Hng dn GeoGebra

Bn chnh thc 3.0

Markus Hohenwarter v Judith Preiner www.geogebra.org, 06/2007

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Tr gip GeoGebra Hiu chnh ln cui: Ngy 17/07/2007 Trang Web GeoGebra: www.geogebra.org Tc gi Markus Hohenwarter, mhohen@math.fau.edu Judith Preiner, jpreiner@math.fau.edu

Tm kim tr gip GeoGebra Online: Tm kim tr gip GeoGebra PDF: Nhn Ctrl + Shift + F trong Adobe Acrobat Reader

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Mc lc Tr gip GeoGebra .................................................................................................... 2 Tm kim tr gip GeoGebra...................................................................................... 2 Mc lc ....................................................................................................................... 3 1. GeoGebra l g? ..................................................................................................... 6 2. Cc v d ................................................................................................................ 7

2.1. Tam gic theo cc gc ..................................................................................... 7 2.2. Phng trnh tuyn tnh y = m x + b ................................................................ 7 2.3. Trng tm ca tam gic ABC ........................................................................... 8 2.4. Chia on thng AB theo t l 7:3 .................................................................... 8 2.5. H phng trnh tuyn tnh theo hai bin x, y.................................................. 9 2.6. Tip tuyn ca hm s f(x)............................................................................... 9 2.7. Tnh ton vi hm a thc............................................................................... 9 2.8. Tch phn ....................................................................................................... 10

3. Nhp i tng hnh hc...................................................................................... 11 3.1. Tng quan...................................................................................................... 11

3.1.1. Menu ng cnh ....................................................................................... 11 3.1.2. Hin v n............................................................................................... 11 3.1.3. Du vt .................................................................................................... 11 3.1.4. Phng to / Thu nh .................................................................................. 12 3.1.5. T l trc................................................................................................... 12 3.1.6. Cch dng hnh....................................................................................... 12 3.1.7. Thanh cng c dng hnh ....................................................................... 12 3.1.8. nh ngha li........................................................................................... 12 3.1.9. Hp thoi Thuc tnh ............................................................................... 13

3.2. Cng c.......................................................................................................... 13 3.2.1. Cc cng c c bn ................................................................................ 13 3.2.2. im ........................................................................................................ 15 3.2.3. Vec-t...................................................................................................... 15 3.2.4. on thng.............................................................................................. 16 3.2.5. Tia ........................................................................................................... 16 3.2.6. a gic .................................................................................................... 16 3.2.7. ng thng ........................................................................................... 16 3.2.8. ng Conic ........................................................................................... 17 3.2.9. Cung trn v hnh qut ............................................................................ 18 3.2.10. S v Gc.............................................................................................. 18 3.2.11. Boolean ................................................................................................. 19 3.2.12. Qu tch ................................................................................................. 20 3.2.13. Cc php bin i hnh hc................................................................... 21 3.2.14. Ch ....................................................................................................... 21 3.2.15. nh ........................................................................................................ 22 3.2.16. Cc thuc tnh ca nh.......................................................................... 22

4. Nhp i tng i s .......................................................................................... 24 4.1. Tng quan...................................................................................................... 24

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4.1.1. Thay i cc gi tr .................................................................................. 24 4.1.2. Minh ha.................................................................................................. 24

4.2. Nhp trc tip ................................................................................................ 25 4.2.1. S v Gc................................................................................................ 25 4.2.2. im v Vec-t........................................................................................ 25 4.2.3. ng thng ........................................................................................... 26 4.2.4. ng Conic ........................................................................................... 26 4.2.5. Hm s f(x) .............................................................................................. 26 4.2.6. Danh sch cc i tng ........................................................................ 27 4.2.7. Cc ton t s hc .................................................................................. 27 4.2.8. Bin s Bool ............................................................................................ 28 4.2.9. Ton t Bool............................................................................................ 29

4.3. Cc lnh......................................................................................................... 29 4.3.1. Cc lnh c bn ...................................................................................... 29 4.3.2. Cc lnh logic (Boolean) ......................................................................... 30 4.3.3. Gi tr ....................................................................................................... 30 4.3.4. Gc.......................................................................................................... 32 4.3.5. im ........................................................................................................ 32 4.3.6. Vec-t...................................................................................................... 34 4.3.7. on thng.............................................................................................. 34 4.3.8. Tia ........................................................................................................... 34 4.3.9. a gic .................................................................................................... 35 4.3.10. ng thng ......................................................................................... 35 4.3.11. ng Conic ......................................................................................... 36 4.3.12. Hm s .................................................................................................. 37 4.3.13. ng cong tham s............................................................................. 38 4.3.14. Cung v Hnh qut................................................................................. 38 4.3.15. nh ........................................................................................................ 39 4.3.16. Qu tch ................................................................................................. 39 4.3.17. Dy s ................................................................................................... 39 4.3.18. Cc php bin i hnh hc................................................................... 40

5. In n v xut thnh tp tin .................................................................................... 42 5.1. In n............................................................................................................... 42

5.1.1. Vng Lm Vic ........................................................................................ 42 5.1.2. Cch dng hnh....................................................................................... 42

5.2. Vng Lm Vic thnh dng nh .................................................................... 42 5.3. Sao chp Vng Lm Vic vo B nh ........................................................... 43 5.4. Cch dng hnh thnh dng trang web.......................................................... 43 5.5. Vng Lm Vic thnh dng Trang Web ......................................................... 44

6. Cc ty chn......................................................................................................... 45 6.1. Bt im......................................................................................................... 45 6.2. n v ca gc............................................................................................... 45 6.3. Hin th s thp phn ..................................................................................... 45 6.4. Lin tc .......................................................................................................... 45 6.5. Kiu im ....................................................................................................... 45 6.6. Kiu gc vung .............................................................................................. 45 6.7. Ta ............................................................................................................ 45 6.8. Tn................................................................................................................. 46 6.9. C ch ........................................................................................................... 46 6.10. Ngn ng ..................................................................................................... 46

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6.11. Vng lm vic .............................................................................................. 46 6.12. Lu cc thit lp........................................................................................... 46

7. Cng c v thanh cng c .................................................................................... 47 7.1. Cng c do ngi s dng nh ngha .......................................................... 47 7.2. Ty chnh thanh cng c ................................................................................ 47

8. Giao din JavaScript ............................................................................................ 48 Danh mc ................................................................................................................. 49

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1. GeoGebra l g? GeoGebra l mt phn mm ton hc kt hp hnh hc, i s v vi tch phn. Chong trnh c pht trin cho vic dy ton trong cc trng hc bi Markus Hohenwarter ti i hc Florida Atlantic. Mt mt, GeoGebra l mt h thng hnh hc ng. Bn c th dng hnh theo im, vec-t, on thng, ng thng, ng conic, cng nh th hm s, v c th thay i chng v sau. Mt khc, phong trnh v ta c th c nhp vo trc tip. Do , GeoGebra c th lm vic vi nhiu loi bin s nh s, vec-t, v im, tm o hm, tch phn ca hm s, v cung cp cc lnh nh Nghim or Cc tr. C 2 ch hin th c trng trong GeoGebra: mt biu thc trong ca s i s tng dng vi mt i tng trong trong ca s hnh hc v ngc li.

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2. Cc v d Chng ta s xem mt vi v d c th thy c cc kh nng ca GeoGebra.

2.1. Tam gic theo cc gc Chn nt im mi trn thanh cng c. Nhn tri chut 3 ln trn vng lm vic to 3 gc A, B, C ca tam gic. Sau , chn nt a gic v nhn ln lt ln 3 im A, B, C. ng tam gic poly1, nhn li ln im A ln na. Trong ca s i s, ta thy hin ln din tch ca tam gic poly1. bit c cc gc ca tam gic, chn nt Gc trn thanh cng c v nhp ln tam gic. By gi, chn nt Di chuyn v ko cc nh ca tam gic thay i tam gic. Nu bn khng cn s dng ca s i s v h trc ta , bn c th n i bng cch s dng menu View.

2.2. Phng trnh tuyn tnh y = m x + b By gi chng ta s tm hiu ngha ca m v b trong phong trnh tuyn tnh y = mx + b bng cch th cc gi tr khc nhau cho m v b. lm nh vy, chng ta c th nhp cc dng di y vo Nhp pha di ca s v bm phm Enter sau mi dng. m = 1 b = 2 y = m x + b By gi chng ta thay i m v b bng cch s dng Nhp hoc nhp trc tip vo ca s i s bng cch nhp phi chut ti mi gi tr v chn nh ngha li. Th cc gi tr m v b sau: m = 2 m = -3 b = 0 b = -1 Ngoi ra, bn c th thay i m v b mt cch d dng bng cch s dng

Cc phm mi (xem Minh ha) Con trt: nhp phi chut ti m hoc b v chn Hin / n i tng

(xem Con trt)

Bng cch lm tng t, chng ta c th kim tra phong trnh cc ng conic:

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E-lip: x^2/a^2 + y^2/b^2 = 1 Hyperbol: b^2 x^2 a^2 y^2 = a^2 b^2 ng trn: (x - m)^2 + (y - n)^2 = r^2

2.3. Trng tm ca tam gic ABC By gi chng ta s bt u dng im trung tm ca 3 im bng cch nhp cc dng sau vo khung nhp lnh v bm phm Enter sau mi dng. Bn cng c th s dng cc nt trn thanh cng c dng hnh. A = (-2, 1) B = (5, 0) C = (0, 5) M_a = TrungDiem[B, C] M_b = TrungDiem[A, C] s_a = DuongThang[A, M_a] s_b = DuongThang[B, M_b] S = GiaoDiem[s_a, s_b] Mt cch khc, bn c th tnh ton trng tm trc tip theo cng thc S1 = (A + B + C) / 3 v dng lnh QuanHe[S, S1] so snh kt qu. Sau , chng ta c th th xem liu S = S1 c cn ng vi cc v tr A, B, C khc. S dng nt Di chuyn v dng chut ko cc im.

2.4. Chia on thng AB theo t l 7:3 V GeoGebra cho php chng ta tnh ton vi vec-t, cho nn y l mt vic d dng. Nhp cc dng sau vo khung nhp lnh v bm phm Enter sau mi dng A = (-2, 1) B = (3, 3) s = DoanThang[A, B] T = A + 7/10 (B - A) Cch khc: A = (-2, 1) B = (3, 3) s = DoanThang[A, B] v = Vecto[A, B] T = A + 7/10 v Trong bc k tip, chng ta s tm hiu v s t, vd: bng cch s dng Con trt v nh ngha li im T l T = A + t v (xem nh ngha li). Vi vic thay i t, bn c th thy im T di chuyn dc theo mt ng thng, ng thng ny c biu din bng phng trnh tham s (xem ng thng): g: X = T + s v Trong bc k tip, chng ta s tm hiu v s t, v d, nh ngha im T l T = A + t v (xem nh ngha li) v s dng mt Con trt. Vi vic thay i gi tr t

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bn s thy im T di chuyn dc theo mt ng thng (ng thng ny c phng trnh tham s (xem ng thng):: X = T + s v)

2.5. H phng trnh tuyn tnh theo hai bin x, y Hai phng trnh tuyn tnh theo x v y c xem nh l hai ng thng. Nghim ca h l giao im ca hai ng thng. Nhp cc dng sau vo khung nhp v n Enter sau mi dng. g: 3x + 4y = 12 h: y = 2x - 8 S = GiaoDiem[g, h] thay i h phng trnh, nhp phi chut vo phng trnh v chn nh ngha li, Bn c th dng chut ko ng thng bng cng Di chuyn hoc xoay chng quanh mt im bng Xoay i tng quanh 1 im.

