tn6i iMoiiliJ BOI DUeNG NANG LttC V A N DUNG T O A N HOC CAO C ^ fl^ GlAl TOAN PHO THfiNG VA N A N G LUC GIAI TOAN SO CA> CHO SINH V | £ N N G A N H SIT PHAM TOlN R NMriiiMtiir Tdm TAT ^ Ning luc da s[.]
Trang 1BOI DUeNG NANG LttC V A N DUNG T O A N HOC CAO C ^
fl^ GlAl TOAN PHO THfiNG VA N A N G LUC GIAI TOAN SO CA>
CHO SINH V | £ N N G A N H SIT PHAM TOlN
R-NMriiiMtiir
Tdm TAT ^ Ning luc da sinh viin su pham biin abindi quan bgng bong viic phit biin ning lpc cho hpc M
ttong pud binh day hgc BH viit binh biy vi mit si minh ti da ning Ivc vin dung toin hgc cao dp dim
toin phi bring vi ning ivc gtdf lodn sa dp da slab van nginh su pham ding btdi chra ra cdc biin phla
di bdi dtiOng dc ning Ivc di
Tikhia: NSng Ive, toin hgc cao dp, biin phi bidng, toin sa cip, supham
1 M i diu
Yiu ciu chuyin dii cdn bin, todn diin gido
dgc nin gido dge tt> ehi yiu nhim bang bf kiin
ttiic sang phii ttiin phim chit vd ndng Ivc nguii
d i ttivc Bin dii hii nguii gido viin phii ttiay dii
ta# duy, cich tiip cin qud tinh gldp dgc Qga d i
cin xdc djnh vd ttang bj chp sinh vlin nhing ndng
Ivc nghi nghiip ddp ing yig ciu dii mil nil trin
Bii vii sinh viin su pham h)in ngpdl cdc ndng luc
Chung v i gldp dgc vd i^y hpc hp cin c i cdc ndng
Igc riing gin vii min Tein i ttuing phi fliing
T i dd d i xdc djnh vd bii duing ning Ivc v$n dgng
todn hpe cao cip d i glil ttidn phi ttiing vd ndng Ive
ttpng qud trinh day hpc
2 Mit s i vin d i v i ndng Ivc v i ning Ivc cia
sinh vlin au pham tpin
Ndng Igc Id mil khdi niim khd ttthi tugng cua
tdm ly hpe Khdi niim ndng Ive dvpc hiiu ttieo nhiiu
nghla khdc nhau Tiin ttii giii, cing nhu p Viit
dang rii quan tdm din vin d i phdt ttiin ndng Igc,
Thsp cdc nhd Tdm 11 hpc, "Ndng luc Id mil
l i hpp phic tap nhing Biuic Bnh Idm II cia mil
nguii, phi hpp vii nhing yiu ciu cua mil hoat
ding nhit djnh, ddm bdo chp hppl ding d i diin
ra c i kit qui" (Pham Minh Hpc, 198g) Tuy nhiin,
Iheo John Erpenback, "Ndng Ive dupe xdy dung
IrSn cp s i t i ttiic, Biiit lip qua gid ttj, ciu ttie nhu
B cic khd ndng, hlnh ttidnh qua ttii nghlim/ cung
e i qua kinh nghlim, hiin ttive hia qua y chP (Jphn
Erpenback,1998) Hpdc De Keteie™ chp
ring-•Ndng ivc id lip hpp cie H ndng tdc ding lin cdc
nil dung ttong mil leal Bnh huing chp ttuie d i glil
quyit edc vin d i dp Bnh huing ndy ddt ra'
Nhu vjy ning luc Id mil khdi niim tich hpp
• Tiw*no 0 * hflc Hftnfl e t c
36>TiiaiiwliiLteUoDvc
n i bap gim ed nhing nil dung, nhing hoat d ^ cin thue Win vd cd nhl>ng tinh huing ttpng di cdc hoat ding dupe diin ra
Dva vdo chuin diu ra ttlnh d i dai hpc khil ngdnh Sv phpm dip tap gidp vlin Tmng hgc pii
phi thing vd edc nghiin c i u Hin quan Ching t£
