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II. grafika
sia aris Tanamedrove daprogramebis enebis ZiriTadi obieqti. Mathematica
sistemis gamosaxulebebis nebismieri mimdevroba Cawerili figurul frCx-
ilebSi warmoadgens sias. wvdoma siis elementebTan xorcieldeba ormagi
kvadratuli frCxilebis gamoyenebiT. Mathematica sistemaSi sul arsebobs
frCxilebis oTxi tipi:
(a+b)c,{a,b,c},f[x],m[[i]] an mPiT.
grafikebis ageba
grafikis asagebad gamoiyeneba Plot funqcia, romelic Seicavs or
aucilebel arguments: funqcia f[x], romlis grafiki unda avagoT (an funq-
ciebis sia), da funqciis gansazRvris are {xmin, xmax}, romelic Seicavs
formalur cvlads x:
Plot[f[x], {x, xmin, xmax}]
Plot@Tan@xD, 8x, -Pi, Pi<D
-3 -2 -1 1 2 3
-6-4-2
246
SevinaxoT miRebuli grafiki rogorc suraTi *.gif (*.bmp,*.jpg,*.pdf)
gafarToebiT.
Export@"c:�grafiki.gif", %D;Import@%D
avagoT y=x^2 funqciis grafiki da SevinaxoT miRebuli grafiki rogorc
suraTi *.jpg gafarToebiT
Export@"c:�ff.jpg", Plot@x^2, 8x, -1, 1<DD;Import@"c:�ff.jpg"D
Plot da Table funqciebi aqvT erTnairi struqtura im TvalsazrisiT, rom
isini Seicaven formalur cvlads (Table funqciisaTvis es cvladi aris
iteratori, Plot funqciisaTvis es cvladi warmoadgens abscisas, romelic
icvleba xmin-dan, xmax-mde). ganvixiloT Semdegi magaliTi.
x = 2;
Plot@x^2, 8x, -3, 3<D
-3 -2 -1 1 2 3
2
4
6
8
aqedan Cans, rom Plot funqciaSi x cvladi aris formaluri,da masze ar
moqmedebs gareT gansazRvruli mniSvneloba x=2.
Expand@Hx + 2L^2D
16
sxva funqciebisagan gansxvavebiT Plot funqcia asrulebis winaswari argu-
mentebis gamoTvlis blokirebas da formaluri cvladi x gamoTvlis pro-
cesSi yovelTvis rCeba ganusazRvreli. winaamRdeg SemTxvevaSi Cven miviReb-
diT Secdomas, radgan formaluri cvladis magivrad iqneboda ricxvi 2:
x=2; Plot[x^2,{x,-3,3}])®Plot[4,{2,-3,3}]. im SemTxvevaSi roca ar
aris saWiro winaswar argumentebis gamoTvlis blokireba, unda visarge-
bloT Evaluate funqciiT, romelSic uyve iqneba Casmuli cvladis
gansazRvruli mniSvneloba. ganvixiloT magaliTi.
Plot@Evaluate@x^2D, 8x, -3, 3<D
-3 -2 -1 1 2 3
2
4
6
8
exla wavSaloT x cvladis mniSvneloba.
x =.
Plot@8Sin�x, 1 � Sin@xD<, 8x, -2, 2<D
-2 -1 1 2
-4
-2
2
4
aq Cven avageT ori funqciis grafiki erT sibrtkeze.
Plot funqciis opciebis gamoyeneba
funqciis grafikis asagebaT xSiradDsaWiroa damatebiTi parametrebis
miTiTeba. damatebiTi parametrebi, romlebic gansazRraven grafikis saxes,
warmodgenili arian opciis saxiT (Options). opcia aris funqciis argu-
menti, romelic Cawerilia lokaluri Casmis formaSi. magaliTad, rom
avagoT Sin[x] funqciis grafiki CarCoSi Plot[x] funqciiaSi davweroT
opcia Frame ® True.
