Help for GeoGebra

GeoGebra 3.2

Markus Hohenwarter and Judith Hohenwarterwww.geogebra.org

GeoGebra3.2

2009-10-30

Markus Hohenwarter, markus@geogebra.org

Judith Hohenwarter, judith@geogebra.org

GeoGebra

http://www.geogebra.org

http://www.geogebra.org/help/search.html

3.2

pegasusroe@hotmail.com

shuneyaune@yahoo.com.tw

crayman33@hotmail.com

FengLin.Lu@gamil.com

jack1012@gmail.com

tsoty@math.ntnu.edu.tw

emailjack1012@gmail.com

2GeoGebra3.2

3

61.GeoGebra?

61.1.

61.1.1.

71.1.2.

71.1.3.

81.2.GeoGebra

81.2.1.

91.2.2.

91.2.3.

101.3.GeoGebra

101.3.1.

101.3.2.

111.3.3.GeoGebra

121.4.GeoGebra

121.4.1.

121.4.2.

131.4.3.

142.

142.1.

142.2.

142.2.1.

162.2.2.

172.2.3.

172.2.4.

172.2.5.

172.2.6.

182.2.7.

192.2.8.

202.2.9.

212.2.10.

222.2.11.

222.2.12.

222.2.13.

232.2.14.

252.2.15.

273.

273.1.

283.2.

283.2.1.

293.2.2.

303.2.3.

303.2.4.

303.2.5.x

313.2.6.

323.2.7.

333.2.8.

343.2.9.

343.2.10.

353.3.

363.3.1.

363.3.2.

373.3.3.

403.3.4.

413.3.5.

433.3.6.

443.3.7.

443.3.8.

443.3.9.

443.3.10.

463.3.11.

473.3.12.

483.3.13.

493.3.14.

503.3.15.

523.3.16.

523.3.17.

563.3.18.

573.3.19.

613.3.20.

613.3.21.

624.

624.1.

644.2.

654.3.

664.4

684.5

694.6

694.7

715.GeoGebra

715.1.

725.2.

735.3.

745.4.

745.5.JavaScript

745.6.

775.7.

785.8.

785.9.

795.10.

80

1. GeoGebra?

GeoGebra Markus Hohenwarter

1.1.

GeoGebra () ()

1.1.1. XE "Graphics View"

XE "Toolbar Help"

XE Help, Toolbar ()

:

: ( ) ( )

1.1.2. XE "Algebra View"

GeoGebra Enter-

: (MacOS: Ctrl-click)

Enter-

GeoGebra Command () F1- XE "Input Bar Help"

XE Help, Input Bar

XE "Command help"

XE Help, Command syntax

XE "Command syntax help"

1.1.3. XE "Spreadsheet View"

GeoGebra XE "Cell name" A 1A1

:

GeoGebra(, , )GeoGebra(A5, C1)

:

1.2. GeoGebra

1.2.1. XE "Customize user interface"

GeoGebra (, , )

XE "Customize Graphics View"

/ ( ).

:

:

(Ctrl +) (Ctrl -)

(MacOS: Ctrl - click)

XE "Zoom Rectangle" (MacOS: Cmd - click)

: (MacOS: Ctrl-click)

XE "Properties Dialog of Graphics View"

XE "Axes, Customize"

XE "Coordinate axes, Customize"

XE "Grid, Customize"

XE "Coordinate grid, Customize"

(MacOS: Ctrl-click)

x y

: Shift- (PC: Ctrl-)

:

XE "Customize toolbar"

XE "Toolbar, Customize"

GeoGebra/

:

1.2.2. XE "Properties Dialog"

XE "Properties"

( XE "Color, Properties" XE "Line style, Properties" XE "Visibility, Properties" ).

(MacOS: Ctrl - click)

()

: ()

(, , , )

:

1.2.3. XE "Context Menu"

(MacOS: Ctrl-click) (, ?) XE "Rename" , XE "Delete" , XE "Trace On" , XE "Animation On" , XE "Coyp to Input Bar" .

: XE "Trace to Spreadsheet, Feature" (). ,

, ( XE "Color" , XE "Size" , XE "Line, thickness" , XE "Line, style" , XE "Filling" ).