d i xuit mil s i ning Igc die ttii cin phdi dat dupe' cOa sinh vlin dai hpp su pham ttidn nhu sau; Ndng ive vin dgng ttidn hpc cap cip d i giii ttidn pU ttiing; Ndng Igc tiin hinh qud ttlnh day hpc loin;
Ndng ivc thiit k i vd si> dgng phupng Bin ttong dsy
hpe Tpdn; Ndng Iue nghiin c i u vd thiit k i bdi iff, Ndng Iue t i chie heat ding ngppi khia Ipdn; Utn)
Ivc giii hjdn so cip; Ning ivc vjn dgng kiin ttlOe-kjdn hpe vie thgc tiin; Ning luc ddnh gid kit qui hpc tip eia hpe sinh Bieo djnh huing phit trSn' ndng Ive; Ndng Ivc nghiin c i u khpa hpc gidc due;
hia; Ning ivc phdt Iriin chupng trinh min luc Ndng Ivc 1dm viic Irin cic ciu tnic (khing glan) ttidn hpe tr£m lupng
3 Thdnh t i c i a ning Ivc vin dgng tpdn hpc cao
s v c i p
3.1 Thinh t6 cia ning Ige vin dgng toin hgc cao cip di glil loin phi thing Xic lip mil quan h i glia chupng trinh toUi
phi thing vil kiin ttiic ttidn dupe ttang bj ttoK
truing su pham
S i dgng mil s i kiin ttiic cia Tpdn phi ttiAig
d i minh hpa chp cde khii niim eia Tcdn hpc cao cip, Tein hpc hiin dpi
S i dgng cdc khdi nlim cia Tcdn cap cip li cing cg d i nhin nhin Tpdn phi ttiing ttieP quaiv
diim ttiing nhit, diy d i vd siu s i e
Su dgng kiin thic Tpin cao cip d i gidi ttiU
mil s i kiin thic khi ttpng chupng ttlnh Tpin Jii
Trang 2^ r
Bling ding ttioi chinh xdc hpa mit s i kiin Blue
ggi] TPdn phi Bling
« y * ' < ' C " 9 l < * " ' l i e T p d n cae cip dinh huing
ttm ttil i*i giai chp mit s i Hal Todn phi ttiing
Sv dgng kiin Blue Tpdn cap cip d i sdng lac
cdc bdi Tcdn phi flidng (ci Bii sdng tao cde bdi
-mu loan mil n h i su dgng t f ttrong dnh xa quan h i bit
biin cdc dnh xa, ciu ttie)
til,, •niiil Idp mil lien h i gil>a kiin Biic Hlnh hpc
USl ^ ' ' ' " * l"f nltiio Hlnh hpc phi ttiing
GinkitcdckiinBiVcTpdnhpccapcip TPin
hpe hiin dpi v i i cde kiin Blue tpdn phi Bling vd
chuyin lai dupe t i Blue khoa hpe sang t i Biic
^ phi ttiing,
r « Sv dgng kiin ttiic tjdn hpe ttong ttving su
Idm quan ttpng aia mil nil dung, chi d i tpna
TO chupng ttinh ttidn phi Bling
• I * ! ^ dgng kiin ttiic ttjdn hpc ttong ttuing su
0*1 p h ^ m n g viic ttm ra bii ttiin gie (ting qudt) eia
W m i f l bii to&icg Bii T i d i sdng lap ra mil k>p
»liil cdcMllPdnnil
• t l S i dgng kiin Blie hjdn hpc ttpng ttuing su
j,^^ chuyin min mii vd khi
] i , 3.2 Thinh li eia ning Ifrc glil toin aireip
g^j Gidi Bldnh thao edc bdi tdp trpng Sdch gldp
Bling trin CP s i nim vlhig kiin ttiic t j i n cp bin,
•1 vin kiin Biic ttong ttuing su phpm, mii liin h i
• ' glia cic min hpc, khd ndng vin dgng hidn hpc vdp
*!' ttivc tiin
iW Nim dupe dgng y ciJa mil bdi tdp, nhim cdc
:?i bdi lip iage tlnh biy tpng Sdch gldp khoa, sdch
it* Idmndp ^
