung toi r~t mong nh~n duQ'c nhfrng y kiSn dong gop, phe binh cua quy Th~y co va cac be;tn nh~m xay dVng dS tai duQ'choan thi~n han Cu6i cling chung toi chan cam an th~y DB Van Nho'n nguai da: tn,l'ctiSp huang d~n, t~n tinh giup dO', cung c~p nhfrng kiSn thuc c~n thiSt giup chung toi hoan dS tai Chuang 1: GIGI THII;:U DE TAl Chu'o'ng 1: Glcn THIEU 1.1 Gin; thi~u BE TAl a~tili Ngay nay, mQi nguoi dSu biSt vai tro tien phong cua Tmin hQc cach m~ng khoa hQc cong ngh~, noi rieng va nSn kinh tS tri thuc, noi chung MQt th\fc tS la dau biSt su d\lng toan hQc nhu mQt cong C\l lam vi~c thi thuong thu dugc nhung kSt qua b~t ngo Ben c~nh do, nhung bai toan d~t thlJc tS khong thS giai quySt mQt cach nhanh chong b~ng tinh toan thu cong, rna phai nho tai kha nang tinh toan cua may tinh Ph~n mSm tinh toan doi la nh~m dap ung nhu c~u cua thlJc ti~n,dua cac tinh toan phuc t~p tra cong C\l lam vi~c d~ dang cho mQi nguoi a a Maple la mQt nhfrng vi d\l diSn hinh Ta da th~y no la bQ chuang trinh tinh toan vai dQ chinh xac cao, dS C?P dSn hftu hSt mQi lInh VlJCcua toan hQc Cai m~nh cua no chinh la ch6 mQi bQ man dSu co thS suod\lng no lam phuang ti~n giang d~y va hQCt?p NSu nhu vai d~i s6, s6 hQc , giai tich, v v Maple co kha d~y du cong C\l dS giang d~y va hQCt?P thi hinh h9C no chi dua nhung cong C\l mang tinh ca sa, xa mai dap (mg dugc nQi dung giang d~y bQ man hinh hQc a cong th\fc Tich nang Tuy nhien, Maple la mQt h~ th6ng ma,no cho phep ta t~o l?p nhung C\l mai b6 sung nhUng gi no chua dS C?P tai Vai ly va yeu c~u tS tren, dS tai " Xay dl:Lnglmg dl:Lnggiai cac bili loan Hinh H9C Gild Kh6ng Gian ChiJu" dugc thlJc hi~n nh~m dua frng d\lng co kha giai cac bai toan hinh hQc khong gian Chuang 1: GIGI THH;:u DE TAl 1.2.Ph~m vi d~ tili Trang thai gian ng~n,d~ tai chi giai quySt duQ'cph~n giai cac bai toan Hinh H9C Giai Tich mang tinh t6ng quat, va chi giai quySt tren cac d6i tuqng hinh h9c dan gian: diem, vector, m?t ph~ng va duang th~ng Va chua co the giai quySt hSt t~t ca cac v~n d~ lien quan ,cling nhu cac d?11gtoan khac cua hinh h9C kh6ng gian Trong tuang lai, m\lc tieu chinh cua d~ tai la ung d\lng thiSt thlJc lTnhVlJCgiao d\lc va dao t?o 1.3.Y nghia V6i vi~c, xay d1Jllgung d\lng giai toan tlJ d9ng dlJa tren ph~n m~m toan h9C ma h6 trQ'r~t Ian vi~c giang d?y Toan, giup cho nguai dung chu d9ng han vi~c h9C toan, tiSp thu nhanh kiSn thuc, phcit trien SlJsang t?o Chung t6i hy V9ng r~ng, cac kSt qua tren