2 leqcia_6.nb
Plot@Sin@xD, 8x, 0, 2 Pi<, Frame ® TrueD
0 1 2 3 4 5 6-1.0
-0.5
0.0
0.5
1.0
aq Frame opciis saxelia, xolo True misi mniSvneloba. opcias SeiZleba
hqondes ramdenime mniSvneloba. gaCumebis principiT erTi maTgani (opciis
mniSvneloba) uyve aris dayenebuli. kerZod, am magaliTSi Frame opciis
mniSvneloba gaCumebis principiT aris False, amitom Cven SevcvaleT am
opciis mniSvneloba da miviReT Sin[x] funqciis grafiki CarCoSi.
Plot@8Sin@xD, Sin@2 xD<, 8x, 0, 2 Pi<, Axes ® 8False, True< D
-1.0
-0.5
0.0
0.5
1.0
Plot@8Sin@xD, Sin@2 xD<, 8x, 0, 2 Π<, Axes ® 8True, False<D
0 1 2 3 4 5 6
Plot@8Sin@xD, Sin@2 xD<, 8x, 0, 2 Π<, Axes ® None, PlotLabel ® funqciis grafiki,
LabelStyle ® Directive@Italic, FontFamily ® "AcadNusx"DD
funqciis grafiki
Plot@8Sin@xD, Sin@2 xD<, 8x, 0, 2 Pi<, PlotStyle ® Thick, Ticks ® None, AxesLabel ® 8X, Y<D
X
Y
SeadareT es magaliTebi. qvemoT aris Plot funqciis opciebis sia.
leqcia_6.nb 3
Options@PlotD
:AlignmentPoint ® Center, AspectRatio ®1
GoldenRatio, Axes ® True,
AxesLabel ® None, AxesOrigin ® Automatic, AxesStyle ® 8<, Background ® None,
BaselinePosition ® Automatic, BaseStyle ® 8<, ClippingStyle ® None,
ColorFunction ® Automatic, ColorFunctionScaling ® True, ColorOutput ® Automatic,
ContentSelectable ® Automatic, CoordinatesToolOptions ® Automatic,
DisplayFunction ¦ $DisplayFunction, Epilog ® 8<, Evaluated ® Automatic,
EvaluationMonitor ® None, Exclusions ® Automatic, ExclusionsStyle ® None, Filling ® None,
FillingStyle ® Automatic, FormatType ¦ TraditionalForm, Frame ® False, FrameLabel ® None,
FrameStyle ® 8<, FrameTicks ® Automatic, FrameTicksStyle ® 8<, GridLines ® None,
GridLinesStyle ® 8<, ImageMargins ® 0., ImagePadding ® All, ImageSize ® Automatic,
ImageSizeRaw ® Automatic, LabelStyle ® 8<, MaxRecursion ® Automatic, Mesh ® None,
MeshFunctions ® 8ð1 &<, MeshShading ® None, MeshStyle ® Automatic, Method ® Automatic,
PerformanceGoal ¦ $PerformanceGoal, PlotLabel ® None, PlotPoints ® Automatic,
PlotRange ® 8Full, Automatic<, PlotRangeClipping ® True, PlotRangePadding ® Automatic,
PlotRegion ® Automatic, PlotStyle ® Automatic, PreserveImageOptions ® Automatic,
Prolog ® 8<, RegionFunction ® HTrue &L, RotateLabel ® True,
Ticks ® Automatic, TicksStyle ® 8<, WorkingPrecision ® MachinePrecision>
ganixileT da SeadareT Semdegi ori magaliTi:
Plot@Sin@xD, 8x, 0, 10<, Frame ® True,
FrameTicks ® Automatic, FrameTicksStyle ® Directive@Orange, 12DD
Plot@Cos@xD, 8x, 0, 10<, Frame ® True, FrameTicks ® All,
FrameTicksStyle ® 88Black, Blue<, 8Red, Green<<D
Tu saWiroa gragikis ageba ramdenime funqciisaTvis erTi da igive opciebis
gamoyenebiT, maSin jobia es opciebi calke CavweroT, magaliTad Semdegi
saxiT:
opt =
8Axes ® 8True, False<, Frame ® False, PlotStyle ® Thick, PlotRange ® 88-2, 2<, 8-2, 2<<<;
amis Semdeg visargebloT Evaluate funqciiT:
4 leqcia_6.nb
Plot@8x^3, Cos@xD<, 8x, -2, 2 <, Evaluate@optDD
-2 -1 0 1 2
Plot@Sin@1 + x � 2 xD, 8x, -Pi, Pi<, Evaluate@optDD
-2 -1 0 1 2
ganvsazRvroT f[x],g[x] funqciebi Semdegi saxiT:
f@x_D := Plot@Sin@xD, 8x, 0, 2 Π<, Axes ® 8True, False<Dg@x_D := Plot@Sin@xD � 2, 8x, 0, 2 Π<, Axes ® 8True, False<D
Show funqciis meSveobiT xorcieldeba funqciis grafikis gamotana.