Khai Oidc vd phdt ttiin nhing bdi tpin cp bin
^ Bldnh nhing bii h}dn m i l dii hii lii gidi phdi c6 su
oj khdi qudt hia, ting hpp nhing kiin Biic md hpc
" sinh dd hpc
S i dgng vin kiin ttiie dvpc ttang bjp ttving
" su pham ttpng viic ttm ra bdi ttjdn gie vd dua m
dinh huing ttpng viic sdng tap mil k>p edc bdi ttidn
!» mii; c i kiin ttiic chuyin sdu d i bii duing hpc
i^i sinh glil
H i Bling hia cdc dang vd cdc cdch gidl chp
if Ong dang bii ttidn, due kit vd blil cich ttang bi
I I nhing tti ttiic phuong phdp ttfpng ing v i i mil nil
dung day hpc
»! Ndng iue luing ttuie nhing khi khin, sai am
K cia hpc sinh ttong qui ttlnh linh hii nhing kiin
Biic, ttpng qud ttlnh gidl lodn;
,- Vin dgng cdc quy ludt ttlit hpc vdp vide sdng
if tao cdc bdi todn chp hpe sinh
4 H i t s i l > i i n p l i d p d l b i l dlring ndng Ivc ndng
cap: ning Ivc gidi todn scr dp chp sinh vlin
ngdnh Su pham tpin
4.1 Rin luyin Id ning giii toin phi thing,
hi thong hda de dfmg loin vi cic phvong phip ^Umg dgng loin ti, tip dui/l sing tao
do bM toin phi thing cho sinh vlin
D i tti ttidnh mit gidp viin day Tpdn truic hit phii Id mil nguii c i khi ning giai todn phi ttiing
t i t T i d i Chung til xdc djnh phucmg ttiie quan ttpng d i phdt ttiin ning Ige day hpc Tcdn chp SV
Su pham l i phdt ttiin ndng lpc giai Todn cho hp
Ching hpn, tteng qud ttlnh day hpe phin kiin ttiic Phuomg phdp day hpe Hlnh hpc khing gian giing viin yiu ciu sinh viin chi trpng liii luyin cdc ki ndng nhu; W ndng v i xdc dinh hlnh, kr ndng
kl ndng ching minh ttpng quan h i song song, kl ning ching minh cie duing ttiing, mdt phing wiing gie, Onh Wiping cdch vd gie glia cde yiu
» : duing Bling, mil phing, gie nhj diin, ttnh diin Bch xung quaJB, tlnh Bii flch edc hlnh khing gian
Chi ttpng chp sinh viin khai ttiip cdc phtrpng phdp khdc nhau giii cie dpng todn hlnh hpe khing gian bing con duing ting hpp Sinh vlin phii biit ttiiil lip mil quan h i glia cde kiin ttiie Hinh
» Tnrtri^ ttung hpe cu s i , eg ttii Id; tdeh cic b i phin phing cin nghiin c i u khil hlnh khing gian bii h>dn khing gian v i bdi ttidn phing nhi cdc hepl ding ttrong Iv hia, n h i s i dgng cdc ttnh chit bit biin qua phip chiiu seng spng, die blil id phip chiiu vuing g i a
Sinh vlin phii ttiinh ttipp M ning chuyin cdc Bnh chit hlnh hpc tt> khing glan ndy sang khing cde hlnh hlnh hpe " Trong qud ttinh day hpe cde hpc phin Dpi s i
So cdp; Hlnh hpc su cip rin luyin chp sinh vlin glil bdi Ipin bing nhiiu cdch, d i xuit edc bdi tpdn ttidn mii
C i ttii k i ra m i l s i cdch ttiic, con duing sing tap nhing bil ttidn mil nhu sau; Vin dgng hai
W i n ly ccr ban cua Triit hpc duy vdt biin ching