cua chung t6i co the duQ'Cphcit trien va ung d\lng thiSt kS cac chuang trinh co the giai t1Jd9ng cac bai toan khac , Chuang 2: MO TA CONG Cl) MAPLE Chu'o'ng 2: • MO TA CONG CD MAPLE Maple hay du9'c gQi h~ th6ng dl;lis6 may tinh v6i kha nang xu ly, thao tac, tinh toan du6i dl;lngSymbolic v6i dQ chinh xac cao tren nhiSu v~n dS toan hQCnhu dl;li s6,giai tich,phuang trinh, b~t phuang trinh va ca nhfrng v~n dS toan cao c~p,dl;lis6 tuy~n tinh Vi V?y, Maple la cong C\l ly tuemg dS tl;lora nhfrng phlin mJm Toan h(Jc chuyen d{lng : co tinh chuyen mon cao,di sau vao ban ch~t cac v~n dS toan hQc nh~m h6 tn;r cho vi~c giang dl;lyva hQCt?p 2.1 TB chu'c Maple Nhli'ng y~u t6 chinh y~u tl;lonen suc ml;lnhcua Maple bao g6m: : Thao tac,tinh toan du6i dl;lngSymbolic la nhli'ng ham,thu t\lc,bi~n tham s6 dm;rc truySn vao la ky hi~u ho?c chi m\lc.Qua vi~c tinh toan se nhanh va dan gian •: Thanh ph~n chu y~u tl;lo nen thu' vi?n kh6ng 16 cua Maple la cac goi (package) M6i package chua cac nhom cau l~nh co cac phep toan lien quan v6i nhau, co thS rna rQng nhiSu chuc nang theo tung linh V\l'C,tu nhu'ng phep tinh cua b?c ph6 thong d~n nhli'ng thuySt tuang d6i t6ng quat .: Kernel, nhan cua h~ th6ng, la mQt nJn tang co' ban cua h~ th6ng Maple, g6m ngon ngli' C c~p cao - chiSm khoang chung 100/0 t6ng kich thu6c cua h~ th6ng Kernel du9'c xem nhu la t6c dQ va hi~u qua Kernel Maple chu y~u thi hanh l~nh tren s6 nguyen, nhli'ng phep toan quan h~ va nhli'ng phep tinh da thuc •: 90% ll;licac thu?t toan Maple du9'c viSt b~ng ngon ngli' Maple va dm;rct?P trung luu trfr thu' vi?n cua Maple Chuang 2: MO TA CONG Cl) MAPLE So' dTthu vi~n cua Maple phong phil, co thS giai quySt nhiSu v~n dS la nha cac d6i tugng package chua cac diu l~nh co thS ma rQng nhiSu chuc nang theo tung lTnh vl,J'c,chu dS ma nguai dung mu6n xay dl,l11gthem dS h6 trg qua trinh lam viec va nghien cuu Ngoai ra,nguai su dlfng co thS tl,J't?O l?p nhfrng cong Clfmai bf>xung cho nhfi'ng gi chua co thu vi~n hi~n t?i Khi do,no co thS dap ung t6t qua trinh nghien cuu, sang t?O va tra nen da d?ng han Day cling chinh 1£1 "tinh mo' " cua Maple Danh stich vai Package tham khiio: • Combinat: bao gbm nhfrng l~nh tinh cac hoan vi va tf>hgp cua danh sach, tren cac s6 nguyen • geo3d: nhfrng l~nh hinh hQc khong gian Euclidean chiSu; dS dinh nghTa, thao tac cac diSm, duang th~ng, m~t ph~ng, tam giac, m~t c~u, kh6i da di~n, V.V • , khong gian chiSu • Linear Algebra: cac