Show@f@xD, g@xDD
0 1 2 3 4 5 6
ganvixiloT Semdegi magaliTebi.
Table@Plot@Cos@x + aD, 8x, -10, 10<D, 8a, 0, 2<D
:-10 -5 5 10
-1.0
-0.5
0.5
1.0
,-10 -5 5 10
-1.0
-0.5
0.5
1.0
,-10 -5 5 10
-1.0
-0.5
0.5
1.0
>
Show@%, Axes ® NoneD
Plot@Sin@x^2D � x, 8x, 0, 10<D
Show@%, PlotRange ® 888, 10<, 8-.3, .3<<, AxesOrigin ® 88.0, 0<D
leqcia_6.nb 5
{8.0, 0}
Plot3D funqcia
zemod moyvanil yvela magaliTSi iyo ganxiluli mxolod erTi cvladis
funqciebi da Sesabamisad Cven vRebulobdiT funqciis grafiki sibrtkeze.
Plot3D funqciis gamoyenebiT SegviZlia avagoT funqciis grafiki sivrceSi:
Plot3D[f[x,y],{x, xmin, xmax},{y, ymin, ymax}]. ganvixiloT magaliTi.
Plot3D@Sin@x + y^2D, 8x, -3, 3<, 8y, -2, 2<D Plot3D@8Sin@xD, Cos@xD<, 8x, 0, 2 Pi<, 8y, 0, 2 Pi
PlotStyle ® 8Red, Blue<D
-2
02
-2-1
01
2
-1.0-0.5
0.0
0.5
1.0
Plot3D@8x^2 + y^2, -x^2 - y^2<,8x, -2, 2<, 8y, -2, 2<,Axes ® 8False, False, False<, Mesh -> NoneD
Plot3D@Sqrt@1 - x^2 - y^2D,8x, -1, 1<, 8y, -1, 1<,Mesh ® 3, ColorFunction ® HueD
-1.0-0.5
0.00.5
1.0
-1.0-0.5
0.00.5
1.00.0
0.5
1.0
Options[Plot3D] gamoyenebiT ganixileT am funqciis opciebi.
ListPlot funqcia
xSirad saWiro aris funqciis grafikis ageba, roca funqcia mocemullia
cxrilis saxiT: {{x1,y1},{x2,y2},...}, sadac yi warmoadgens funqciis
mniSvnelobas Sesabamis xi wertilSi. am SemTxvevaSi gamoiyeneba ListPlot
funqcia. ganvixiloT ramdenime magaliTi.
6 leqcia_6.nb
ListPlot@881, 2<, 82, 3<, 83, 4<, 84, 5<<, PlotStyle ® [email protected]
1.5 2.0 2.5 3.0 3.5 4.0
2.53.03.54.04.55.0
ListPlot@881, 2<, 82, 3<, 83, 4<, 84, 5<<, PlotStyle ® [email protected], Joined ® TrueD
1.5 2.0 2.5 3.0 3.5 4.0
2.53.03.54.04.55.0
8ListPlot@Table@8Sin@xD, Cos@xD<, 8x, 0, 10, 0.1<D, AspectRatio -> AutomaticD, ListPlot@Table@8Sin@xD, Cos@xD<, 8x, 0, 10, 0.1<D, AspectRatio -> Automatic, AxesOrigin ® 80, 2<D<
:-1.0 -0.5 0.5 1.0
-1.0
-0.5
0.5
1.0
,
-1.0 -0.5 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
1.5
>
ListPlot@Table@8Sin@nD, Sin@2 nD<, 8n, 50<DD
-1.0 -0.5 0.5 1.0
-1.0
-0.5
0.5
1.0
a = Table@8x Sin@xD, x Cos@xD<, 8x, 0, 4.5 Pi, 0.05 Pi<D;ListPlot@a, AspectRatio -> Automatic, Joined ® True, PlotStyle -> RedD
-10 -5 5 10
-5
5
10
ListPlot funqciis argumenti SeiZleba iyos Cveulebrivi sia {y1,y2,...},
sadac yi warmoadgens funqciis mniSvnelobas Sesabamis i wertilSi
(i=1,2,3,...). am SemTxvevaSi Cven vRebulobT wertilebi
{{1,y1},{2,y2},{3,y3},...}.