2.6. Tip tuyn ca hm s f(x) GeoGebra cung cp mt lnh tm tip tuyn ca hm f(x) ti x = a. Nhp cc dng sau vo khung nhp lnh v bm Enter sau mi. a = 3 f(x) = 2 sin(x) t = TiepTuyen[a, f] Khi ta cho s a thay i lin tc (xem Minh ha), ng tip tuyn s trt dc theo th ca hm s f. Mt cch khc tm tip tuyn ca hm f ti im T thuc hm f. a = 3 f(x) = 2 sin(x) T = (a, f(a)) t: X = T + s (1, f'(a)) Bn cnh , bn cng c th v tip tuyn ca hm s bng phng php hnh hc:

Chn nt im mi v nhp chut ln th ca hm s f v im A thuc hm f.

Chn nt Tip tuyn v nhp chut ln lt ln hm f v im A. By gi, chn Di chuyn v dng chut ko im A dc theo hm s. Theo cch ny, bn c th quan st thy c tip tuyn cng chuyn ng theo.

2.7. Tnh ton vi hm a thc Vi GeoGebra, bn c th tm nghim, cc tr, im un ca hm a thc. Nhp cc dng sau vo khung nhp lnh v bm Enter sau mi dng. f(x) = x^3 - 3 x^2 + 1

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R = Nghiem[f] E = CucTri[f] I = DiemUon[f] Chn nt Di chuyn v dng chut ko hm s f. By gi, bn c th di chuyn th hm s f vi chut. Trong phn ny, c th tnh o hm cp 1 v o hm cp 2. Nhp cc dng sau vo khung nhp v n Enter sau mi dng. DaoHam[f] DaoHam[f, 2]

2.8. Tch phn tnh tch phn, GeoGebra dng chc nng phn hoch hm s. Nhp cc dng sau vo khung nhp v n Enter sau mi dng. f(x) = x^2/4 + 2 a = 0 b = 2 n = 5 L = PhanHoachDuoi[f, a, b, n] U = PhanHoachTren[f, a, b, n] Thay i cc gi tr a, b, v n (xem Minh ha; xem Con trt) bn c th thy c nh hng ca cc tham s ny trong vic phn hoch. thay i n, bn c th nhp phi chut vo s n v chn Thuc tnh. C th tnh tch phn xc nh bng lnh TichPhan[f, a, b], v tm nguyn hm F bng lnh F = TichPhan[f].

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3. Nhp i tng hnh hc Trong chng ny chng ta s tm hiu cch s dng chut to v sa i cc i tng trong GeoGebra.

3.1. Tng quan Ca s hnh hc ( bn phi) hin th dng hnh hc ca cc im, vec-t, on thng, a gic, hm s, ng thng, ng conic. Mi khi ta tr chut ln cc i tng ny, i tng s c t sng v xut hin mt ch thch k bn i tng. Ghi ch: i khi, ca s hnh hc c gi l vng lm vic. Ta c th dng chut v nhiu loi i tng trong vng lm vic (xem Cng c). V d: nhp chut ln vng lm vic v im mi (xem im mi), tm giao im (xem Giao im ca 2 i tng), hoc v hnh trn (xem Hnh trn). Ghi ch: Nhp p chut ln mt i tng trong ca s i s c th chnh sa i tng .

3.1.1. Menu ng cnh Khi nhp phi chut ln mt i tng s hin ra mt menu ng cnh bn c th: chn cc thuc tnh i s (ta cc hoc ta -cc, n hoc hin cc phng trnh), i tn, nh ngha li, Xa. Chn Thuc tnh trong menu ng cnh s hin ra mt ca s bn c th thay i my sc, knh thc, dy ng thng, kiu ng thng, mu nn ca i tng.

3.1.2. Hin v n

Cc i tng hnh hc c th c hin th (hin) hoc n i (n). S dng nt Hin / n i tng hoc Menu ng cnh. Biu tng bn tri i tng trong ca s i s cho chng ta bit c tnh trng ca i tng ( hin hoc n). Ghi ch: Bn cng c th s dng Chn hin hoc n i tng hin / n mt hoc nhiu i tng.

3.1.3. Du vt Cc i tng hnh hc c th li vt ca chng trn mn hnh khi di chuyn. S dng Menu ng cnh m hoc tt du vt. Ghi ch: Chc nng Lm ti ch hin th trong menu Hin th s xa sch ht cc du vt.

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3.1.4. Phng to / Thu nh Khi nhp chut phi ln vng lm vic, mt menu ng cnh s xut hin cho php bn phng to (xem thm Phng to) hoc thu nh (xem thm Thu nh) vng lm vic. Ghi ch: phng to mt vng xc nh no , nhp phi chut ln vng lm vic v ko chn vng .

3.1.5. T l trc Nhp phi chut ln vng lm vic v chn Thuc tnh hin ra menu ng cnh v bn c th:

Thay i t l gia truc x v trc y n / hin tng h trc ring l Thay i kiu hin th trc (kiu nh du khong chia, mu sc, kiu ng

thng)

3.1.6. Cch dng hnh Cch dng hnh tng tc (Hin th, Cch dng hnh) l bng hin th cc bc dng hnh. Bn c th s dng thanh cng c dng hnh nm pha di ca s thc hin li tng bc dng hnh cng nh thm v thay i trnh t cc bc dng hnh. Vui lng tm hiu chi tit trong phn tr gip ca Cch dng hnh. Ghi ch: S dng im dng trong menu Hin th bn c th nh ngha chnh xc cc bc dng hnh nh l im dng. Bn c th to im dng trong qu trnh dng hnh qui nhm cc i tng. Khi xem qua qu trnh dng hnh bng thanh cng c dng hnh, cc nhm hnh (i tng) cng c th hin cng lc.

3.1.7. Thanh cng c dng hnh GeoGebra cung cp thanh cng c dng hnh bn c th xem qua cc bc dng hnh. Chn Thanh cng c dng hnh trong Hin th hin th thanh cng c dng hnh pha di vng lm vic.

3.1.8. nh ngha li S dng menu ng cnh ca i tng nh ngha li i tng . y l mt cch hu ch thay i hnh sau khi v. Bn c th chn nt Di chuyn v nhp p chut ln i tng ph thuc trong ca s i s m hp thoi nh ngha li.

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V d: chuyn mt im A bt k vo ng thng h, chn nh ngha li cho im A v nhp vo hp thoi Diem[h]. g b im A ra khi ng thng, nh ngha li im A v nhp vo mt ta bt k. Mt v d khc: Bin i ng thng h qua 2 im A, B thnh on thng AB. Chn nh ngha li v nhp vo hp thoi DoanThang[A, B]. nh ngha li l mt cng c linh hot thay i hnh v. Nn nh rng n cng ln thay i th t cc bc dng hnh trong Cch dng hnh.

3.1.9. Hp thoi Thuc tnh Hp thoi thuc tnh cho php bn thay i thuc tnh ca i tng (mu sc, kiu ng thng). Bn c th m hp thoi bng chc nhp phi chut ln i tng v chn Thuc tnh, hoc chn Thuc tnh trong menu Chnh sa. Trong hp thoi, cc i tng c xp theo loi (im, ng thng, ng trn) bn c th thao tc d dng vi nhiu i tng. Bn c th thay i cc thuc tnh ca i tng c chn trong cc th khung bn phi.

3.2. Cng c Cc cng c di y nm trn thanh cng c. Nhn vo mi tn nh gc di bn phi ca mt biu tng trn thanh cng c hin ra cc cng c khc. Ghi ch: Vi tt c cc cng c dng hnh, bn u c th d dng to im mi bng cch nhp chut ln vng lm vic.

Chn mt i tng chn mt i tng,nhp chut ln i tng .

i tn i tng i tn mt i tng, ch cn nhp tn mi vo hp thoi i tn ca i tng .

3.2.1. Cc cng c c bn

Di chuyn Bn c th s dng chut ko v th cc i tng t do. Khi bn nhp chn mt i tng trong cng c Di chuyn, bn c th:

Xa i tng bng nt Del Di chuyn i tng bng cc phm mi tn (xem Minh ha)

Ghi ch: n phm Esc cng c th chuyn sang cng c Di chuyn. n gi phm Ctrl chn nhiu i tng cng lc. hoc

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n gi nt tri chut v ko chn mt vng hnh ch nht i qua cc i tng cn chn. Sau bn c th di chuuyn cc i tng ny bng cch dng chut ko mt trong s . Vng chn ny cng c dng ch nh mt phn ca hnh in, xut hnh (xem In v Xut ra thnh tp tin khc).

Xoay i tng quanh 1 im Chn tm xoay trc. Sau , dng chut chn i tng v xoay.

Quan h gia 2 i tng Chn 2 i tng bit quan h ca 2 i tng (c th xem thm cu lnh Quan h).

Di chuyn vng lm vic Nhn gi nt tri chut v ko vng lm vic di chuyn h trc ta . Ghi ch: Bn c th n gi phm Ctrl v ko chut di chuyn vng lm vic. Vi cng c ny, bn c th dng chut ko gin tng trc ta . Ghi ch: Khi ang s dng cc cng c khc, bn c th ko gin trc ta bng cch n gi phm Shift (hoc Ctrl) v dng chut ko trc ta .

Phng to Nhp chut ln vng lm vic phng to (xem thm Phng to / Thu nh)

Thu nh Nhp chut ln vng lm vic thu nh (xem thm Phng to / Thu nh)

Hin / n i tng Nhp chn i tng hin th hay n i tng . Ghi ch: Cc i tng khi bn n s c t sng. Cc thay i s c p dng ngay khi bn chuyn qua cng c khc.

Hin / n tn Nhp chn i tng hin th hay n tn ca i tng .

Sao chp kiu hin th Cng c ny cho php bn sao chp cc thuc tnh bn ngoi (mu sc, kch thc, kiu ng thng) ca mt i tng cho nhiu i tng khc. Trc tin, chn i tng ngun sao chp thuc tnh. Sau , nhn chn cc i tng ch p dng cc thuc tnh ny vo.

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Xa i tng Nhn chn i tng m bn mun xa.

3.2.2. im

im mi Nhn chut ln vng lm vic v mt im mi. Ghi ch: Khi ta nh nt tri chut ra, ta im s c c nh. Bng cch nhp chut ln on thng, ng thng, a gic, ng conic, th hm s hoc ng cong, bn s to mt im trn i tng (xem thm lnh im). Nhp ln ni giao nhau ca 2 i tng s to giao im ca 2 i tng ny (xem thm lnh Giao im).