l~nh d?i s6 tuySn tinh dS t?O nhli'ng lo?i ma tr?n d~c bi~t, tinh toan tren cac ma tr?n vai chi s6 lan, cac ma tr?n tuySn tinh • ListTools: cac cau l~nh thao tac tren List • Maplets: goi chua cac cau l~nh dS t?O cac cua sf>, hQp tho?i, va cac giao di~n trl,J'cquan khac nh~m giao tiSp vai nguai su dlfng, cung c~p dfr li~u cho Maple • Plots: l~nh ve cac lo?i db thi d~c bi~t khac nhau, bao gbm db thi cac duang, ve db thi cac ham ~n va chiSu, ve db thi tren cac h~ th6ng trlfc to? dQ khac • CodeGeneration: chuySn code Maple sang cac ngon ngu'l?p trinh khac nhu: C, Fortran, Java, MATLAB va Visual Basic • • PolynomialTools: tinh toan tren cac da thuc Chuang 2: MO TA CONG Cl) MAPLE • Scientific Constants: v~t 1)1, hoa hQc , h6 trg vi~c tinh tmin cac d~i IUQTIg • XML Tools: xu ly dfr li~u XML Maple 2.2 Nhii'ng u'ng d\lllg cua Maple toan hQc 2.2.1 Maple va'; linh loan sa hoc Maple la cong Cl,lm~nh, cho phep tinh toan vai nhfrng s6 fon > 99!; 933262154439441526816992388562667004907159682643816214685929 638952175999932299156089414639761565182862536979208272237582 511852109168640000000000000000000000 Phan tich mQt 86 thua 86 nguyen t6 thi dan gian, nhung vi~c tim mQt 86 nguyen t6 lan, hay nh~n biSt mQt 86 Ian co phai la nguyen t6 hay khong la mQt vi~c hoan toan khong dS dang, vi no doi hoi kh6i lugng tinh toan nit Ian Vai Maple ta 8e dS dang thvc hi~n dugc: > a := 122333444455555666666777777788888888999999999: > ifactor(a); (3)(12241913785205210313897506033112067347143)(3331) Maple cho phep thvc hi~n cac phep toan 86 hQc tren cac 86 th~p phan (d~u ph~y dQng) vai dQ chinh xac y Trong thvc tS, Maple co thS XlI' ly cac 86 vai hang tram nghin chfr 86 Vi dl,l,ta tinh 86 Pi chinh xac dSn 500 chfr 86 th~p phan j I ChUffilg 2: MO TA CONG ClI MAPLE > evalf(Pi,500); _ 3,1415926535897932384626433832795028841971693993751058209749445 92307816406286208998628034825342117067982148086513282306647093 84460955058223172535940812848111745028410270193852110555964462 29489549303819644288109756659334461284756482337867831652712019 09145648566923460348610454326648213393607260249141273724587006 60631558817488152092096282925409171536436789259036001133053054 88204665213841469519415116094330572703657595919530921861173819 32611793105118548074462379962749567351885752724891227938183011 9491 2.2.2 Maple voi nhil'ng dang (Olin cO'sit Bi~u thu'c 1a mQt nhfrng d?ng cO' ban nh~t cua Toan, no co th~ la tlap an, ma cling co th~ la