leqcia_6.nb 7
ListPlot@Table@Sin@iD, 8i, 1, 9, 0.3<D, Filling ® AxisD
5 10 15 20 25
-1.0
-0.5
0.5
1.0
s1 = Table@Mod@i � 2, 10D � 10, 8i, 100<D;ListPlot@s1, Filling ® TopD
20 40 60 80 100
0.2
0.4
0.6
0.8
ListPlot@RandomInteger@5, 810<D, PlotStyle ® 8Red, [email protected]<D
2 4 6 8 10
1
2
3
4
5
ganixileT PistPlot funqciis opciebi: Options[ListPlot].
ParametricPlot, ParametricPlot3D funqciebi
funqcia ParametricPlot
arsebobs kidev erTi mniSvnelovani xerxi grafikuli obieqtebis age-
bisaTvis. amisaTvis gamoiyeneba funqcia ParametricPlot[{f[t],g[t-
]},{t,a,b}] romelic qmnis wirs aRwerili wertiliT {f[t],g[t]}, roca
tÎ[a,b].
ParametricPlot@8Cos@uD, Sin@uD<, 8u, 0, 2 Pi<D
-1.0-0.5 0.5 1.0
-1.0
-0.5
0.5
1.0
ParametricPlot@8Sin@uD u , Cos@uD u<, 8u, 0, 100<,Axes ® False, PlotStyle -> Directive@Red, ThickDD
8 leqcia_6.nb
ParametricPlot@8 Sin@uD + 7 u , Cos@uD u<, 8u, 0, 100<,Axes ® False, PlotStyle -> Directive@Blue, Thick, DashedDD
ParametricPlot@882 Cos@tD, 2 Sin@tD<,
82 Cos@tD, Sin@tD<, 8Cos@tD, 2 Sin@tD<, 8Cos@tD, Sin@tD<<, 8t, 0, 2 Pi<D
-2 -1 1 2
-2
-1
1
2
bolo magaliTSi moyvanilia oTxi parametriulad mocemuli funqciis
grafiki erT naxazze. Semdeg magaliTSi Cven vRebulobT elipss.
ParametricPlot@82 Cos@uD, Sin@uD<, 8u, 0, 2 Pi<D
-2 -1 1 2-1.0-0.5
0.51.0
ganvixiloT Semdegi ori magaliTi.
Show@8Plot@x, 8x, -1, 1<D, ParametricPlot@8Cos@uD, Sin@uD<,8u, Pi � 4, 5 Pi � 4<, PlotStyle ® RedD<, AspectRatio ® AutomaticD
-1.0 -0.5 0.5 1.0
-1.0
-0.5
0.5
1.0
Show@8Plot@x � 2, 8x, -2, 2<D, ParametricPlot@82 Cos@uD, Sin@uD<,8u, Pi � 4, 5 Pi � 4<, PlotStyle ® RedD<, AspectRatio ® AutomaticD
-2 -1 1 2
-1.0-0.5
0.51.0
funqcia ParametricPlot3D
ParametricPlot3D[{f[u],g[u],h[u]},{u,umin,umax}] funqciis meSveobiT
vRebulobT grafikul obieqts sivrceSi. ganixileT ParametricPlot, Para-
metricPlot3D funqciebis opciebi: Options[ParametricPlot3D], Options[-
ParametricPlot].
leqcia_6.nb 9
ParametricPlot3D@8Sin@uD, Cos@uD, u � 10<, 8u, 0, 20<, PlotStyle -> Directive@Green, ThickDD
-1.0-0.5
0.00.5
1.0
-1.0-0.5
0.00.5
1.0
0.00.51.0
1.5
2.0
am magaliTSi Cven miviReT mwvane wiri sivrceSi. ganvixiloT Semdegi magal-
iTi.