id nguyin ly v i mii Gin h i vd nguyin ly v i sv phdt ttiin; Vdn dgng suy ludn c i ly v i suy ludn kigle- Vin dgng cic cip pham tti v i cil chung vd cdi riing bdn chdt vd hiin trpng, nil dung vd hlnh ttiie -Vin dgng tdm ly hpc liin ttring, phuung phdp giai ttidn cua tdc gid G Pplya; Thing qua day hpc
tf"-ratal tstii 37
Trang 3t>di tdp todn luydn tdp cho sinh iridn cdch t»ln dii chung Gido vidn cd thi t l chi>c cho hgc sinh Ham hrcmg doong nhin nh$n ^nh 11 b^ todn theo nhiiu cdc bdi todn mfli thflng qua cdc hoat dflng sau: cdch khdc nhau din din cdc cdch chi>ng minh, gidi - Xdt ttuflng hyp tam gidc SAB diu canh a Ta
todn khdc nhau Tir dfl luy$n @p cdc cdch huy dflng doyc t^i todn sau:
Idin ttiirc khdc nhau cho sinh vidn Khi ttiyc hi$n Bdi todn: Cho A SAB diu canh a M Id ttun bi$n phdp ndy d n quan tdm cdc dfli toyng quan h$ dilm cua AB, mflt dofl^g thing d bit kl cIt cfc
fating bdi todn doyc xem xdt cdi d$t ttang cdc mfl canh SA, SM, SB lln loyt tai A', M', B' Cht>ng mnli
hinh khdc nhau; Ching han xem h> di^n Id bfl phdn ^ 1 1 - ^
cua hinh hflp, h;j' theo cdc kiai h> di#n d l cfl cdc '^"S '^'*"SB'-"'SM'''
teai hlnh h ^ toang i>ng ngoai tiip nfl 0#c bi|t chd Y A , , A, i j, ^ i ttyng diin dat cdc djnh II, cdc bdi todn ttieo cdc cdch 'JA \!^"^ '''^ "^ ^"^ d di qua di4m^ toong doang toong ttilch vfli cdch gidi khdc nhau ^ °' f f ? '^! *° „L
Ching han khai ttidc mil lidn hd gi[>a cdi lidng, , f *' *°^"= ^ho A SAB Gpi M Id ttung dilm
cdi Chung dirge nhllu tdc gia nghidn ci>u vdn dyng ^\^°; ""^^ T * " ^ *^^"9 *^ ™* '^' ^^^ A d t cdc vdo day hyc khdm phd 'Khdm phd phdt ttiln tCr "^"^ ^l, *^' '^"' °"" ^^^'^^ """^ ^"^ mflt t)di toin ttidnh nhiiu bdi h>dn mfli ttieo quan ^^^
- Xdt tnj^ng hyp dotmg ttiing d dl qua ttpng tdm tam gidc ta cfl ttil ddt bdi ttidn:
Bdi todn Cho tam gidc ABC Mflt dodng ttili^
d bit kl d t cdc c^nh SA, SB lln li>yt tai A' B' SM
Co ^^^,3 SA' SB'
a, Ching minh ring duing ttiing d luin di qua mil diim c i djnh
diim mil cdi riing nim ttpng nhiiu cdi chung khdc
nhau* vd Tim til cic kiin ttiic mil, bdi ttidn mii
t i nhiiu ttving hpp riing Biep hr Bring nhiiu cil
qudr" "Mil cdi riing e i ttii Id ttuing hpp die biil
cia nhiiu cdi chung khdc nhau" vd "Mil cdi chung,
dem ddc biil had ling b i phin khdc nhau, bing
nhing cdch khdc nhau s i chp nhiiu cdi riing khic
nhaui*i
Qua vide Bip cin phupng phdp day hpc khdm ^ u , ^ ,
phd, mii liin h i biin ching cua cip pham tti "Cil "• ™ ' ' ™ ^ ''' "" ' ^ " S '™"9 " sao ctio riing vd cil chung" vd ling hpp y kiin cia cdo tie ' " , ' " ^ ^'^^ ^*'^' "''* " • ' = ' " " -gid ching lii xin niu ra mil s i djnh huing nhim T" " '^'^ ''*' ' " * " * * " '* '^' '""S- " ' * *