tl6u tI~ cua mQt bai toan, Cho nen cac bai toan, bi~u thuc cang ng~n g bt:=cos(x)" 5+sin(x) "4+ 2*cos(x)" 2-2 *sin(x)"2-cos(2 *x); j bt := cos(x) :2 :2 + sin(x) + cos(x) - sin(x) - cos(2 x) > simplify(bt); cos(x) (cos(x) + 1) Tuang til d6i vai phan thu'c, ta dung l~nh normal chu~n t~c (gian uac til va m~u s6) Vi dV: > pt:=(x"3-y"3)/(x"2+x-y-y"2); d~ dua vS d?ng Chuang 2: MO TA CONG CV MAPLE X - Y pt:= -:2 X +X-y-y :2 > normal(pt); :2 :2 X +y X+ •.V x+1+v Nh~c d~n toan khong th~ nao khong nh~c d~n phU'o'ng trinh Co nhi@u d?ng phuong trinh: phuong trinh d?i s6, phuong trinh vo ty, h~ phuong trinh, b~t phuong trinh, day, ta se th~y duQ'ctinh don giim ffi9i v~n d@phuc t?P cua Maple: chi vai l~nh solve ta co th~ giai t~t ca cac d?ng phuong trinh tren k~ ca phuong trinh co tham s6 Vi d1,1: Giai phuong trinh co h~ s6 a > pt:=x"3-a*x"2/2+ 13*x"2/3=13*a*x/6+ 1O*x/3-5*a/3; :2 13:2 13 pt := x - - Q X + - x = - Q > solve(pt,{x}); 10 X +- x- 3 Q ChUffi1g 5: PHUONG PHA.P SUY DIEN V A THU.AT GIAI 53 •• 5.2.1.2 Cac bu'o'c XU' If BU'o'c 1: -KiSm tra xem cae d6i tugng lu?t co tucmg duong vai cae d6i tugng Bai toan if (tuong duong) then Ooto buae else KSt thue qua trinh kiSm tra BU'o'c 2: - Tim danh saeh (OL) cae d 6i tugng su d\Jng lu?t theo thu' tg - Tim t?P hgp (T) cae d6i tugng trong gia thuySt bai toano BU'o'c 3: - Hoan vi cae d6i tugng (T) cae danh saeh (OR) cae d6i tugng bai toan theo thu tg eua danh saeh (OL) - Phat sinh bang quan h~ d6i tugng [OL,OR] BU'o'c 4: - Duy~t l~n luge cae bang quan h~ - ChuySn d6i cae quan h~ lu?t cae quan h~ bai toan b~ng bang quan h~ [OL,OR] 00 to buae If (t~t ea cae quan h~ tuong duong lu?t dSu t6n t~i bai toan) then Ooto buae else KiSm tra vai bang quan h~ khae Chuang 5: PHVdNG PHAp SUY OlEN V Po THUAT GIAI 54 BU'o'c 5: - Ghi nh?n thong tin cua lu?t gam (GT, KL ) - K@tthuc qua trinh kiSm tra, Vi d\!l: Ta co lu?t - Cho vector u song song v6i vector v, va vuong goc v6i vector w nen ta co vector v vuong goc v6i vector w R:=Table([ Object=[[VECTOR,u,v,w]], GT=[[pal,u,v ],[per,u,w ]], KL=[[per,v,w]] ]); - Gici Slr cac s\!'ki~n bai toan BT:=table([ Obj ect=[[VECTOR,m,n,k]], Rela tion=[[pal,ill,n], [per ,ill, k]], ]); Bu'ucl : -Cac d6i tUQ'ng lu?t va bai toan (BT) Vector [VECTOR,u,v,w] va [VECTOR,m,n,k] nen d\!ng dUQ'c.