ParametricPlot3D@8Cos@tD H3 + r Cos@t � 2DL, Sin@tD H3 + r Cos@t � 2DL, r Sin@t � 2D<,8r, -1, 1<, 8t, 0, 2 Pi<, Mesh ® NoneD
-20
24
-2
0
2-1.0-0.50.00.51.0
am magaliTSi aris ori parametri: r da t.
ParametricPlot3D@884 + H3 + Cos@vDL Sin@uD, 4 + H3 + Cos@vDL Cos@uD, 4 + Sin@vD<,
88 + H3 + Cos@vDL Cos@uD, 3 + Sin@vD, 4 + H3 + Cos@vDL Sin@uD<<,8u, 0, 2 Pi<, 8v, 0, 2 Pi<, PlotStyle ® 8Red, Green<D
0
5
10
02
46
8
0
2
4
6
8
grafikebis animacia. Animate da Manipulate funqciebi
SevqmnaT Sin[x] funqciis animacia. jer ganvixiloT am funqciis grafiki,
roca icvleba x argumenti.
Plot@Sin@xD, 8x, -10, 10<D
-10 -5 5 10
-1.0
-0.5
0.5
1.0
10 leqcia_6.nb
Plot@Sin@x + 1D, 8x, -10, 10<D
-10 -5 5 10
-1.0
-0.5
0.5
1.0
Plot@Sin@x + 2D, 8x, -10, 10<D
-10 -5 5 10
-1.0
-0.5
0.5
1.0
Animate funqciis meSveobiT SevqmnaT animacia:
Animate@Plot@Sin@x + aD, 8x, -10, 10<D, 8a, 0, 5<D
a
-10 -5 5 10
-1.0
-0.5
0.5
1.0
aq a icvleba 0-dan 5-mde bijiT 1. ganvixiloT animaciis Seqmnis meore
xerxi.
ManipulateBPlot@Sin@x + aD, 8x, -10, 10<D, 8a, 0, 5<,
BaseStyle ® Red, FrameLabel ® "sinx funqciis animacia"F
a
-10 -5 5 10
-1.0
-0.5
0.5
1.0
sinx funqciis animacia
aqac a icvleba 0-dan 5-mde bijiT 1.
leqcia_6.nb 11
AnimateAPlotAt Ix2 - 1M, 8x, -2, 2<,Axes ® 8True, False<, PlotRange ® 88-1, 1<, 8-4, 2<<E, 8t, 0, 4<E
t
-1.0 -0.5 0.0 0.5 1.0
aRvniSnoT, rom Manipulate funqciia gamoiyeneba ara mxolod grafikis
animaciisaTvis, aramed sxva saxis amocanebSi. ganvixiloT magaliTebi.
Manipulate@N@Pi, nD, 8n, 1, 20<D
n 3.1415926535898
a =.; Manipulate@Expand@Ha + bL^nD, 8n, 1, 10, 2<D
na3 + 3 a2 b + 3 a b2 + b3
bolo magaliTSi n icvleba 1-dan 10-mde bijiT 2.
ganvixiloT da SevadaroT Semdegi ori magaliTi.
Manipulate@Plot@Sin@a xD + Sin@b xD, 8x, 0, 10<D, 8a, 1, 5<, 8b, 1, 5<D
a
b
2 4 6 8 10
-2
-1
1
2
12 leqcia_6.nb
Animate@Plot@Sin@a xD + Sin@b xD, 8x, 0, 10<D, 8a, 1, 5<, 8b, 1, 5<D
a
b
2 4 6 8 10
-2
-1
1
2
aq a da b cvladebi icvlebian erTdroulad 1-dan 5-mde bijiT 1.