khdm phd phdt hiin cde kiin ttiie ttiing qua day hpe " ' " l ' * " ' * " '''*"9 trung diim cua duing ttiing AB
chii d i hinh hpc; Dv dpin phdt hiin djnh huing '* " " ' 9 '*"' '^ ''* ^ * * " ' 'eng ttpng Idm lam iii giii cdc bdi tcdn hlnh hpc ttiep ttr ttring di t i 9 * ° ' '^'\* "*" " ' * " 9 ' < " " "^"S' '="' 9lic, t i *
ttuing hpp riing din ttuing hpp Chung liyttuing "*'>''9<Jiul4ededonhlnhddcbiilttpngkhinjgl«n hpp ridng sol sdng chp ttuing hpp chung vd vin " " ' = ' ' * " hai chiiu, ba chiiu Ta dl din bdi ttidn: dgng ttuing hpp riing gpi y phuOTig phdp d i giii ' BdllpdniChphinhchipSABC.GplGldttpns quyil ttuing hpp chung; T i c Id ta di tt> sv khdp sdt ? ! " ' ' " ' 9'*° ABC, mit mil phing (o) cil cdc wnh mil lip hpp dii lupng sang mil Idp nhi han - hav =*• SB, SO, SG lin lupt tai A', B', C, G' Ching
,.r-minh ring; £±+.SS.^.^,,^
chl mil dii ttrpng - chia ttpng mit tdp diu; Khdm
mil theo quan diim mit cdi Hing nim ttong nhiiu Bdi todn niy e i nhiiu huing giii; s i dgng Bdi
™ ? ^ " S ^ ^ 1 i r t i * •=*' * " " 9 * " ^ "*= "^ P * "^^"S ra khil hinh hpc khing gian di gUt
blil hp4thoptt>ngbi phin khdc nhau ta ttiu dupe cing cg vie to; s i dgng Bii Bch vv
r S ^.^ i ^ l r * ' "^ " ' * ' "^"5 "^ ""• "'^ " " ' Ta tiip tgc xem bdi todn ndy id cil chung, gHo
chua cdc bdi loan Viin t i chie cho hpc sinh phdt hiin bdi ttidn m«
VI dg 1 Cho ASAB Gpi M id ttung diim cua Bling qua edc heal ding:
S ' "sJf'^JS ' ^ J ' h " ''^' " ^ •*"= '=""' • ^ * ' » " » " SABC diu ta dupe bdi ttidn;
5 ^ !.M, SB ldn lupt tpi A, M', B' Ching minh ring Bil todn Cho t i diin SABC diu cpnh a Gel Q
^ * ~ 2 ~ l i ^"9 Iim lam gidc ABC, mil mil phing (a) t *
"1 SB' SM' "'' • - * » - - — — _ _ _
Bdi ttidn ndy c i cdch gidl; k i ttiim cde duing
M n g phg qua A vd B spng spng v i i duing Uiing d
rii su dgng dinh 11 Taiet; s i dgng cing cg diin tich
oe chimg minh; su dgng kiin ttiie vecttr
Niu ta xem kit qui bdi todn ttin i i mil cdi
U-TuciigoliiittUoiigc
cde canh SA, SB, SC, SG lin lupt tai A', B', C, S
1 1 _ S
•SSG'
• Xit mit phing (a) di qua dinh A cua t i difs
ta e i bdi tcdn;
Bil tPin Cho hinh chip SABC Gpl Q Id ttgo)
' Ching minh ling — + — +
-SA' SB' s
i-i
Trang 4^'!^iI^«°L^ ABC m i l m i l phing (a) qua A d t edc D i ttivc hiin dupe cdc hoat ding t i n ttpng cann SB, SC, SG ldn lupt tai B', C, G' Chung minh qud tlnh day hpe giang viin cin luu y nhung vin
•^"'^ "§-§'-§• °> 8i4 tri khang dii v.v • * - ^ ^ dvng mit s i Bnh huing che sinh viin lip Tip duyit cho sinh vlin khai Bide ttim ndng * ^ "*= 1 * ^ ' ^ **'' H ^ ">*' lien h i glia kiin
Sdch gjde khoa todn phi ttiing bing cdch ting qudt 1^*^ * ° ^ hpc cao c ^ vd todn hpc phi Bling trong hpd m i ring tt> m i l bii ttidn Bidnh chuii cdc bdi tiin ttinh hlnh Bldnh vd vin dgng kiin Blue todn hpc