(Trong truang hQ'p BT chi co [VECTOR,m,n] thi lu?t tren khong ap d\!ng dSu la lu?t ap Vector duQ'c) Chuang 5: PHUONG PHAp SUY DIEN vA THUAT GIAI 55 Bu'o'c 2: -Ta co danh sach cac d6i tUQ'ngtrong lu~t OL:=[u,v,w] -Ta co cac d6i tUQ'ngtrong BT T:=[[m,n,k]] - Ta co hoan vi cua T:=([m, n, k], [m, k, n], [n, m, kJ, [n, k, mJ, [k, m, nJ, [k, n, m]) -+ Ta co t~t ca bang quan h~ d6i tUQ'ng([u,v,w], [m, n, k]), ([u,v,w], [m, k, n]), ([u,v,w], [k, n, m]) -Ta xet bang quan h~ ([u,v,w], [m, k, n]) : [pal,u,v],[per,u,w]-+ [pal,m,k],[per,m,n] ( theo thu tg um,vk, wn)trong truang hQ'p kh6ng thoa, chuySn sang bang quan h~ khac NSu qua trinh chuySn d6i chi c~n quan h~ kh6ng thoa thl co thS kh6ng c~n kiSm tra cac quan h~ l~i Nhu tren ta co quan h~ [pal,m,k] kh6ng t6n t~i -+ chuySn sang bang quan h~ khac -Ta xet bang quan h~ ([u,v,w], [m, n, k]) : [pal,u,v ],[per,u,w]-+ [pal,m,n],[per,m,k] ( theo thu tg um,vn, wk) truang hQ'pnay tho a Ta suy kSt lu~n [per,v,w] KSt thuc go to buac -Ghi nh~n quan h~ mai [per,v,w] Chuang 5: PHUdNG PHAp SUY DIEN vA THUAT GIAI 56 Vi D1,l2: Ta co lu?t : Cho diSm M xae dinh ,Vector v xae dinh, m~t ph~ng (P) M thuQe P, v vuong goe vai (P) -+ m~t ph~ng P xae dinh R:=Table([ Objeet=[[VECTOR,v] , [Point,M] , [Plane,PJ], GT=[[TRUE,M] , [TRUE, v] , [per,v,P] , [bel,M,P] ] , KL=[[TRUE,P]] ]); - Gi:i su cae SI,1' ki~n bili toan BT:=table([ Obj eet=[[VECTOR, u] , [Point,N ,K] , [Plane,Q]], Relation=[[TRUE,N] , [TRUE,K] , [TRUE,u], [per,u,Q] , [bel,N,Q]], Expression=[ ] Determination=[ ] Goal=[P] J); Bu'O'cl : -Cae d6i tUQ'ng lu?t [VECTOR,v],[Point,M],[Plane,P] -Cae d6i tUQ'ng BT [ECTOR,u],[Point,N,K],[Plane,Q] co thS ap dl,lng lu?t Bu'o'c 2: -Cae d6i tUQ'ng lu?t [VECTOR, v]' [Point,M], [Plane,P] tuong tv tren ta co :OL:=[v,M,P] -Cae d6i tUQ'ng BT Tl :=[VECTOR,u],T2:=[Point,N,K] T3 :=[Plane,Q] Chuang 5: PHVONO PHAp SUY OlEN vA THUAT olAI 57 B ,ritc 3: - Ta co hmin vi eua T:=([u, N, Q],[u, K, Q]) -+ Ta co t~t ea bang quan h~ o6i tuqng ([v,M,P] , [u, N, Q]) , ([v,M,P] , [u, K, Q]) -Ta xet bang quan h~ ([v,M,P],[u, K, Q]) : [TRUE,M] -+[TRUE,K] ( theo thtl' tv v~u, M~K, P~Q) (Th6a oiSu ki~n BT) [bel,M,P]~[bel,K,Q] (Khong th6a) KSt thue kiSm tra ehuySn sang bang quan h~ khae -Ta xet bang quan h~ ([v,M,P],[u, N, Q]): [TRUE,M]-+[TRUE,N]( theo thu tv v~u, M~N, [TRUE,v]-+[TRUE,v] (th6a) [per,v,P] -+ [per,u,Q](th6a) [bel,M,P]-+ [bel,N,Q](th6a) P~Q) -Ta co thS suy KL : [TRUE,P]-+[TRUE,Q] -KSt thue qua trinh kiSm tra lu~t Goto buO'e Bu'o'c 5: -Ghi nh~n cae quan h~ [TRUE,N], [TRUE,v], [per,u,Q] ,[bel,N,Q] tren va kSt lu~n [TRUE,Q] 5.2.2 Thuat toan sup diin tiJn 5.2.2.1 so.tla thu{tt toan suy diin tiJn Chuang 5: PHVdNG PHAp SUY OlEN V A THUAT GIAI Ghi nh?n Bai Toan va m\lc tieu 58 Tim lu?t suy diSn dS giai , Dau "Bat Khong tim duQ'c lai giai khong tim dm.