Manipulate@ParametricPlot@8Sin@uD u , Cos@uD u<, 8u, 0, k<,
Axes ® False, PlotStyle -> Directive@Red, ThickDD, 8k, 1, 100<D
k
SevqmnaT Semdegi obieqti.
opTable@o_, n_D :=
TableForm@Table@o@n1, n2D, 8n1, 1, n<, 8n2, 1, n<D, TableHeadings ® 8Range@nD, Range@nD<DManipulate@opTable@o, nD, 8n, 1, 10<, 8o, 8Plus, Times, Subtract, Divide<<D
n
o Plus Times Subtract Divide
1 2 3
1 2 3 4
2 3 4 5
3 4 5 6
ganvixiloT Tu rogor muSaobs funqcia opTable:
opTable@o_, n_D :=
TableForm@Table@o@n1, n2D, 8n1, 1, n<, 8n2, 1, n<D, TableHeadings ® 8Range@nD, Range@nD<D
Table@Plus@n1, n2D, 8n1, 1, 3<, 8n2, 1, 3<D �� TableForm
2 3 4
3 4 5
4 5 6
leqcia_6.nb 13
8opTable@Plus, 3D, opTable@Times, 3D, opTable@Times, 4D, opTable@Divide, 3D<
:1 2 3
1 2 3 4
2 3 4 5
3 4 5 6
,
1 2 3
1 1 2 3
2 2 4 6
3 3 6 9
,
1 2 3 4
1 1 2 3 4
2 2 4 6 8
3 3 6 9 12
4 4 8 12 16
,
1 2 3
1 11
2
1
3
2 2 12
3
3 33
21
>
Manipulate@opTable@o, nD, 8n, 1, 10<, 8o, 8Plus, Times, Subtract, Divide<<D
n
o Plus Times Subtract Divide
1 2
1 11
2
2 2 1
damatebiTi funqciebi
ganvixiloT MenuView, ActionMenu, Tooltip, PopupView funqciebis
sintaqsi da SevadaroT gamoTvlis Sedegi:
MenuView@8"I" ® 1, "II" ® 2, "III" ® 3, "IV" ® 4, "V" ® 5<, 4DMenuView@Table@Plot@Sin@n xD, 8x, 0, 10<D, 8n, 5<DD
ActionMenu@"Print Factorials", 8"4!" ¦ Print@4!D, "7!" ¦ Print@7!D, "10!" ¦ Print@10!D<D
Tooltip@x + y, "label"DPlot@Tooltip@8Sin@xD, Cos@xD<D, 8x, 0, 10<DPlot@Tooltip@Sin@xD, "sine"D, 8x, 0, 10<D
PopupView@8a, b, x + y, z<DPopupView@Table@Plot@Sin@n xD, 8x, 0, 10<D, 8n, 3<DD
ganvixiloT Rilakis Seqmnis ori martivi magaliTi:
a = Grid@88PasteButton@ΑD, PasteButton@ΒD<, 8PasteButton@ΓD, PasteButton@∆D<<,Frame ® True, Spacings ® 81, 1<, Background ® GreenD
ButtonA"faqtoriali", Print@10!DE
arsebobs ferebis ori standartuli sistema da Mathematica-Si
Sesabamisad aris ori funqcia: CMYKColor da RGBColor. ganvixiloT
Semdegi ori magaliTi:
Plot@x^2, 8x, -1, 1<,PlotStyle ® [email protected], 0.1, 0.3D,
Plot@x^2, 8x, -1, 1<,PlotStyle ® [email protected], 0.1, 0.3D,
-1.0 -0.5 0.5 1.0
0.20.40.60.81.0
-1.0 -0.5 0.5 1.0
0.20.40.60.81.0
14 leqcia_6.nb
Û davaleba
1. aageT F(x)= x^2+Sin[53x] funqciis grafiki {-2,2} Sualedze.