ttidn cao cip
VI dg 2: Tu bai toin, Ching minh ling ^ ^ u '^'* » i tii sung h i ttiing bdi tip trong
niu 1 Id Idm ving ttin nil Bip tam gide ABC ttil; oic bii giang ttidn hpc cao dip nhim tdng cuing
i,M*blB+cJc.O- n C i ttii biin dii (1) ttrpng ? P ' ^ ' * " 8 "^ l " " * ^ ^ ^" "«' ''""^ k'^"
J _ _ _ ^ Blue loin hpc phi Bling
dupng v i l -r^JA*-rJ>jB+^rtJC=H2l, (Trong d i B i sung cie ehu d i ttong tdi liiu hving din
r Id bdn kinh ving ttin nil t i p lam gidc ABC) Khi cde hopt ding khai ttido mil liin h i gilTa kiin ttiie
d i (2) lupng dupng v i i S|i4+S,ffl+s,/C-6 (3), loin hpe cap cip v i Win ttiic ttidn hpc phi Bling
vii S,; S,; S, id diin tieh cde tam gidc IBC- ICA lAB - ^ " ' f ° * ^ ™ ° ' "b^a I w t* * » o obo
• f i d i i n l i i e i c b i l t o d n l S n ^ m d l p h i n p ^ ^h^l^in twin ^ edc h o l d i n g gin kit glia glia ttpng khing gian Ching hpn: "Niu 0 id d i i S S ' " * " * " t i i n hpe cao cip vd kiin ttiie todn hpe
t<l|g|rn2Bi4ng chia tam gidc ABC khing ttiuflc "^ ^ \ ^ „ u ^
- - a "iiivi Binh huing day hpc Tpdn cap cip ttiep
huing spl sdng vd gin v i i chupng tlnh Tedn phi sinh viin Todn
Ching han, khai Bide mii liin h i glia hlnh hpe
|ip chia canh cia tam gidc ttil c i ttii
» (-) Uiich hpp sap chp ding ttiic
sau diy dung; ± S | 5 3 ± s , O f l ± i , 5 c 5 ( 4 ) , V i i S ;
S,; S, id diin Bch cdc tam gide OBC; OCA; OAB",
O i Idm dupe diiu ndy gidp viin phii lap ra cap cip vd hlnh hpc phi ttiing; C i ttii ttiep cdc dupe oil mil tt> nhing cil dd c i bing viic die buing nhu phdt hiin co s i hlnh hpc cae cip cua sdu m i ring khai ttidc m i l cdch ttiil d i tt> nhing binh hpc phi ttiing giip hiiu sdu sic hlnh hpc phi cdi ban diu, c i ttii khi ttil la 1dm d i di d i don giin Ibino vd nhin nhin hlnh hpc phi Biing ttiep quan ting dii lupng hpic tpp ra nhing bdi todn c i nhiiu l?o bii hidn phi ttiing, djnh huing cae cip glil ttnh huing gin dupe v i i ttive t i , ttiin hinh hpc phi Bling Mii liin h i ndy Id nil dung
3.1 Tip dugtt cho sinh vlin khal thic mil seminar hip din vl n i v i a e i ttnh cO (Win thic phi
Hin hi glia Uin Ihic toin hgc cao cip vH Min Ibing dd dup>c hpe i t u i n g phi Biing), v i a c i
Theo tdc gid Ode Tam d i Bivc hiin biin phip bpe), v i a bie ciu nil glia ttidn hpc cap cip, todn trin cin ttiuc hiin edc hoat ding sau ttpng qud ttlnh bpe hiin dpi vd Tnmg hpe phi ttiing nhim giip sinh
"'W boc: viin ttiiy dupe y nghTa cua viic hpc cde min Todn Giing viin glip sinh viin su pham todn phdn cao cip i ttuing dpi hpc, hlnh ttidnh nhu ciu cin Bch nhin nhdn cde tu Bring ning cit cua todn hpe din su hpp tdc v i i nhau rit Km, cin ttanh luin vii