1.3. GeoGebra

1.3.1. XE "Navigation Bar"

GeoGebra GeoGebra

(2/7)

1.3.2. XE "Construction Protocol"

XE "Protocol"

-

-

Home-

End-

Delete -

XE "Construction Protocol, Change order of steps"

()

XE "Export, Construction protocol as webpage"

XE "Construction protocol as webpage, Export"

GeoGebra

, , ,

: HTML (Firefox Internet Explorer) (: OpenOffice Writer)

1.3.3. GeoGebra XE "Change settings"

XE "Settings, Change"

GeoGebra

GeoGbra GeoGbra

GeoGbra()

1.4. GeoGebra

1.4.1. XE "Print"

XE "Graphics View, Print"

XE "Print, Graphics View"

GeoGebra ()()

: Enter

XE "Construction Protocol, Print"

XE "Print, Construction Protocol"

()

()()

: /

1.4.2.

XE "Export, Graphics View"

XE "Graphics View, Export"

GeoGebra

12

12

'()(dpi)

XE "Graphics View to clipboard, Export"

XE "Export, Graphics View to clipboard"

((png, eps))

PNG (PNG)(: Microsoft Word )

: (cm) ( )

1.4.3. XE "Export, Dynamic Worksheet" XE "Dynamic Worksheet, Export"

XE "Export, Interactive worksheet" XE "Interactive worksheet, Export"

XE "Export, Interactive webpage" XE "Interactive webpage, Export"

GeoGebra (html)

(GeoGebra)(:)(applet)

html , (circle.html) -

ggb , ( circle.ggb) - GeoGebra

geogebra.jar ()- GeoGebra

( circle.htmlcirclet.ggb geogebra.jar files) ()

HTML - circle.html -(Mozilla, Internet Explorer)JavaJavahttp://www.java.com , Java

(FrontPageOpenOffice Writer)HTML

2.

2.1.

XE "Graphics View:Geometric input" ()

/GeoGebra ( ! )( )() ( )

2.2. XE "Construction Tools"

/

: Ctrl-

XE "Rename, Fast option"

OK

2.2.1. XE "General tools, Tool"

XE "Tools, General tools"

XE "Copy Visual Style, Tool"

XE "Format, Copy Visual Style, Tool"

XE "Visual Style, Copy"

()

XE "Delete:Delete Object, tool"

XE "Tool:Delete Object"

:

XE "Move: Tool"

XE "Tool:Move"

Delete-

( )

: Esc-

XE "Move Graphics View, Tool"

: Shift-(MS Windows: Ctrl-)

:

XE "Record to Spreadsheet, Tool"

: GeoGebra

XE "Relation, Tool"

( Relation).

XE "Rotate around Point, Tool"

XE "Show/Hide Label, Tool"

XE "Show/Hide Object, Tool"

:

XE "Zoom In, Tool"

( )

XE "Zoom Out, Tool"

( )

2.2.2. XE "Points"

XE "Intersect Two Objects, Tool"

()

:

XE "Midpoint or Center, Tool"

XE "New Point, Tool"

:

( )

: ( ).

2.2.3. XE "Vectors"

() XE "Vector between Two Points, Tool"

() XE "Vector from Point, Tool"

A v B = A + v A B

2.2.4. XE "Segments"

() XE "Segment between Two Points, Tool"

A B AB

() XE "Segment with Given Length from Point, Tool"

A

: a B A.

2.2.5. XE "Rays"

() XE "Ray through Two Points, Tool"

A BA B

2.2.6. XE "Polygons"

XE "Polygon, Tool"

XE "Regular Polygon, Tool"

XE "Polygon, Regular, Tool"

A B nn ( A B)

2.2.7. XE "Lines"

XE Angle Bisector, Tool

A, B, CB

1

XE "Best Fit Line, Tool"

( FitLine)

() XE Line through Two Points, Tool

A BA B(B - A)

XE Parallel Line, Tool

g A A g g

XE Perpendicular Bisector, Tool

s A B ()

s AB ( PerpendicularVector)

XE Perpendicular Line, Tool

g A A g

g ( PerpendicularVector).