2. ggamoTvaleT Semdegi gamosaxuleba:
Plot@Evaluate@S = Input@"Please input a function of x to plot on the unit interval"DD,8x, -4, 4<, PlotLabel ® Style@Framed@SD, Background ® Lighter@GreenDD,LabelStyle ® Directive@Bold, RedDD
3. ganixileT Semdegi sami obieqti:
Manipulate@Plot@x^2, 8x, -1, 1<,PlotStyle ® [email protected], 0.1, 0.3, kD, [email protected]<D, 8k, 0.1, 1, 0.01<D
Manipulate@Plot@x^2, 8x, -1, 1<,PlotStyle -> 8RGBColor@red, green, blueD, [email protected]<D,
8red , 0.01, 1, 0.01<, 8green, 0.01, 1, 0.01<, 8blue, 0.01, 1, 0.01<DManipulate@Plot@Sin@xD, 8x, 0, 10<,
PlotLabel ® Style@"sinHxL", LargeD, LabelStyle ® 8c, s<D,88c, Red, "color"<, Red<, 88s, Plain, "style"<, 8Plain, Italic, Bold<<D
4. aageT fAx_, y_E := ã-100 HHx-.5L^2 + y^2L funqciis grafiki. ganixileT am amocanis
moyvanili ori amoxsna da Sesabamisi funqciebi (opciebi): Plot3D, Parametric-Plot3D.
f@x_, y_D := ã-100 HHx-.5L^2 + y^2L H* I amoxsna *LPlot3D@f@x, yD, 8x, -1, 1<, 8y, -1, 1<, PlotPoints ® 850, 50<,PlotRange ® 8-1, 1<, Boxed ® False, Axes ® FalseD
h@x_, y_D := Exp@-100 HHx - .5L^2 + y^2LD H* II amoxsna *LParametricPlot3D@8r Cos@ΘD, r Sin@ΘD, h@r Cos@ΘD, r Sin@ΘDD<, 8r, 0, 1<, 8Θ, -Π, Π<,Boxed ® False, Axes ® False, PlotPoints ® 850, 50<, PlotRange ® 8-1, 1<D
5. gamoTvaleT da gamoiyeneT sxvadasxva opcia:
ParametricPlot@88Sin@5 tD Cos@tD, Sin@5 tD Sin@tD<, 8Cos@tD, Sin@tD<<,8t, 0, 2 Pi<, AspectRatio ® 1D
ParametricPlot3D@8Cos@ΦD Sin@ΘD, Sin@ΦD Sin@ΘD, Cos@ΘD<,8Φ, 0, 2 Pi<, 8Θ, 0, Pi<, Boxed ® False, Axes ® FalseD
ParametricPlot3D@8Cos@uD, Sin@uD, 2 v<, 8u, 0, 2 Pi<, 8v, 0, 1<DParametricPlot3D@8v Cos@uD, v Sin@uD, 2 v<, 8u, 0, 2 Pi<, 8v, 0, 1<DParametricPlot3D@
8H2 + Cos@vDL Cos@uD, H2 + Cos@vDL Sin@uD, Sin@vD<, 8u, 0, 2 Pi<, 8v, 0, 2 Pi<DParametricPlot3D@8Cos@uD, Sin@uD + Cos@vD, Sin@vD<, 8u, 0, 2 Π<, 8v, -Π, Π<DParametricPlot3D@8u Sin@tD, u Cos@tD, t<,
8t, 0, 8<, 8u, -1, 1<, Mesh ® None, Axes ® False, Boxed ® TrueDParametricPlot3D@8Sin@uD, Cos@vD, Sin@uD Sin@vD<, 8u, 0, 2 Pi<, 8v, 0, 2 Pi<, Axes ® FalseD
6. gamoTvaleT Semdegi ori gamosaxuleba:
ListLinePlot@Table@8Cos@k 2 Pi � 7D, Sin@k 2 Pi � 7D<, 8k, 0, 21, 3<D,Frame ® False, Axes ® False, Filling ® AxisD
ListPlot@Table@8Cos@k 2 Pi � 5D, Sin@k 2 Pi � 5D<, 8k, 0, 21, 3<D,Joined ® True, Axes ® False, Filling ® AxisD
7. ras dabeWdavs Semdegi programa?
Manipulate@Style@RotateLeft@Range�9, iD �� TableForm, Red, 14D,8i, 0, Length�Range�9 - 1, 1<D
leqcia_6.nb 15