phi thing ttin mil quan diim cao, xem xit nhiiu nhau di hdn ttiinh nhiim vg ddt ra
BV Win riing l i cua ttidn hpc ttidnh h i ttiing ling W dg 3: Sir dgng Win Biic hinh hpc Afln v i
Ihinhitqudn hlnh hpe EuclkJedi sdng lao ra edc bdi tedn hlnh
Khi sinh Vlin dugc xem xit mii quan h i glia hpc ap cip
lodn hpc ln>u ttupng i ttuing dpi hpe v i edc Bii Nhing bdi ttidn, djnh II cua hlnh hpc cae cio diim biin ching s i gip phin giip hp y ttiic dinh ting qudt Dp d i Mil la xit n = 2 n = 3 ttil nhino buing gidi tpdn phi Biing bing ttr ttring tpdn hpc bdi todn, djnh U d i tti Bldnh bii todn dinh 11 pi1= cao cip, todn hpc hiin dpi vd sau d i chuyin tdi hlnh hpc sp eip
sang cdch giii phi ttiing Trin cp s i 11 luin d i , niu HS dd biit mit dinh
HI L ' ^ t M " * ° "H * ' ' / ' « " 3 ] « * b huing 11, mil bil todn tteng mil phing (ttte Id ing v i l n =
glil c*: bdi l<^" SP d p , Ipdn phi Biing t i Win 2) chia dung hodn todn 4 bi? i i i n cia X h i m
taZdC^^-^^'^" *' "" « =^">'*" £^t"S'i;r'titnp"kS^"''*'?.'^*^«'^'*" " " " Ket qud ttrpng t r teng khing gian (ing vil n = 3)
sia-nuiniaiii.jii
Trang 5CQng chua dung hodn hidn cic bit biin cua nhim
biin dii trpng i>ng
Nhlhig ktldi niim cua hlnh hpc cap cip c i Bii
ting quit ttr khdng gian 2 - chiiu lin khing glan
3-chiiu Id:
• Bpn hlnh; Tam gide »• T i diin
• Hip; Hlnh binh hdnh » Hlnh hip
Hinh vuing >• Hlnh lip phupng
Hlnh c h i nhdt > Hinh hip chi nhit
• SJiu ciu; Duing t i n »- Mit c^u
• Phuong Bch cua mit dilm dii vii mil siiu ciu:
Phvong ttch cua »-Phuong Bch ciia
mil diim dii vii mil diim dii vii
mil duing ttin mil mil ciu
& mic d i cao hon, t i djnh 11, bdi hidn eua hlnh
hpc so cip, c i ttii ting qudt ttidnh dinh II, bdi ttidn
chiiu tCr n =2 n = 3 lin Bldnh s i chiiu n ting qudt
vd ttiay cic khdi niim cua hlnh hpc so cip bil khdi
niim cia hlnh hpc cao cip;
• Tam gidc, h> diin ^ Don hlnh
• Hlnh binh hdnh, hlnh hip > Hip
• Duing ttin, mil ciu k- Siiu ciu
• Phuong Bch cua r Phuong Bch cia
mil diim dii vii mit mil ciu dii v i l
mil duing ttin diim mil siiu ciu,
Sau khi Ihu doge bdi todn trong khing glan n
-chiiu, su dgng cdc bit ding ttiic ling qudt vd edc
Win ttiic cia khing gian n - chiiu d i biin dii bdi
lodn v i cdc bdi ttidn ting qudt mii, V i i cie bil todn
mil niy, cho n = 2 vd n = 3 ta s i duoc cie bii todn
hlnh hpc so cip mii ttrpng Ong [6],
Vldg4: Xit bdi Ipdn "Chp tam gide ABC nil
tiip duing ttin Idm 0 Duing tung ttiyin CC, pit
duing ttin tpl diim ttii hal D Ching minh ring
CA" t CB" = 2 CC, CD", ta c i bdi todn m i ring
cho tt> diin; "Cho t i diin ABCD nil ttip hlnh ciu
cua tam gIdc ABC) cit mit ciu tal diim ttii hai E
T i bdi ttidn phing ban diu vd kit quícia bdi