Giao im ca 2 i tng Giao im ca hai i tng c th c xc nh theo 2 cch. Nu bn

nh du hai i tng: xc nh tt c cc giao im ca hai i tng (nu c).

Nhp chut vo ni giao nhau ca hai i tng: ch xc nh mt giao im ti .

i vi on thng, tia, cung trn, ch nh c ly giao im xa hay khng (xem Hp thoi thuc tnh). Tnh nng ny c th dng ly giao im nm trn phn ko di ca i tng. V d, phn ko di ca mt on thng hoc mt tia l mt ng thng.

Trung im hoc tm im Nhp chn...

Hai im xc nh trung im. on thng xc nh trung im. ng conic xc nh tm.

3.2.3. Vec-t

Vec-t qua 2 im Xc nh im gc v im ngn ca vec-t.

Vec-t qua 1 im Xc nh mt im A v mt vec-t v v im B = A + v v vec-t t A n B.

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3.2.4. on thng

on thng Xc nh 2 im A v B v on thng AB. Chiu di ca doni thng AB s c hin th trong ca s i s.

on thng vi di cho trc Nhp chn im A v nhp vo hp thoi hin ra chiu di on thng. Ghi ch: on thng AB c di a v ch c th quay quanh im A vi cng c Di chuyn

3.2.5. Tia

Tia i qua 2 im Xc nh 2 im A v B v mt tia t im A v i qua im B. Phng trnh ca ng thng ng vi tia AB s c hin th trong ca s i s.

3.2.6. a gic

a gic Xc nh t nht 3 im nh ca a gic. Sau , nhp chn tr li im u tin ng a gic li. Din tch ca a gic s c hin th trong ca s i s.

a gic u Xc nh 2 im A, B v nhp vo hp thoi xut hin mt s n v mt a gic u n nh (bao gm c A v B).

3.2.7. ng thng

ng thng Xc nh 2 im A v B v ng thng qua A v B. Hng ca vec-t ch phng l (B - A).

ng song song Chn ng thng g v im A v ng thng qua A v song song g. Hng ca ng thng l hng ca ng thng g.

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ng vung gc Xc nh ng thng g v mt im A v mt ng thng qua A v vung gc vi g. Hng ca ng vung gc l hng ca vec-t php tuyn (xem thm lnh VectoPhapTuyen) ca g.

ng trung trc Xc nh on thng s hoc 2 im A, B v ng trung trc ca an thng AB. Hng ca ng trung trc l hng ca vec-t php tuyn (xem thm lnh VectoPhapTuyen) ca on thng s hoc AB.

ng phn gic ng phn gic ca mt gc c th c xc nh theo 2 cch:

Xc nh 3 im A, B, C v ng phn gic ca gc ABC , B l nh. Xc nh 2 cnh ca gc.

Ghi ch: Vec-t ch phng ca ng phn gic c di l 1.

Tip tuyn Tip tuyn ca ng conic c th c xc nh theo 2 cch:

Xc nh im A v ng conic c v tt c cc tip tuyn qua A v tip xc vi c.

Xc nh ng thng g v ng conic c v tt c cc tip tuyn ca c song song vi g.

Chn im A v hm s f v tip tuyn ca hm f ti x = x(A).

ng i cc hoc ng knh ko di Cng c ny s v ng i cc hoc ng knh ko di ca ng conic. Bn c thThis mode creates the polar or diameter line of a conic section. You can either

Chn 1 im v 1 ng conic v ng i cc. Chn 1 ng thng hoc 1 vec-t v 1 ng conic v ng knh ko

di.

3.2.8. ng Conic

ng trn khi bit tm v 1 im trn ng trn Chn im M v im P v ng trn tm M v qua P. Bn knh ng trn l MP.

ng trn khi bit tm v bn knh Sau khi chn tm M, s xut hin mt hp thoi, hy nhp di bn knh vo.

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ng trn qua 3 im Chn 3 im A, B, and C v ng trn qua 3 im. Nu 3 im thng hang th ng trn s suy bin thnh ng thng.

ng Conic qua 5 im Chn 5 im v mt ng conic qua 5 im . Ghi ch: Nu 4 trong 5 im thng hng, th s khng v c ng conic.

3.2.9. Cung trn v hnh qut Ghi ch: Gi tr i s ca cung chnh l di ca cung. Gi tr ca hnh qut l din tch ca hnh qut.

Hnh bn nguyt Chn 2 im A v B v hnh bn nguyt qua on thng AB.

Cung trn khi bit tm v 2 im trn cung trn Chn 3 im M, A, v B v mt cung trn c tm M, v 2 im u mt A, B. Ghi ch: im B khng nm trn dy cung.

Hnh qut khi bit tm v 2 im trn hnh qut Chn 3 im M, A, v B v mt hnh qut c tm M, v 2 im u mt A, B. Ghi ch: im B khng nm trn dy cung.

Cung trn qua 3 im Chn 3 im v mt cung trn qua 3 im.

Hnh qut qua 3 im Chn 3 im v mt hnh qut qua 3 im.

3.2.10. S v Gc

Khong cch hay chiu di Cng c ny s xc nh khong cch gia 2 im, 2 ng thng, hoc 1 im v 1 ng thng. Cng c ny cng cho ta bit c chiu di ca mt ng thng, mt cung trn.

Din tch Cng c ny cho php bn tnh din tch ca mt hnh a gic, hnh trn, e-lip.

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H s gc Cng c ny cho php bn tnh h s gc ca mt ng thng.

Con trt Ghi ch: Trong GeoGebra, con trt l minh ha hnh hc ca mt gi tr (s) t do hoc mt gc t do. Nhp chut ti bt k ni no trn vng lm vic to mt con trt cho mt gi tr (s) t do hoc mt gc t do. Mt ca s mi s xut hin cho bn bit tn, khong [min, max] ca s hoc gc, cng nh canh l v b rng ca con trt (theo pixel). Ghi ch: Bn c th d dng to mt con trt cho mt gi tr (s) t do hoc mt gc t do c bng cch hin th i tng (xem Menu ng cnh; xem cng c

Hin / n i tng). C th c nh v tr ca con trt trn mn hnh hoc vi tng quan vi h trc ta (xem Hp thoi thuc tnh cho s v gc tng ng).

Gc Cng c ny s v

Gc vi 3 im cho trc Gc vi 2 on thng cho trc Gc vi 2 ng thng cho trc Gc vi 2 vec-t cho trc Cc gc trong ca a gic

Tt c cc gc s c gii hn ln t 0 n 180. Nu bn mun hin th gc i xng, chn Gc i xng trong Hp thoi thuc tnh.

Gc vi ln cho trc Chn 2 im A, B v nhp vo hp thoi ln ca gc. Cng c ny s to mt im C v mt gc , vi l gc ABC.

3.2.11. Boolean

Hp chn hin / n i tng Nhn chut ln vng lm vic to mt hp chn hin hoc n nhiu i tng, Trong ca s hin ra, bn c th ch nh i tng no s b tc ng bi hp chn.

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3.2.12. Qu tch

Qu tch Xc nh mt im mun v qu tch (B) ph thuc vo mt im khc (A). Sau do01 nhp chut vo im A. Ghi ch: im B phi l mt im trn mt i tng (nh: ng thng, on thng, ng trn).

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V d: Nhp f(x) = x^2 2 x 1 vo khung nhp lnh. V mt im A trn trc x (xem im mi; xem lnh im). V im B = (x(A), f(x(A))), im B ph thuc vo im A. Chn cng c Qu tch v nhp chn ln lt ln im B v im A. Ko im A dc theo trc x thy im B di chuyn theo ng qu tch ca

n.

3.2.13. Cc php bin i hnh hc Cc php bin i hnh hc cho im, ng thng, ng conic, a gic, nh.

i xng qua tm u tin, chn i tng cn ly i xng, Sau , nhp chn im s lm tm i xng.

i xng qua trc u tin, chn i tng cn ly i xng, Sau , nhp chn ng thng s lm trc i xng.

Xoay i tng quanh tm theo mt gc u tin, chn i tng cn xoay. K tip, nhp chn im s lm tm xoay mark the object to be rotated. Sau , mt hp thoi s xut hin bn nhp gc quay vo.

Tnh tin theo vec-t u tin, chn i tng cn tnh tin. Sau , chn vec-t tnh tin.

Thay i hnh dng kch thc theo t l u tin, chn i tng cn thay i hnh dng kch thc. K tip, chn im lm tm co gin. Sau , mt hp thoi s xut hin bn nhp h s t l co gin vo.

3.2.14. Ch

Ch Vi cng c ny bn c th to vn bn (nh: ghi ch, ch thch) hoc cc cng thc LaTeX trong ca s hnh hc.

Nhp chut ln vng lm vic to mt khung nhp vn bn ti v tr ny. Nhp chut ln mt im to mt khung nhp vn bn, v tr ca khung

nhp s ph thuc v tr ca im ny (khi di chuyn im th v tr ca khung cng di chuyn theo).

Sau , mt hp thoi s xut hin bn nhp ni dung vn bn vo.

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Ghi ch:: C th s dng cc gi tr ca i tng to vn bn ng.

Nhp vo M t This is a text vn bn tnh im A = + A vn bn ng s dng gi tr ca im A a = + a + cm vn bn ng s dng gi tr ca on thng A

V tr ca vn bn s c c nh trn mn hnh hoc lin h vi h trc ta (xem Thuc tnh ca vn bn).

Cng thc LaTeX Vi GeoGebra bn c th vit cc cng thc ton hc. thc hin, bn nhn chn ti hp chn Cng thc LaTeX trong hp thoi Vn bn nhp cng thc ton hc theo c php LaTeX. Di y l mt vi c php LaTeX quan trnng. bit thm, vui lng xem qua cc ti liu v LaTeX.

C php LaTeX Kt qu a \cdot b ba \frac{a}{b}

ba

\sqrt{x} x \sqrt[n]{x} n x \vec{v} vG \overline{AB} AB x^{2} 2x a_{1} 1a \sin\alpha + \cos\beta cossin + \int_{a}^{b} x dx ba xdx \sum_{i=1}^{n} i^2 =ni i1 2

3.2.15. nh

Chn nh Cng c ny cho php bn chn nh vo hnh v ca bn.

Nhp chut ln vng lm vic ch nh gc tri di ca nh. Clicking on the drawing pad specifies the lower left corner of the image.

Nhp chut ln mt im ch nh im ny s trng vi v tr gc tri di ca nh.

Sau , mt hp thoi s xut hin cho php bn chn tp tin nh chnvo.

3.2.16. Cc thuc tnh ca nh V tr

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V tr ca nh s c nh trn mn hnh hoc tng quan vi h trc ta (xem Thuc tnh ca nh), c xc nh bng ba im ba gc ca hnh, Chc nng ny cho bn s tin li thay i hnh dng, kch c, xoay, lm mo hnh.