>,c tim dUQ'c Ap Sll d\lng lu?t suy ki~n mai, KiSm tra mlfc tieu K~t Thuc d~t ml,lc tieu SO'DB Thu{lt toan suy diln tiin Chua d~t ml,lc tieu I Chuang 5: PHUONG PHAp SUY OlEN V A THUAT GIAI 59 5.2.2.2 Cac bu'o'cXU' Ii Buo'c 1: - Ghi nh?n cac d6i tUQ'ng(Objects) ,cac quan h~ (Relation) gifra eac d6i tUQ'ngva xac dinh mvc tieu (Goal) cua vao danh saeh cae SlJ ki~n F - Kh6i t(;10danh sach lerigiai (LG) la r6ng (Danh sach cac lu?t suy diSn dil duQ'c duy~t qua) Tim lu?t r danh sach cae lu?t R If (nSu r co thS ap dVng duQ'ccho t?P SV'ki~n F ) then Goto buac Else -Dung thu?t toano -Return FALSE; - Ghi nh?n cac quan h~ mai suy tu lu?t r vao t?P SlJki~n F - Luu lu?t r vao danh sach lerigiai (LG) - KiSm tra mvc tieu if (8(;1tmvc tieu) then - Dung thu?t toan - Return LG else Goto buac Chuang 5: PHUONG PHAp SUY DIEN vA THUAT GIAI 60 Vi lif' minh hru Giii Slr ta co danh sach Iu?t nhu sau: R :=( R 1=MQt di~m va mQt vector chi phuO'ng cua mQt duang th~ng xac dinh -+duang th~ng xac dinh R2=MQt duang th~ng d xac dinh song song vO'idl-+ vector chi phuang cua d cling Ia vector chi phuang cua d R3=MQt duang th~ng (d) dfi xac dinh va (d) thuQc m?t ph~ng (P) => phat sinh mQt vector chi phuO'ng cua m?t ph~ng (P) R4=MQt m?t ph~ng co mQt di~m xac dinh thuQc m?t ph~ng va C?Pvector chi phuO'ng xac dinh thi phuO'ng trinh m?t ph~ng duQ'cxac dinh R5=Duang th~ng (d) II m?t ph~ng (P) va duang th~ng (d) cung phuang v6i vector u => u II (P) ] Vi dl} : Tim phuO'ng trinh duang th~ng I qua di~m A va v6i d Giii Slr A va d xac dinh BU'o'c 1: - T?p sv ki~n F : F:= ( Objects=[[Point A],(Line d,l]] Relation=((TRUE,A], (TRU E,d], (beI,A,I]] Goal=[l] ] - Lai giiii LG:= (]; (Danh sach cac lu?t suy diSn dfi duy~t qua) Chuang 5: PHUONG PHAp SUY DIEN vA THUAT GIAI 61 BU'o'c 2: -Duy~t lfin luqt cac lu~t Ri R va Ri chua t6n t~i LG -Ta tim duqc lu~t R2.Goto Buac BU'o'c 3: - Tu R2 ta co duqc vector v // I va v xac dinh - C~p nh~t vao F F:=[ Objects=[[Point A],[Line d,l],[VECTOR,v]] Relation=[[TRUE,A ],[TRUE,d],[bel,A,l], [TRUE,v], [pal,v,l]] Goal=[l] ] - LG:=[R2] Bu'o'c 4: - KiSm Tra Goal: I vfrn chua xac dinh - GoTo buac BU'o'c 2: - Duy~t lfin luqt cac lu~t Ri R va Ri chua t6n t~i LG - Ta tim duqc lu~t RI.Goto Buac BU'o'c 