todn trong tu ttong khing gian ta c i gii ttiuyit
»ng quit sau; Trong khing glan Eucllde n-chiiu
e cho n-don hlnh vii cde dinh A , A A , Ạ
'SJt^ S ' i*"."^" ®<°''"- "^l G B^ng'tdm
cil siiu ciu lai diim ttii hai B Ching minh ỉng
t,'<Á='AjạẬ
• ^
h,n,.I: T''"' ""• "a**" 0^ thao
i i khoa hpc IM d,yhgc eic min Toin sa dp
i(ng cho sinh vlin Irong hgc lip
U-TiiBiigiaiiitaliiiigc
Seminar l i m i l hlnh ttiuc hpc lip, nghiin p), rit ttilch hpp v i i phuong phdp hpc lip, nghiin cOa
o bdc cao ding, dai hpc vi n i phdt huy dupcUi ttch cue heat ding cua sinh viin vd phupng g,]
đp tpp cua nhd hiring, c i tdc dgng phdt ttiin M
h i i vd hlnh Bldnh phuong phdp 1dm viic khoa In
cho sinh vlin
Hpc tip, nghiin eiru Bloc hlnh ttiic semia ttiec ding nghla s i tao ra sp hung ttii, say ni nghiin ciu Bm hiiu chdn ly vd c i tdc dgi^ lifa din sv sing tao nhl>ng phuong phdp, 1dm cho i M bil duing ning Iue tu duy phi phdn, y chl kitnti
Id phim chit trung ttiue wM kit qui vd mpi nguji Ching han, ehi d i sau đy cua min hlnli hot
so cip 4 bie dai hpe e i ttii tiin hdnh Olio iula
nhim vd seminar chp sinh viin; Vin di xiy dm
hinh hgc i tniing phi thing
Cdc chi d i c i thi t i chie Blip ludn nhim vl seminar eia nil dung niy Id;
- Ching minh m i l s i djnh 11 bing cdch suy bta Ipgie dva vdp h i tiin d i Hilbert;
- Tim vd phin ttch Bii hiin cia h i ttin di Img min Tein i ttuing phi Biing;
- LI Bluyil v i phip dp dopn thing vd II fliuyil vịdiin tieh trong Hlnh hpe Eudlde;
- Cie hlnh hpc phi Eudldẹ
Cdc ehi d i cia nil dung ndy s i giilp sinh vHn nim dupe co s i eua min Hlnh hpe day i tui»(
phi thing, rin luyin cic than tdc tu duy dinjIMt Iim quen v i l phuong phdp Bin d i , chlnh xdc H i dupe khdi niim hlnh hpc 4 tiring phi thing, Cdu lac b i khpa hpe Id m i l hinh Oiile hpc lip,
nghiin ciu c i tdc dgng m i ring vd di sdu Bm A
Hpat ding edu lpc b i khpa hpc tao cho sinh i«ii ndng ivc hpp tdc, tinh ttiin ning ding, tdc phonj Un viic khoa hpc N i glip sinh viin nam ving nr"~
nil dung cin Biiil thing qua nhing din ching hpa hip din, sinh ding Ding ttiii dam din '
viin nhing hiiu biit mii m i vd ttivc l i r
Nil dung hoat ding edu lac b i e i Ihi id: Tin hiiu siu v i lodn phi ttiing nhing vin d i chuyii sdu cia todn Win dai; ttii giii vd h i Uiing hia tt*
phi ttiing; hii thio, ttanh luin cic vin d i phgc w cho idm bdi tip lin, I
6 K i t l u | n _ Thvc Bin su pham chp ttiiy ring sinh vlfti ( i l
klii khdn khi gidi edc bdi ttidn so cip vd vdn dvni Win thic cap cip d i gidi cdc bdi todn phi Blinj.»
gip phin bii duing che sinh vlin ttpng qud Wnt)
day hpc, ching tii đ dua ra mil s i biin phdp i
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