1. gc th nht (gc tri bn di nh) 2. gc th hai (gc phi bn di nh)

Ghi ch: Gc ny ch c th chnh sa sau khi chnh gc th 1. Gc ny chnh chiu rng ca nh.

4. gc th t (gc tri bn trn nh) Ghi ch: Gc ny ch c th chnh sa sau khi chnh gc th 1. Gc ny chnh chiu cao ca nh.

Ghi ch: Xem thm lnh Gc nh V d: To ba im A, B, v C tm hiu v chc nng ca cc im gc nh.

Chn im A l im gc nh th nht v B l im gc nh thc hai. Di chuyn im A v B bng cng c Di chuyn bn c th d dng thy c nh hng ca chng i vi nh..

Chn im A l im gc nh th nht v im C l im gc nh th t v di chuyn chng thy nh hng ca chng i vi nh.

Cui cng, bn c th xc nh 3 im gc nh v di chuyn chng thy chng lm thay i nh ca bn.

Bn va thy c lm th no thay i v tr v kch thc ca nh. Nu bn mun gn nh vo mt im A v chnh chiu rng bng 3 v chiu cao bng 4 n v, bn lm theo cc bc sau::

1. Gc th nht: A 2. Gc th hai: A + (3, 0) 4. Gc th ba: A + (0, 4)

Ghi ch: Nu bn di chuyn im A bng cng c Di chuyn, nh ca bn s khng thay i kch thc.

nh nn Bn c th cho mt nh tr thnh nh nn (Thuc tnh ca nh). nh nn s xp ng sau h trc ta , v bn khng th dng chut chn n na. Ghi ch: thay i thuc tnh ca nh nn, chn Thuc tnh t menu Chnh sa.

Trong sut C th lm cho mt nh tr nn trong sut c th nhn thy cc i tng hoc trc ta ng sau n. Bn c th thit lp trong sut ca nh bng cch chnh gi tr t mu nn t 0 % n 100 % (xem Thuc tnh ca nh).

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4. Nhp i tng i s Trong chng ny chng ta s tm hiu cch s dng bn phm to v sa i cc i tng trong GeoGebra.

4.1. Tng quan Gi tr, ta , phng trnh ca cc i tng t do v i tng ph thuc c hin th trong phn ca s i s (bn tri). Cc I tng t do khng ph thuc vo bt k i tng no khc v c th c thay i trc tip. Bn c th to v sa i cc i tng bng cch s dng khung nhp lnh pha di mn hnh GeoGebra (xem Nhp trc tip; xem Lnh). Ghi ch: Lun n phm Enter sau mi dng lnh nhp vo khung nhp lnh.

4.1.1. Thay i cc gi tr Cc i tng t do c th c thay i trc tip; ngc li, cc i tng ph thuc th khng. thay i gi tr ca i tng t do, ghi ln gi tr c bng cch nhp gi tr mi vo khung nhp (xem Nhp trc tip). V d: Nu bn mun thay i gi tr ca mt s c a = 3, nhp a = 5 vo khung nhp v n phm Enter. Ghi ch: Cch khc: trong ca s i s, chn nh ngha li trong Menu ng cnh; hoc trong ca s hnh hc, nhp p chut ln i tng khi ang kch hot cng c Di chuyn.

4.1.2. Minh ha

thay i mt gi tr s hoc mt gi tr gc lin tc, chn cng c Di chuyn. Sau ,nhp chn con s hoc gc v n phm + hoc . Nhn gi cc phm trn bn c th to mt minh ha. V d: Nu ta ca mt im ph thuc vo mt s k nh P = (2 k, k), im s di chuyn dc theo mt ng thng khi k c thay i lin tc.. Vi cc phm mi tn, bn c th di chun bt k i tng t do no vi cng c

Di chuyn (xem Minh ha; xem Di chuyn). Ghi ch: Bn c th iu chnh khong thay i gi tr (bc nhy) bng Hp thoi thuc tnh ca i tng ny. Phm tt:

Ctrl + phm mi tn cho bn bc nhy 10 n v Alt + phm mi tn cho bn bc nhy 10 n v

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Ghi ch: Mt im trn mt ng thng c th di chuyn dc theo ng thng bng cc phm + hoc (xem Minh ha).

4.2. Nhp trc tip GeoGebra c th lm vic vi s, gc, im, vec-t, on thng, ng thng, ng conic, th hm s v ng cong tham s. By gi chng ta s tm hiu cch nhp vo khung nhp cc i tng ny theo ta hoc phng trnh. Ghi ch: Bn cng c th s dng cc ch s cho tn i tng, v d A1 hoc SAB c th nhp vo l A_1 hoc s_{AB}.

4.2.1. S v Gc S v gc s dng du . phn cch phn thp phn. V d: Bn phi nhp s r l r = 5.32. Ghi ch: Bn c th s dng hng s v s -le (Euler) e cho cc biu thc v cng thc bng cch chn chng trong danh sch lit k k bn khung nhp. Gc c tnh theo () hoc radian (rad). Hng s c th c nhp vo l pi (s s gip bn thun tin hn khi nhp n v radian). V d: Gc c th c nhp theo ( = 60) hoc theo radian ( = pi/3). Ghi ch: GeoGebra tnh ton theo n v radian. Biu tng l hng s /180 chuyn t sang radian.

Con trt v Cc phm mi tn Cc gi tr ca cc con s v cc gc c lp c th c trnh by nh l con trt trn ca s hnh hoc (xem cng c Con trt). Bng cc phm mi tn, bn cng c th thay i gi tr ca s hoc gc trong ca s i s (xem Minh ha).

Gi tr gii hn Cc gi tr ca cc con s v cc gc c lp c th c gii hn trong mt khong [min, max] (xem Hp thoi thuc tnh). Khong ny cng c s dng cho Con trt. Cho mi gc ph thuc, bn c th chn n c th tr thnh gc phn x hay khng (xem Hp thoi thuc tnh).

4.2.2. im v Vec-t im v vec-t c th c nhp theo ta -cc hoc ta cc (xem S v Gc). Ghi ch: im c k hiu bng ch in hoa, vec-t c k hiu bng ch thng. V d: v im P v vec-t v,

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theo ta -cc: P = (1, 0) v v = (0, 5). theo ta cc: P = (1; 0) v v = (5; 90).

4.2.3. ng thng Mt ng thng c nhp di dng phng trnh tuyn tnh theo dng tng qut x, y hoc theo dng tham s. Trong c hai dng, tt c cc n s c nh ngha trc u c th s dng (v d: d, im, vec-t). Ghi ch: Bn c th nhp tn ca ng thng vo trc phng trnh ca ng thng v ngn cch chng bng du hai chm (:). V d:

Nhp vo g : 3x + 4y = 2 v ng thng g. nh ngha tham s t (t = 3) trc khi nhp vo phng trnh ng thng

g di dng tham s: g: X = (-5, 5) + t (4, -3). Trc tin, nh ngha tham s m = 2 v b = -1. Sau , bn c th nhp

vo phng trnh g: y = m x + b v ng thng g tng ng vi m v b trn (y = 2x 1).

Trc x v trc y Hai trc ta c dng trong cc cu lnh vi ten gi Trc-x v Trc-y. V d: Lnh DuongVuongGoc[A, Truc-x] s v ng thng qua A v vung gc vi trc x.

4.2.4. ng Conic Mt ng conic c th c nhp di dng phng trnh bc hai theo x, y. C th s dng cc bin c nh ngha trc (nh: s, im, vec-t). Bn c th nhp tn ca ng conic vo trc phng trnh ca ng conic v ngn cch chng bng du hai chm (:). V d:

Elip ell: ell: 9 x^2 + 16 y^2 = 144 Hyperbol hyp: hyp: 9 x^2 16 y^2 = 144 Parabol par: par: y^2 = 4 x ng trn k1: k1: x^2 + y^2 = 25 ng trn k2: k2: (x 5)^2 + (y + 2)^2 = 25

Ghi ch: Nu bn nh ngha trc hai tham s a = 4 and b = 3, bn c th nhp vo phng trnh ng elip l ell: b^2 x^2 + a^2 y^2 = a^2 b^2.

4.2.5. Hm s f(x) nhp mt hm s, bn c th s dng cc bin nh ngha trc (nh: s, im, vec-t) v cc hm s khc. Examples:

Hm s f: f(x) = 3 x^3 x^2

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Hm s g: g(x) = tan(f(x)) Hm s: sin(3 x) + tan(x)

Tt c cc hm s c sn (nh: sin, cos, tan) c m t trong phn di v cc ton t s hc (xem Cc ton t s hc). Trong GeoGebra, bn c th s dng cu lnh tnh Tch phn v o hm ca hm s. Bn c th s dng cc gi tr f(x) hoc f(x), ly o hm ca mt hm f(x) c xc nh. V d: u tin, nh ngha hm s f l f(x) = 3 x^3 x^2. Sau , nhp vo khung nhp g(x) = cos(f(x + 2)) xc nh hm s g. Thm vo , bn c th tnh tin th ca mt hm s theo mt vec-t (xem lnh Tnh tin) v c th dng chut di chuyn mt hm s t do bng cng c (xem cng c Di chuyn).

Khong gii hn hm s gii hn mt hm s trong khong [a, b], ta s dng lnh HamSo (xem lnh Hm s).

4.2.6. Danh sch cc i tng S dng cp du ngoc mc to mt danh sch cc i tng (nh: im, on thng, ng trn). V d:

L = {A, B, C} s cho ta mt danh sch cha 3 im c xc nh l A, B, v C.

L = {(0, 0), (1, 1), (2, 2)} s cho ta mt danh sch cha cc im c nhp vo.

4.2.7. Cc ton t s hc nhp cc s, ta , phng trnh (xem Nhp trc tip) bn c th s dng cc biu thc s hc vi cc du ngoc n. Di y l cc ton t c dng trong GeoGebra:

Ton t Nhp vo cng + tr - nhn * hoc phm space tch v hng * hoc phm space chia / ly tha ^ hoc 2 giai tha ! hm Gamma gamma( ) du ngoc n ( )

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Ton t Nhp vo ta x x( ) ta y y( ) gi tr tuyt i abs( ) du sgn( ) cn bc 2 sqrt( ) cn bc 3 cbrt( ) s ngu nhin t 0 n 1 random( ) hm m exp( ) hoc x logarit (c s t nhin, c s e) ln( ) hoc log( ) logarit c s 2 ld( ) logarit c s 10 lg( ) cos cos( ) sin sin( ) tan tan( ) arccos acos( ) arcsin asin( ) arctan atan( ) cos hypebolic cosh( ) sin hypebolic sinh( ) tan hypebolic tanh( ) arcos hypebolic acosh( ) arcsin hypebolic asinh( ) arctan hypebolic atanh( ) s nguyn ln nht nh hn hoc bng floor( ) s nguyn nh nht ln hn hoc bng ceil( ) lm trn round( )

V d:

Trung im M ca on thng AB c th c nhp vo nh sau: M = (A + B) / 2.

di vec-t v c tnh l: l = sqrt(v * v). Ghi ch: Trong GeoGebra, bn c th thc hin cc php tnh vi im v vec-t.