3: - Tu RI ta co duqc I xac dinh tu diSm A, va vector v Chuang 5: PHVONG PHAp SUY DIl~N V A THUAT GIAI 62 - C?P nh?t van F F:=[ Objects=[[Point A],[Line d,l],[VECTOR,v]] Relation=[[TRUE,A], [TRUE,d], [bel,A,l],[TRUE, v],[pal, v,l] [TRUE,l,A,v] ] Goal=[l] ] - LG:=[R2,Rl] BU'o'c 4: - KiSm tra Goal: I xac dinh theo Rl - Dtrng thu?t toan return LG:=[R2,Rl]; Chuang 6: nANH GIA - HUaNG PHAT TRIEN 63 ChU'o'ng 6: DANH GIA - HUaNG PHAT TRIEN • 6.1 Tom t~t nhii'ng nQi dung kh6i clla ung d\lllg giai tg dQng • Dua ngan ngfr quy uac cho vi~c nh~p d~ vao ung d\lllg Cac quy uac chung cua ngan ngfr - Cac til khoa ngan ngfr quy uac va cac til khoa • T6 Chll'Ctri - thuc bai toan hinh hQCva lu~t suy diSn Xay d\rng c~u truc dfr li~u bai toano T6 chu'c va cai d~t danh sach cac lu~t giai Cac thu~t toan kiSm tra tinh xac dinh clla cac d6i tUQ'ng • Lai giai chi ti@tcho cac bai toan va hinh ve minh ho? • Giai duQ'c nhi~u d?ng bai lien quan d@ncac d6i tUQ'llg hinh hQc duang th~ng,diSm,vetor, m~t ph~ng Chum1g 6: DANH GIA - HUONG PHAT TRIEN 64 6.2 H~n eh~ eua u'ng d1}ng - Trong thai gian ng~n, vi~c dua mQt ngon ngfr mang tinh ch~t qui uac chung cho t~t ca cac bai toan d?ng Hinh HQCGiai Tich Khong Gian se khong tranh kh6i nhfrng thiSu sot cho viSc d?c ta cac bai toan cho ung d\lng Hi~n t?i dS tai chi giai quySt duQ'c ph~n giai cac bai toan Hinh HQCGiai Tich mang tinh t6ng quat, va chi giai quySt tren cac d6i tUQ'nghinh hQc dan gian: diSm, vector, m?t ph~ng,m?t c~u va duang th~ng 6.3 HU'o'ng phat tri~n tu'o'ng lai - (J'ng d\lng c~n duQ'cphat triSn vS ngon ngfr qui uac, cling nhu vi~c b~t 16i ch?t che han vS lTI?tcu phap qua trinh nh~p dS bai - Citi tiSn ngon ngfr quy uac dS Slr d\mg , dS nha han nh~p li~u bai toano - Ngoai ra, cac thu~t toan c~n duQ'c cai tiSn, nh~m xac dinh duQ'c lai giai nhanh han, thong qua vi~c luu trfr va nh~n biSt cac m~u va lai giai cac bai toan chu~n t~c ma chung ta thuang g?p Va cling c~n them vi~c giai bi~n lu~n bai toano - Trong tuang lai, m\lc tieu chinh cua dS tai la ung d\lng thiSt th\fc lTnhV\fCgiao d\lC va dao t?o l PUT) LT)C l.Cac d~Dg bili toaD cO'baD 1.11>i~m: Tim giao diSm eua Tim hinh ehiSu eua Tim diSm d6i xlmg -x+2y+z+ 1=0 Tinh kho~mg cae til 1)/2=(z+ 1)/(-2) dt d(2t, 1-t,3+t) va m~.tphing x+y+z-10=0 diSm M(l ,-1,2) tren m~t phing x+3y-z+2=0 eua diSm M(2, -3,1) d6i v6i m~t phing P diSm M(2,3, 1) dSn dUOngthing d x+2=(y- 1.21>",0'og Th~og : " ViSt Pt duong thing qua diSm