4.2.8. Bin s Bool Bn c th s dng cc bin Bool true v false trong GeoGebra. V d: Nhp a = true hoc b = false vo khung nhp v n phm Enter.

Hp chn v Cc phm mi tn Cc bin Bool t do c trnh by l mt hp chn trn vng lm vic (xem cng c

Hp chn hin / n i tng). Bng cc phm mi tn trn bn phm, bn cng c th thay i cc bin Bool trong ca s i s (xem Minh ha).

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4.2.9. Ton t Bool Bn c th s dng cc ton t Bool trong GeoGebra: Ton t V d Loi

bng hoc == a b hoc a == b s, im, ng thng, ng conic a, b khng bng hoc != a b hoc a != b s, im, ng thng, ng conic a, b nh hn < a < b s a, b ln hn > a > b s a, b nh hn hoc bng hoc = b s a, b v a b bin logic a, b hoc a b bin logic a, b khng hoc ! a hoc !a bin logic a song song a b ng thng a, b vung gc a b ng thng a, b

4.3. Cc lnh S dng cc cu lnh, chng ta c th to mi v sa i cc i tng c. Chng ta c th t tn cho kt qu ca mt cu lnh bng cch nhp tn (v theo sau l du =) vo pha trc cu lnh . Trong v d sau, im mi c t tn l S. V d: tm giao im ca hai ng thng g v h, bn c th nhp vo S = GiaoDiem[g,h] (xem lnh Giao im). Ghi ch: Bn cng c th s dng cc ch s cho tn i tng, v d A1 hoc SAB c th nhp vo l A_1 hoc s_{AB}.

4.3.1. Cc lnh c bn

Quan h QuanHe[i tng a, i tng b]: hin th mt hp thoi cho chng ta bit

mi quan h ca i tng a v i tng b. Ghi ch: lnh ny c th cho chng ta bit hai i tng c bng nhau hay khng, im c nm trn ng thng hoc ng conic hay khng, ng thng tip xc hay ct ng conic.

Xa Xoa[i tng a]: Xa i tng a v cc i tng lin quan vi n.

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Yu t YeuTo[Danh sch L, s n]: yu t th n trong danh sch L

4.3.2. Cc lnh logic (Boolean) If[iu kin, a, b]: to mt bn sao ca i tng a nu iu kin l ng

(true), v i tng b nu iu kin l sai (false). If[iu kin, a]: to mt bn sao ca i tng a nu iu kin l ng

(true), v i tng khng xc nh nu iu kin l sai (false).

4.3.3. Gi tr

di DoDai[vect v]: di ca vec-t v DoDai[im A]: di vec-t v tr ca A DoDai[hm s f,s x1, s x2]: di th hm f gia x1 v x2 DoDai[hm s f, im A, im B]: di th hm f gia hai im A v B

trn th DoDai[ng cong c, s t1, s t2]: di th ng cong c gia t1 v

and t2 DoDai[ng cong c, im A, im B]: di th ng cong c gia hai

im A v B trn ng cong Dodai[danh sch L]: di ca danh sch L (s cc yu t c trong danh sch)

Din tch DienTich[im A, im B, im C, ...]: Din tch ca hnh a gic xc

nh bi cc im A, B, C cho trc DienTich[conic c]: Din tch ca conic c (hnh trn hoc hnh e-lip)

Khong cch KhoangCach[im A, im B]: Khong cch gia hai im A v B KhoangCach[im A, ng thng g]: Khong cch gia im A v ng

thng g KhoangCach[ng thng g, ng thng h]: Khong cch gia ng

thng g v ng thng h. Ghi ch: Khong cch ca hai ng thng giao nhau bng 0. Chc nng ny dng tnh khong cch gia hai ng thng song song.

S d SoDu[s a, s b]: S d ca php chia a : b

Phn nguyn PhanNguyen[s a, s b]: Phn nguyn ca php chia a : b

H s gc HeSoGoc[ng thng g]: H s gc ca ng thng g. Ghi ch: Lnh ny s

v mt tam gic m t dc v bn c th thay i kch thc ca tam gic (xem thm Hp thoi thuc tnh).

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cong DoCong[im A, hm s f]: cong ca hm f ti im A DoCong[im A, ng cong c]: cong ca ng cong c ti im A

Bn knh BanKinh[ng trn c]: Bn knh ca ng trn c

Chu vi Conic ChuViConic[conic c]: Tnh chu vi ng conic c (ng trn hoc e-lip)

Chu vi a gic ChuViDaGiac[a gic poly]: Chu vi a gic poly

Tham s tiu ThamSoTieu[parabol p]: Tham s tiu ca parabol p (khong cch gia ng

chun v tiu im)

di trc th nht DoDaiTrucThuNhat[conic c]: di trc chnh ca ng conic c

di trc th hai DoDaiTrucThuHai[conic c]: di trc th hai ca ng conic c

Tm sai TamSai[conic c]:Tm sai ca ng conic c

Tch phn TichPhan[hm s f, s a, s b]: Tnh tch phn ca hm f(x) t a n b.

Ghi ch: Lnh ny cng s v ra din tch ca vng b chn gia th hm s f v trc x.

TichPhan[hm s f, hm s g, s a, s b]: Tnh tch phn ca hm f(x) - g(x) t a n b. Ghi ch: Lnh ny cng s v ra din tch ca vng b chn gia th hm s f v th hm s g.

Ghi ch: Xem Tch phn bt nh

Phn hoch di PhanHoachTren[hm s f, s a, s b, s n]: Phn hoch di hm s f

trong an [a, b] thnh n hnh ch nht.

Phn hoch trn PhanHoachTren[hm s f, s a, s b, s n]: Phn hoch trn hm s f

trong an [a, b] thnh n hnh ch nht..

Lp Lap[hm s f, gi tr x0, s n]: Lp li hm s f n ln theo gi tr ban u

x0 cho trc. V d: Cho hm s f(x) = x^2, lnh Lap[f, 3, 2] s cho ta kt qu l (32)2 = 27

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Min v Max Min[s a, s b]: S nh nht trong hai s a v b Max[s a, s b]: S ln nht trong hai s a v b

H s tng quan HeSoTuongQuan[im A, im B, im C]: Tr v h s tng quan ca

ba im cng tuyn (ba im thng hng) A, B, and C, vi BA = * BC hoc A = B + * BC

H s kp HeSoKep[im A, im B, im C, im D]: H s kp ca bn im

cng tuyn (bn im thng hng) A, B, C, and D, vi = HeSoTuong Quan[A, B, C] / HeSoTuongQuan[A, B, D]

4.3.4. Gc

Gc Goc[vect v1, vect v2]: Gc to thnh bi vec-t v1 v v2 (t 0 n 360) Goc[ng thng g, ng thng h]: Gc to thnh hai vec-t ch phng

ca hai ng thng g v (t 0 n 360) Goc[im A, im B, im C]: Gc to thnh bi BA v BC (t 0 n 360).

im B l nh. Goc[im A, im B, gc alpha]: Gc v t B, c nh l A v c ln

bng . Note: im Xoay[B, A, ] cng s c to. Goc[conic c]: Gc xon ca trc chnh ca ng conic c (xem lnh Trc) Goc[vect v]: Gc to thnh bi trc x v vec-t v Goc[im A]: Gc to thnh bi trc x v vec-t v tr ca im A Goc[s n]: i mt s n thnh gc (kt qu t 0 n 2pi) Goc[a gic poly]: Tt c cc gc trong ca a gic poly

4.3.5. im

im Diem[ng thng g]: im thuc ng thng g Diem[conic c]: im thuc ng conic c (ng trn, e-lip, hyperbol) Diem[hm s f]: im thuc hm f Diem[a gic poly]: im thuc a gic poly Diem[vec-t v]: im thuc vec-t v Diem[im P, vec-t v]: im P cng vec-t v

Trung im v Tm TrungDiem[im A, im B]: Trung im on thng AB TrungDiem[on thng s]: Trung im on thng s Tam[conic c]: Tm ca ng conic c (ng trn, e-lip, hyperbol)

Tiu im TieuDiem[conic c]: (Tt c) cc tiu im ca ng conic c

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nh nh[conic c]: (Tt c) cc nh ca ng conic c

Trng tm TrongTam[a gic poly]: Trng tm ca a gic poly

Giao im GiaoDiem[line g, ng thng h]: Giao im ca hai ng thng g v h GiaoDiem[ng thng g, conic c]: Tt c cc giao im ca ng thng g

v ng conic c (ti a l 2) GiaoDiem[ng thng g, conic c, s n]: Giao im th n ca ng

thng g v ng conic c GiaoDiem[conic c1, conic c2]: Tt c cc giao im ca hai ng conic c1

v c2 (ti a l 4) GiaoDiem[conic c1, conic c2, s n]: Giao im th n ca hai ng conic

c1 v c2 GiaoDiem[hm a thc f1, hm a thc f2]: Tt c cc giao im ca hai

th hm s ca hm a thc f1 v f2 GiaoDiem[hm a thc f1, hm a thc f2, s n]: Giao im th n ca

hai th hm s ca hm a thc f1 v f2 GiaoDiem[hm a thc f, ng thng g]: Tt c cc giao im ca th

hm s hm a thc f v ng thng g GiaoDiem[hm a thc f, ng thng g, s n]: Giao im th n ca

th hm s hm a thc f v ng thng g GiaoDiem[hm s f, hm s g, im A]: Giao im ca hai hm f v g theo

mt gi tr im A ban u (phng php Newton) GiaoDiem[hm s f, ng thng g, im A]: Giao im ca hm f v

ng thng g theo mt gi tr im A ban u (phng php Newton) Ghi ch: xem thm Giao im ca hai i tng

Nghim Nghiem[hm a thc f]: Tm tt c cc nghim ca hm a thc f(x)=0 (cc gi

tr tm c s c biu din l cc im trn th) Nghiem[hm s f, s a]: Tm mt nghim ca hm s f theo mt gi tr a ban

u (phng php Newton) Nghiem[hm s f, s a, s b]: Tm mt nghim ca hm s f trong on [a,

b] (regula falsi)

Cc tr CucTri[hm a thc f]: Tt c cc cc tr ca hm a thc f (cc gi tr tm

c s c biu din l cc im trn th)

im un DiemUon[hm a thc f]: Tt c cc im un ca hm a thc f

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4.3.6. Vec-t

Vect Vecto[im A, im B]: Vec-t t im A n im B Vecto[im A]: Vec-t v tr ca im A

Vect ch phng VectoChiPhuong[ng thng g]: Vec-t ch phng ca ng thng g. Ghi

ch: Mt ng thng c phng trnh ax + by = c s c vec-t ch phng l (b, - a).

Vect ch phng n v VectoChiPhuongDonVi[ng thng g]: Vec-t ch phng n v (c ln

bng 1) ca ng thng g VectoChiPhuongDonVi[vect v]: Vec-t c cng phng, chiu vi vec-t v

cho trc v c ln bng 1

Vect php tuyn VectoPhapTuyen[ng thng g]: Vc-t php tuyn ca ng thng g. Ghi

ch: Mt ng thng c phng trnh ax + by = c s c vec-t php tuyn l (a, b).

VectoPhapTuyen[vect v]: Vc-t php tuyn ca vec-t v. Ghi ch: Mt vec-t c ta (a, b) s c vec-t php tuyn l vec-t (- b, a).

Vect php tuyn n v VectoPhapTuyenDonVi[ng thng g]: Vec-t php tuyn n v (c ln

bng 1) ca ng thng g VectoPhapTuyenDonVi[vect v]: Vec-t vung gc vi vec-t v v c ln

bng 1

Vect cong VectoDoCong[im A, hm s f]: Vec-t cong ca hm s f ti im A VectoDoCong[im A, ng cong c]: Vec-t cong ca ng cong c ti

im A

4.3.7. on thng

on thng DoanThang[im A, im B]: on thng qua hai im A, B DoanThang[im A, s a]: on thng qua A (im bt u) v c di l a.

Ghi ch: im kt thc on thng cng s c v.

4.3.8. Tia

Tia Tia[im A, im B]: Tia bt u t im A v i qua im B Tia[im A, vect v]: Tia bt u t im A v c cng hng vi v

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4.3.9. a gic

a gic DaGiac[im A, im B, im C,...]: a gic xc nh bi cc im A, B,

C, cho trc DaGiac[im A, im B, s n]: a gic u n nh (gm c hai nh A, B)

4.3.10. ng thng

ng thng DuongThang[im A, im B]: ng thng qua hai im A v B DuongThang [im A, ng thng g]: ng thng qua A v song song vi

ng thng g DuongThang [im A, vect v]: ng thng qua im A v c cng hng

vi vect v

ng vung gc DuongVuongGoc[im A, ng thng g]: ng thng qua im A v vung

gc vi ng thng g DuongVuongGoc[im A, vector v]: ng thng qua im A v vung gc

vi vector v

ng trung trc DuongTrungTruc[im A, point B]: ng trung trc ca on thng AB DuongTrungTruc[on thng s]: ng trung trc ca on thng s

ng phn gic DuongPhanGiac[im A, im B, im C]: ng phn gic ca gc c

to bi 3 im A, B, v C. Ghi ch: im B l nh ca gc. DuongPhanGiac[ng thng g, ng thng h]: Hai dng phn gic ca

gc to thnh bi hai ng thng g v h.

Tip tuyn TiepTuyen[im A, conic c]: (Tt c) cc ng tip tuyn qua im A v

tip xc vi ng conic c TiepTuyen[ng thng g, conic c]: (Tt c) cc ng tip tuyn vi

ng conic c v song song vi ng thng g TiepTuyen[s a, hm s f]: ng tip tuyn vi hm f(x) ti x = a TiepTuyen[im A, hm s f]: ng tip tuyn vi hm f(x) ti x = x(A) TiepTuyen[im A, ng cong c]: ng tip tuyn vi ng cong c ti

im A

Tim cn TiemCan[hyperbola h]: Hai ng tim cn ca hyperbol h

ng chun DuongChuan[parabol p]: ng chun ca parabol p

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Trc Truc[conic c]: Hai trc ca conic c

Trc th nht TrucThuNhat[conic c]: Trc th nht (Trc chnh) ca conic c

Trc th hai TrucThuHai[conic c]: Trc th hai ca conic c

ng i cc DuongDoiCuc[im A, conic c]: ng i cc ca im A tng quan vi

conic c

ng knh DuongKinh[ng thng g , conic c]: ng knh ca ng conic c song

song vi ng thng g DuongKinh[vect v, conic c]: ng knh ca ng conic c cng hng

vc vec-t v

4.3.11. ng Conic

ng trn DuongTron[im M, s r]: ng trn tm M v bn knh r DuongTron[im M, on thng s]: ng trn tm M v bn knh bng

Dodai[s] DuongTron[im M, im A]: ng trn c tm M v i qua im A DuongTron[im A, im B, im C]: ng trn qua ba im A, B v C

ng trn mt tip DuongTronMatTiep[im A, hm s f]: ng trn mt tip ca hm s f ti

im A DuongTronMatTiep[im A, curve c]: ng trn mt tip ca ng cong c

ti im A

E-lip Elip[im F, im G, s a]: E-lip c tiu im l F v G v di trc chnh

l a. Ghi ch: iu kin: 2a > KhoanCach[F, G] Elip[im F, im G, on thng s]: E-lip c tiu im l F v G v di

trc chnh bng di on thng s (a = DoDai[s]).

Hyperbol Hyperbol[im F, im G, s a]: Hyperbol c tiu im l F v G v di

trc chnh l a. Ghi ch: iu kin: 2a > KhoangCach[F, G] Hyperbol[im F, im G, on thng s]: Hyperbol c tiu im l F v G

v di trc chnh bng di on thng s (a = DoDai[s]).

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Parabol Parabol[im F, ng thng g]: Parabol c tiu im l F v ng chun

l g

Conic Conic[im A, im B, im C, im D, im E]: ng conic qua nm

im A, B, C, D, v C. Ghi ch: Bn im khng c thng hng.

4.3.12. Hm s

o hm DaoHam[hm s f]: o hm ca hm s f(x) DaoHam[hm s f, s n]: o hm cp n ca hm s f(x) Ghi ch: Bn c th s dng f(x) thay v DaoHam[f], cng nh l f(x) thay v DaoHam[f, 2].

Tch phn TichPhan[hm s f]: Tch phn bt nh ca hm s f(x) Ghi ch: Xem Tch phn xc nh

Khai trin KhaiTrien[hm s f]: Khai trin hm a thc f.

V d: KhaiTrien[(x - 3)^2] s l x2 - 6x + 9

Khai trin Taylor KhaiTrienTaylor[hm s f, s a, s n]: Khai trin Taylor cho hm sf(x)

ti x = a n cp n

Hm s HamSo[hm s f, s a, s b]: Hm s, bng f trong on [a, b] v khng xc

nh bn ngoi on [a, b]

Hm s c iu kin Bn c th s dng cc cu lnh logic (Bool) If (xem lnh If) to mt hm s c iu kin. Ghi ch: Bn c th s dng o hm v tch phn cho cc hm ny nh cc hm s khc. V d: = If[x < 3, sin(x), x^2] s cho ta mt hm s f(x) bng:

sin(x) nu x < 3 v x2 nu x 3.

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4.3.13. ng cong tham s DuongCong[biu thc e1, biu thc e2, tham s t, s a, s b]:

ng cong tham s trong h ta -cc cho bi biu thc theo x l e1 v biu thc theo y l e2 (theo tham s t) trong on [a, b]

V d: c = DuongCong[2 cos(t), 2 sin(t), t, 0, 2 pi] DaoHam[ng cong c]: o hm ca ng cong c Ghi ch: C th tnh ton vi ng cong tham s nh cc hm s trong cc biu thc s hc khc. V d: Nhp vo c(3) s cho ta im nm trn ng cong c ng vi tham s t=3 Ghi ch: Bn c th xc nh mt im mi trn ng cong bng cng c im mi (xem cng c im mi; xem thm lnh im). Nu cc gi tr a v b l cc gi tr ng, bn c th s dng con trt (xem cng c Con trt).

4.3.14. Cung v Hnh qut Ghi ch: Gi tr i s ca mt cung trn chnh l chiu di ca cung v ca mt hnh qut chnh l din tch ca hnh qut.

Hnh bn nguyt HinhBanNguyet[im A, im B]: Hnh bn nguyt qua on thng AB.

Cung trn CungTron[im M, im A, im B]: Cung trn c tm M gia 2 im A, B.

Ghi ch: im B khng nm trn cung trn.

Cung trn qua 3 im CungTronQua3Diem[im A, im B, im C]: Cung trn qua 3 im A, B,

v C

Cung Cung[conic c, im A, im B]: Cung ca ng conic gia hai im A, B

trn ng conic (ng trn hoc e-lip) Cung[conic c, s t1, s t2]: Cung ca ng conic gia hai gi tr ng vi

hai tham s t1 v t2 ca ng conic: o ng trn: (r cos(t), r sin(t)) ; vi r l bn knh o E-lip: (a cos(t), b sin(t)) ; vi a v b l di hai trc ca e-lip

Hnh qut HinhQuat[im M, im A, im B]:Hnh qut c tm M giaCircular sector

with midpoint M between two points A and B. Note: point B does not have to lie on the arc.

Hnh qut qua 3 im HinhQuatQua3Diem[im A, im B, im C]: Hnh qut qua 3 im A, B,

v C

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Sector Sector[conci c, im A, im B]: Conic section sector between two points

A and B on the conic section c (circle or ellipse) Sector[conic c, s t1, s t2]: Conic section sector between two parameter

values t1 and t2 on the conic section c for the following parameter forms: o Circle: (r cos(t), r sin(t)) where r is the circle's radius o Ellipse: (a cos(t), b sin(t)) where a and b are the lengths of the first and

second axis

4.3.15. nh

Gc nh GocAnh[nh, s n]: Gc nh th n ca nh (ti a l 4 gc)

4.3.16. Qu tch

Qu tch QuiTich[im Q, im P]: ng qu tch ca im Q (im Q ph thuc vo

im P). Ghi ch: im P phi l im trn mt i tng (nh: ng thng, on thng, ng trn).

4.3.17. Dy s

Dy s DaySo[biu thc e, bin s i, s a, s b]: Danh sch cc i tng

c to bng biu thc e v c ch s i thay i t a n b. Example: L = DaySo[(2, i), i, 1, 5] s to mt dy cc im c honh y t 1 n 5

DaySo[Biu thc e, bin s i, s a, s b, s s]: Danh sch cc i tng c to bng biu thc e v c ch s i thay i t a n b vi bc nhy l s.

V d: L = Dayso[(2, i), i, 1, 5, 0.5] s to mt dy cc im c honh y t 1 n 5 vi bc nhy l 0.5

Ghi ch: V cc tham s a v b l cc s thay i lin tc nn bn c th dng Con trt cho bin s ny.

Cc lnh v dy s YeuTo[danh sch L, s n]: yu t th n ca danh sch L DoDai[danh sch L]: di ca danh sch L Min[danh sch L]: Yu t c gi tr nh nht trong danh sch L Max[danh sch L]: Yu t c gi tr ln nht trong danh sch L

Lp DanhSachLap[hm s f, s x0, s n]: Danh sch L vi di n+1 vi cc

thnh phn l s lp li ca hm s f bt u t gi tr x0.

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V d: Sau khi nh ngha hm s f(x) = x^2, lnh L = Danhsachlap[f, 3, 2] s cho bn mt danh sch L = {3, 32, (32)2} = {3, 9, 27}

4.3.18. Cc php bin i hnh hc Nu bn to tn mi cho kt qu bin i ca mt trong cc lnh sau y, i tng c s c gi li, ng thi mt i tng mi c to. Ghi ch: Lnh DoiXung[A, g] s cho ta im l i xng ca im A qua ng thng g v di chuyn im A n v tr mi. Nhp vo B = DoiXung[A, g] s to mt im B v tr i xng ca im A nhng im A vn c gi li v tr c.