A(2,0,-1) va e6 veeto chi phuong n(-1,3,5) ViSt Pt duong thing qua A(3,4,1) va song song dUOng thing d(l+25t,4t,5+ 3t) ViSt phuong trinh hinh ehiSu vuong g6e eua duong thing d(2xy+z+ 1=0,x+2y-z-3=0) len m~t phing Oxy ViSt pt duong thing qua A(3,2,-1) va vuong g6e v6i m~t phing 2xy+7z-1 =0 ViSt pt duong thing qua A(I,0,5)va vuong g6c v6i duong thing d(1+2t,3-2t, 1+t) d 1(1-t,2+t, 1-3t) ViSt pt duong thing qua A(O,1,-1) va vuong g6c v6i duong thing d(1 Ox-y+z-1=0,2x+y-4z-5=0) X6t vi tri tuong d6i eua d:(x-l)/2=(y+5)=(z-3)/4 va d : (x-6)/3=(y+ 1)/2=z+2 X6t vi tri tuong d6i eua dt d: (x-12)/4=(y-9)/3=z-l va mf(P) : 3x+5yz-22=0 L~p pt duong thing vuong g6c v6i mf Oxz va e~t dUOngthing d(t,4+t,3-t) ,d 1(1-2t-3+t,4-5t) lO.ViSt pt duong thing qua M(O,l,l) va vuong g6e v6i d: (x-l)/3=y+2=z va e~t dUOngthing dl(x+y-z+2=0,x+ 1=0) •• • 11.ViSt pt duang th~ng qua M(O,1,-1) ,vuong goc va cAt d(x+4y1=O,x+z=O) 12.Cho mfP (x+y+z-l=O) va duang th~ng d(1,O,-I).ViSt pt duang th~ng qua giao diSm cua P va d,n~m mfP va vuong goc v6i d I3.Phuong trinh duang th~ng qua diSm va cAt2 duang th~ng khac I4.Phuong trinh duang th~ng d thuQc P va cAtdl,d2 1.3Mat Ph~ng : • .• ' ViSt phuong trinh m?t ph~ng qua diSm A(3,-1,2) B(1,-I,O) C(-1,2,3) ViSt phuong trinh m?t ph~ng trung tn,l'c cua do~mAB,biSt A(1,-3,5) 8(2,1,-1 ) ViSt phuong trinh m?t ph~ng qua M(1,2,-I) N(0,1,2) va II v6i Oz Cho hai rn?t ph~ng co phuong trinh : (P) 2x-rny+3z-6-m=0 va (Q) (m+3)x-2y+(5rn+l)z-lO=O V6i gia tri nao thi : -P va Q song song -P va Q trung -P va Q cAtnhau ViSt phuong trinh m?t ph~ng chuc d(x+y+z-4=O,2x-y+5z-2=0) va song song d 1(2-t, 1+2t,5+ 2t) ViSt phuong trinh duang th~ng qua A(1,2,-3) va vuong goc v6i duang th~ng d(2x-y-z=O,x+y-l =0) va dl (2-t, 1+t, 1-2t) TAl LIEU TRAM KHAo • Ti~ng Vi~t [1] Ph~unHuy Dien, Tinh toan, 19p trinh va giang dQYtoan hQCtren Maple, [25-26,30,40, 123, 190, 197-199], NXB khoa hQc va ky thu~t, 2002 [2] Tr&nVan H(;1o- Le Kh~c Bao - NguySn MQng Hy - Tr&n Duc Huyen, Hinh hQc giai tich 12, BQ giao d\lCva dao t(;10,1992 [3] Hoang KiSrn - D6 Van Nhon - Le Hoai B~c, M6 hinh tri thzk: MQng CObjects, [84-97], ky ySu HQi nghi khoa hQc APPSITT 97, Ha NQi ? Ti~ng Anh [4] Maple learning guide, Maplesoft, a division of Waterloo Maple Inc, 2003 [5] Maple introductory programming guide" Maplesoft, a division of Waterloo Maple Inc, 2003 [6] Maple advanced programming guide" Maplesoft, a division of Waterloo Maple Inc, 2003