Tnh tin TinhTien[im A, vect v]: Tnh tin im A theo vec-t v TinhTien[ng thng g, vect v]: Tnh tin ng thng g theo vec-t v TinhTien[conic c, vect v]: Tnh tin ng conic c theo vec-t v TinhTien[hm s c, vect v]: Tnh tin th hm s f theo vec-t v TinhTien[a gic poly, vect v]: Tnh tin a gic poly theo vec-t v. Ghi

ch: Cc nh v cc cnh ca a gic mi cng s c to. TinhTien[nh pic, vect v]: Tnh tin nh pic theo vec-t v TinhTien[vect v, im P]: Tnh tin vec-t v n im P Ghi ch: xem thm cng c Tnh tin theo vec-t

Xoay Xoay[im A, gc phi]: Xoay im A quanh trc ta mt gc Xoay[vector v, gc phi]: Xoay vec-t v mt gc Xoay[ng thng g, gc phi]: Xoay ng thng g quanh trc ta mt

gc Xoay[conic c, gc phi]: Xoay conic c quanh trc to mt gc Xoay[a gic poly, gc phi]: Xoay a gic poly quanh trc ta mt gc .

Ghi ch: Cc nh v cc cnh ca a gic mi cng s c to. Xoay[nh pic, gc phi]: Xoay nh pic quanh trc to mt gc Xoay[im A, gc phi, im B]: Xoay im A quanh im B mt gc Xoay[ng thng g, gc phi, im B]: Xoay ng thng g quanh im B

mt gc Xoay[conic c, gc phi, im B]: Xoay conic c quanh im B mt gc Xoay[a gic poly, gc phi, im B]: Xoay a gic poly quanh im B

mt gc . Ghi ch: Cc nh v cc cnh ca a gic mi cng s c to. Xoay[nh pic, gc phi, im B]: Rotates image pic by angle around point

B Ghi ch: Xem thm cng c Xoay i tng quanh tm theo mt gc

i xng DoiXung[im A, im B]: i xng ca im A qua im B DoiXung[ng thng g, im B]: i xng ca ng thng a qua im B DoiXung[conic c, im B]: i xng ca conic c qua im B DoiXung[a gic poly, im B]: i xng ca a gic poly qua im B. Ghi

ch: Cc nh v cc cnh ca a gic mi cng s c to.

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DoiXung[nh pic, im B]: i xng ca nh pic qua im B DoiXung[im A, ng thng h]: i xng ca im A qua ng thng h DoiXung[ng thng g, ng thng h]: i xng ca ng thng g qua

ng thng h DoiXung[conic c, ng thng h]: i xng ca conic c qua ng thng h DoiXung[a gic poly, ng thng h]: i xng ca a gic poly qua

ng thng h. Ghi ch: Cc nh v cc cnh ca a gic mi cng s c to.

DoiXung[nh pic, ng thng h]: i xng ca nh pic qua ng thng h Ghi ch: Xem thm cng c i xng qua tm; v i xng qua trc

Thay i hnh dng kch thc ThayDoiHinhDangKichThuoc[im A, s f, im S]: Thay i khong

cch im A t gc S theo h s t l f ThayDoiHinhDangKichThuoc[ng thng h, s f, im S]: Thay i

khong cch ng thng h t gc S theo h s t l f ThayDoiHinhDangKichThuoc[conic c, s f, im S]: Thay i hnh dng

kch thc conic c t gc S theo h s t l f ThayDoiHinhDangKichThuoc[polygon poly, s f, im S]: Thay i

hnh dng kch thc a gic poly t gc S theo h s t l f. Ghi ch: Cc nh v cc cnh mi ca a gic mi cng s c to

ThayDoiHinhDangKichThuoc[nh pic, s f, im S]: Thay i hnh dng kch thc nh pic t gc S theo h s t l f

Ghi ch: Xem thm cng c Thay i hnh dng kch thc theo t l

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5. In n v xut thnh tp tin

5.1. In n

5.1.1. Vng Lm Vic Bn c th tm thy mc Xem trc khi in ca vng lm vic trong menu H s. Bn c th ty chnh tiu , tc gi, ngy thng v t l bn in (theo cm). Ghi ch: Bm phm Enter cp nht cc thay i vo bn xem trc khi in.

5.1.2. Cch dng hnh m ca s xem trc khi in ca cch dng hnh, trc tin bn cn m Cch dng hnh (menu Hin th). Bn s tm thy mc Xem trc khi in trong menu H s ca ca s mi xut hin. Ghi ch: Bn cng c th cho n hoc hin cc ct khc nhau: Tn, nh ngha, Dng lnh, Dng i s v im dng ca cch dng hnh (xem menu Hin th ca Cch dng hnh). Trong ca s Xem trc khi in ca Cch dng hnh, bn c th nhp vo tiu , tc gi v ngy thng trc khi in cch dng hnh. Pha di ca s cch dng hnh c mt thanh cng c dng hnh. Thanh cng c ny cho php bn xem tng bc dng hnh (xem Thanh cng c dng hnh). Ghi ch: S dng ct im dng (menu Hin th) bn c th nh ngha tng bc dng hnh c th bng cc im dng nhm cc i tng li. Khi th hin cc bc dng hnh chnh l lc cc nhm i tng c hin th cng mt thi im.

5.2. Vng Lm Vic thnh dng nh Bn c th tm thy mc Vng Lm Vic thnh dng nh trong menu H s, Xut. Ti , bn c th nh t l (theo cm) v phn gii (theo dpi) cho tp tin kt xut. Kch thc tht ca nh kt xut c hin th pha di ca s. Khi xut vng lm vic thnh nh, bn c th xut thnh cc nh dng sau:

PNG Portable Network Graphics y l nh dng nh theo im nh (pixel). phn gii cng cao cho cht lng nh cng tt (thng th 300dpi l ). Khng nn thay i t l nh dng PNG trnh gim cht lng nh. Tp tin nh dng PNG thng c dng cho cc trang web (html) v chng trnh Microsoft Word.

43

Ghi ch: Khi bn chn mt tp tin nh dng PNG vo mt ti liu Word (menu Insert, Image from file), xc nh kch thc nh l 100%. Nu khng, t l nh (theo cm) s b thay i.

EPS Encapsulated Postscript y l mt nh dng nh theo vc-t. nh dng EPS c th thay i t l m khng nh hng n cht lng nh. Cc tp tin nh dng EPS thng c dng trong cc chng trnh x l nh vc-t nh Corel Draw v h thng x l vn bn chuyn nghip nh LATEX. phn gii ca nh dng EPS lun l 72dpi. Gi tr ny ch dng tnh ton kch thc tht ca nh theo cm v khng nh hng n cht lng nh. Ghi ch: Hiu ng trong sut khng c hiu qu i vi cc a gic v ng conic c t mu khi s dng dng EPS.

SVG Scaleable Vector Graphic (xem nh dng EPS pha trn)

EMF Enhanced Meta Format (xem nh dng EPS pha trn)

PSTricks dng cho LaTeX

5.3. Sao chp Vng Lm Vic vo B nh Bn c thm tm thy mc Sao chp Vng Lm Vic vo B nh trong menu H s, Xut. Tnh nng ny sao chp mn hnh vng lm vic vo b nh h thng di dng nh PNG (xem nh dng PNG). nh ny c th dn vo cc chng trnh khc (v d Microsoft Word). Ghi ch: xut cch dng hnh theo mt t l nht nh (theo cm) bn hy dng mc Vng Lm Vic thnh dng nh trong menu H s, Xut (xem Vng Lm Vic thnh dng nh).

5.4. Cch dng hnh thnh dng trang web m ca s Xut cch dng hnh, trc tin bn cn m Cch dng hnh t menu Hin th. Ti bn c th tm thy mc Xut thnh dng trang web trong menu H s. Ghi ch: Bn c th n hoc hin cc ct ca cch dng hnh trc khi xut thnh dng trang web (xem menu Hin th ca cch dng hnh). Trong ca s xut ca cch dng hnh, bn c th nhp tiu , tc gi v ngy thng ca cch dng hnh v bn c th ty chn xut nh vng lm vic cng vi ca s dng i s ca cch dng hnh hay khng.

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Ghi ch: Tp tin HTML xut ra c th c xem bng cc trnh duyt web (v d: Mozilla, Internet Explorer) v c th chnh sa bng nhiu chng trnh x l vn bn (v d: Frontpage, Word).

5.5. Vng Lm Vic thnh dng Trang Web Trong menu H s, Xut, bn s tm thy mc Vng Lm Vic thnh dng Trang Web (html). Trong ca s xut, bn c th nhp tiu , tc gi v ngy thng cho Vng Lm Vic. Th Tng quan cho php bn thm vn bn vo pha trn v pha di hnh (v d: mt ch thch cho cch dng hnh v cc bc dng hnh). Cch dng hnh c th c tch hp vo trong trang web hoc c m bng cch bm mt nt. Th Nng cao cho php bn thay i tnh nng ca cch dng hnh (v d: thay i biu tng, nhp p nt chut m ca s chng trnh) cng nh thay i giao din hin th (v d: hin th thanh cng c, thay i chiu cao, chiu rng). Ghi ch: Khng nn nhp gi tr chiu cao v chiu rng vng dng hinh qu ln c th hin th y trn trnh duyt web. Mt vi tp tin c to thnh khi xut vng lm vic:

tp tin html (v d: cricle.html) tp tin ny cha vng lm vic tp tin ggb (v d; circle_worksheet.ggb) tp tin ny cha cch dng hnh

theo GeoGebra geogebra.jar (c vi tp tin) cc tp tin ny cha c chng trnh GeoGebra

v bn c th tng tc vi vng lm vic Tt c cc tp tin (v d: tp tin circle.html, circle_worksheet.ggb v geogebra.jar) phi t trong cng mt th mc (ng dn) th phn dng hnh mi lm vic. Bn cng c th sao chp tt c cc tp tin n mt th mc khc. Ghi ch: Tp tin HTML c xut ra (v d: circle.html) c th c m bng tt c cc trnh duyt web (v d: Mozilla, Internet Explorer, Safari). phn dng hnh lm vic, my tnh ca bn phi ci t chng trnh Java. Bn c th download min ph Java t trang web: http://www.java.com. Nu bn mun ang s dng my ni mng ca trng hc, hy yu cu ngi qun tr ci t Java ln my. Ghi ch: Bn c th chnh sa cc vn bn trn phn dng hnh bng nhiu chng trnh x l vn bn (v d: Frontpage, Word) bng cch m tp tin HTML.

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6. Cc ty chn Cc ty chn chung c th thay i bng menu Ty Chn. thay i cc ty chn cho i tng, bn hy dng Menu ng cnh.

6.1. Bt im Xc nh chc nng Bt im bt hay tt hoc c bt cc im vo li hay khng

6.2. n v ca gc Xc nh cc gc c hin th di dng () hoc raian (rad). Ghi ch: Lun c th nhp gi tr bng 2 cch ( v raian).

6.3. Hin th s thp phn Cho php bn ty chnh cch hin th s ch s thp phn t 0 n 5 s.

6.4. Lin tc GeoGebra cho php bn bt / tt chc nng tm lin tc trong menu Ty chn. Chng trnh dng mt php truy tm theo hng lin tc gi cho cc giao im (ng thng hnh nn, hnh nn hnh nn) lun gn vi v tr c ca chng v trnh giao im nhy. Ghi ch: Mc nh, php truy tm ny trng thi tt. i vi cng c do ngi dng nh ngha (xem Cng c do ngi s dng nh ngha) th n cng trng thi tt.

6.5. Kiu im Xc nh cc im c hin th di dng du chm hoc du cng.

6.6. Kiu gc vung Xc nh gc vung s c hin th kiu hnh ch nht, du chm hoc ging vi cc gc khc.

6.7. Ta Xc nh ta im c hin th theo kiu A = (x, y) hoc A(x | y).

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6.8. Tn Bn c th cho hin th hoc n tn ca mt i tng mi c to. Ghi ch: Mc T ng s hin th cc tn i tng khi khung danh sch cc i tng c m lc to i tng mi.

6.9. C ch Xc nh c ca cc nhn v ch theo n v pt.

6.10. Ngn ng GeoGebra l chng trnh a ngn ng. Bn c th thay i ngn ng s dng. Thay i ny c tc dng i vi tn lnh v tt c cc gi tr u ra.

6.11. Vng lm vic M mt hp thoi thit lp cc thuc tnh ca Vng lm vic (v d: li v h trc ta , mu nn).

6.12. Lu cc thit lp Chng trnh GeoGebra s ghi nh cc thit lp bn thng s dng (cc thit lp trong menu Ty chn, thanh cng c v vng lm vic hin ti) nu bn chn Lu cc thit lp trong menu Ty chn.

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7. Cng c v thanh cng c

7.1. Cng c do ngi s dng nh ngha Da trn mt cu trc c sn, bn c th to mt b cng c ring cho GeoGebra. Sau khi chun b cu trc cc cng c, chn To mi cng c trong menu Cng c. Trong hp thoi mi xut hin, bn c th xc nh cc i tng u vo v u ra cho cng c v chn tn cho biu tng cng c v lnh. V d: Cng c v hnh ch nht

Dng hnh ch nht bt u bng hai im A v B. Dng cc nh khc v lin kt chng li bng cng c a gic c c hnh ch nht poly1.

Chn To mi cng c trong menu Cng c. Xc nh i tng u ra: Nhn chut vo hnh ch nht hoc chn trn

menu x xung. Xc nh i tng u vo: GeoGebra t ng xc nh cc i tng u

vo cho bn (trng hp ny: im A v im B). Bn cng c th chnh cc i tng u vo bng cch s dng menu x xung hoc nhn chut vo chng trong vng lm vic.

Xc nh tn cng c v tn hm cho cng c mi ca bn. Tn cng c s xut hin trn thanh cng c ca GeoGebra, tn lnh c th c s dng trong phn nhp lnh ca GeoGebra.

Bn cng c th chn hnh cho biu tng ca cng c. GeoGebra s t ng thay i kch thc biu tng cho thch hp vi thanh cng c.

Ghi ch: Cng c ca bn c th c s dng bng chut hoc bng phn nhp lnh. Tt c cc cng c c t ng lu li trong tp tin ggb. Bn c th s dng hp thoi Qun l cng c (menu Cng c) xa mt cng c hoc chnh sa tn v biu tng cho cng c. Bn cng c th lu cc cng c c chn vo mt tp tin GeoGebra Tools (ggt). Tp tin ny c th dng np cc cng c vo vng lm vic (menu H s, M). Ghi ch: M mt tp tin ggt s khng thay i vng lm vic ca bn nhng tp tin ggb th ngc li.

7.2. Ty chnh thanh cng c Bn c th ty chnh thanh cng c trong GeoGebra bng cch chn Ty chnh thanh cng c trong menu Cng c. iu ny c bit hu dng trong trng hp xut Vng lm vic thnh dng trang web gim bt s cng c trn thanh cng c. Ghi ch: Cc ty chnh hin ti ca thanh cng c c lu cng vi tp tin ggb ca vng lm vic.

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8. Giao din JavaScript Ghi ch: Giao din JavaScript ca GeoGebra rt hu ch cho nhng ai c kinh nghim v HTML. GeoGebra applets cung cp giao din JavaScript nng cao kh nng tng tc ca Vng lm vic dng trang web. V d, bn c th to mt nt bm to ngu nhin cc thng s cho vng lm vic. Xin vui lng xem ti liu GeoGebra Applets and JavaScript bit thm cc v d v thng tin v cch s dng JavaScript trong GeoGebra applets.

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Danh mc

n 11

nh 22

chn nh 22 gc 39 v tr 22

nh nn 23

B bn knh

cu lnh 31 Bool

bin s 28 cu lnh 30 ton t 29

C cch dng hnh 12 cn bc ba 28 cn bc hai 28 ceil 28 chn

nh, cng c 22 ch 21

chia 27 chnh sa 11 ch 21

cng c 21 chu vi conic

cu lnh 31 chu vi a gic

cu lnh 31 c ch

ty chn 46 con trt

cng c 19 cng 27 cng c 13

ngi dng t nh ngha 47 qun l 47 ty chnh 47

cng thc 22 conic

cu lnh 37 cos 28 cc tr

cu lnh 33 cung trn

bit tm v hai im trn cung trn, cng c 18 cu lnh 38 qua ba im, cng c 18

D a gic

cu lnh 35 cng c 16 u, cng c 16

a gic u cng c 16

danh sch 27 o hm

cu lnh 37 du 28 du ngoc n 27 du vt 11 dy s 39

cc lnh khc 39 di chuyn 40

cng c 13 vng lm vic, cng c 14

im 25 bt im

ty chn 45 cu lnh 32 kiu, ty chn 45 ngoi ng thng, nh ngha li 12 trn ng thng, nh ngha li 12

im mi cng c 15

im un cu lnh 33

din tch cng c 18

nh cu lnh 33

nh dng kiu hin th 14

nh ngha li 12 cong

cu lnh 31 vec-t

cu lnh 34 di trc th hai ca conic

cu lnh 31 di trc th nht ca conic

cu lnh 31 on thng

cu lnh 34 qua hai im, cng c 16 vi di cho trc, cng c 16

i cc cu lnh 36

i cc hoc ng knh ko di cng c 17

i tn 11 i xng

cu lnh 40 ng cong 38 ng cong tham s 38 ng conic 26

qua nm im, cng c 18 ng knh

cu lnh 36 ng song song

cng c 16 ng thng 26

bin i thnh on thng, nh ngha li 12

50

cu lnh 35 qua hai im, cng c 16

ng trn bit tm v bn knh, cng c 17 bit tm v mt im trn ng trn, cng c 17 cu lnh 36 qua ba im, cng c 18

ng trn mt tip 36

F floor 28

G gi tr

thay i 24 gi tr tuyt i 28 giai tha 27 giao im

cu lnh 33 hai i tng, cng c 15

gii hn hm s 27

gc 25 cu lnh 32 cng c 19 n v 45 vi ln cho trc, cng c 19

gc nh nh cu lnh 39

H hm Gamma 27 hm lng gic

arccos 28 arccos hyperbolic 28 arcsin 28 arcsin hyperbolic 28 arctan 28 arctan hyperbolic 28 cos 28 cos hyperbolic 28 sin 28 sin hyperbolic 28 tan 28 tan hyperbolic 28

hm lng gic 27 hm m 28 hm s 26

cu lnh 37 hm m 28 khong gii hn 27

hm s c iu kin cu lnh 37

h s gc cng c 19

h s kp cu lnh 32

h s tng quan cu lnh 32

h sgc cu lnh 30

hin 11 hin / n

i tng, cng c 14 tn, cng c 14

hnh bn nguyt cu lnh 38 cng c 18

hnh qut 38 bit tm v hai im trn hnh qut, cng c 18 cu lnh 38, 39 qua ba im, cng c 18

hp chn hin / n i tng 19

hyperbol cu lnh 36

I if

cu lnh 37 in n

cch dng hnh 42 vng lm vic 42

J JavaScript 48

K khai trin

a thc 37 khai trin a thc

cu lnh 37 khai trin Taylor

cu lnh 37 khong cch

cu lnh 30 cng c 18

kiu gc vung ty chn 45

kiu hin th sao chp 14

L lm trn 28 lp 39

cu lnh 31 lnh 29 lin tc

ty chn 45 logarit 28 lu cc thit lp

ty chn 46 ly tha 27

M max

cu lnh 32 menu ng cnh 11 min

cu lnh 32 minh ha 24

N nghim

cu lnh 33 ngn ng

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ty chn 46 nhn 27 nhp trc tip 25

P parabol

cu lnh 37 phn gic

cng c 17 phn hoch di

cu lnh 31 phn hoch trn

cu lnh 31 phn nguyn

cu lnh 30 phng to / thu nh 12

phng to, cng c 14 thu nh, cng c 14

Q quan h

cu lnh 29 cng c 14

qun l cng c 47 qu tch 20

cu lnh 39 cng c 20

S sao chp kiu hin th

cng c 14 sin 28 s d

cu lnh 30 s ngu nhin 28 s thp phn

ty chn 45

T tm sai

cu lnh 31 tan 28 tham s tiu

cu lnh 31 thanh cng c dng hnh 12 thay i hnh dng kch thc

cu lnh 41 i tng t im, cng c 21

thuc tnh 13 hp thoi 13

tia cu lnh 34 qua hai im, cng c 16

tch phn cu lnh 31, 37

tch v hng 27 tip tuyn

cu lnh 35 cng c 17

tiu im cu lnh 32

tnh tin 40 cu lnh 40

theo vec-t, cng c 21 ta

ta x 28 ta y 28

ta x 28 ta y 28 ton t s hc 27 trng tm

cu lnh 33 tr 27 trc

cu lnh 36 t l 12 trc-x, trc-y 26

trc th hai ca conic cu lnh 36

trc th nht ca conic cu lnh 36

trc-x 26 trung im

cu lnh 32 cng c 15

trung trc cu lnh 35 cng c 17

ty chnh thanh cng c 47 ty chn 45

V vec-t 25

cu lnh 34 qua hai im, cng c 15 t im, cng c 15

vec-t ch phng cu lnh 34

vect ch phng n v cu lnh 34

vect php tuyn cu lnh 34

vect php tuyn n v cu lnh 34

vng lm vic thnh trang web 44 ty chn 46 vo b nh tm 43 xut 42

vung gc cu lnh 35 cng c 17

X xa 11

cu lnh 29 i tng, cng c 15

xoay cu lnh 40 i tng quanh tm, cng c 21 quanh tm, cng c 14

xut 42, 43, 44

Y yu t

cu lnh 30