XE Polar or Diameter Line, Tool

XE Tangents, Tool

AcA c

g cg c

A f f x = x(A)

x(A) A x A A

2.2.8. XE "Conic Sections"

() XE Circle with Center and Radius, Tool

M

() XE Circle with Center through Point, Tool

M P MP

MP

() XE Circle through Three Points, Tool

A, B, C

() XE "Compass, Tool"

XE Compasses, Tool

() XE Conic through Five Points, Tool

XE Ellipse, Tool

XE Hyperbola, Tool

XE Parabola, Tool

2.2.9. XE "Arcs"

XE "Sectors"

() XE Circular Arc with Center between Two Points, Tool

M AB

A B

() XE Circular Sector with Center between Two Points, Tool

MA B

A B

() XE Circumcircular Arc through Three Points, Tool

AB CA, B C

() XE Circumcircular Sector through Three Points, Tool

ABCA, B C

() XE Semicircle, Tool

A B AB

2.2.10. XE "Numbers"

XE "Angles"

XE Angle, Tool

:

: 180 180

XE "Angle with Given Size, Tool"

A B C ABC

XE "Area, Tool"

XE Distance or Length, Tool

XE Slider, Tool

: GeoGebra(; / )

[, ] ()

()()

:

Alt-O (MacOS: Ctrl-O) XE Degree symbol

Alt-P (MacOS: Ctrl-P) pi XE Pi symbol

XE "Slope, Tool"

2.2.11. XE "Boolean"

XE "Checkbox to Show/Hide Objects, Tool"

( )

2.2.12. XE "Loci"

XE "Locus"

XE Locus, Tool

A B A B

: A ( )

:

f(x) = x^2 2 x 1

xA ( ; ).

B = (x(A), f'(x(A)))A

BA

xAB

2.2.13. XE "Transformations"

XE "Geometric transformations"

XE Dilate Object from Point by Factor, Tool

UK English: Enlarge Object from Point by Factor XE Enlarge Object from Point by Factor, Tool

XE Reflect Object about Line, Tool

UK English: Reflect Object in Line XE Reflect Object in Line, Tool

Reflect Object about Point XE Reflect Object about Point, Tool

UK English: Reflect Object in Point XE Reflect Object in Point, Tool

XE "Reflect Point about Circle, Tool"

UK English: Reflect Point in Circle XE Reflect Point in Circle, Tool

XE Rotate Object around Point by Angle, Tool

XE Translate Object by Vector, Tool

2.2.14. XE "Text"

XE "Insert, Text"

XE Insert Text, Tool

LaTeX

:

XE Dynamic Text

XE Text, Dynamic ( Point A =)

: GeoGebra +

This is a text

This is a text()

"Point A = " + A

Point A= ( 3.05, 2.54 )

"a = " + a + "cm"

a = 5.87 cm

: xx "xx"GeoGebraxx

: (, ) +

LaTeX XE Formula

GeoGebra LaTeX LaTeX

: LaTeX( { }

LaTeX LaTeX

LaTeX

a \cdot b

b

a

\frac{a}{b}

b

a

\sqrt{x}

x

\sqrt[n]{x}

n

x

\vec{v}

\overline{AB}

AB

x^{2}

2

x

a_{1}

1

a

\sin\alpha + \cos\beta

b

a

cos

sin

+

\int_{a}^{b} x dx

b

a

xdx

\sum_{i=1}^{n} i^2

=

n

i

i

1

2

2.2.15.

XE Image, Insert

XE Insert Image, Tool

XE Insert, Image, Tool

: Alt-click

XE Image, Position

XE Picture, Position

1()

2(): 1

4(): 1

: Corner

:

A, B, C

A B AB

A C

:

A 34

1 A

2 A + (3, 0)

3 A + (0, 4)

: A

:

XE Image, Transparency

XE Transparent, Image

0% 100%

3.

3.1.

()GeoGebra( ; )

:Enter

: Enter

XE Name objects

XE Object, Name

XE Name, Point

XE Point, Name GeoGebra C = (2, 4), P = (1; 180), Complex = 2 + i

XE Name, Vector

XE Vector, Name Geogebra v = (1, 3), u = (3; 90), complex = 1 2i

XE Name, Line

XE Line, Name

XE Name, Conic section

XE Conic section, Name g: y = x + 3, c: (x-1)^2 + (y 2)^2 = 4, hyp: x^2 y^2 = 2

XE Name, Function

XE Function, Name f(x) = or g(x)= h(x) = 2 x + 4, q (x) = x^2, trig(x) = sin(x)

:

Geogebra

: A_1 S_{AB}A1 SAB

XE Values, Change

XE Objects, Change

( ) a = 3, a = 5Enter

Move Enter

XE Input Bar History

XE Input Bar, Show input

XE Object:Insert:Name in Input Bar

XE Insert:Name in Input Bar

XE Name:Insert in Input Bar : F5

: F5

XE Object:Insert:Value in Input Bar

XE Insert:Value in Input Bar

XE Value:Insert in Input Bar : (, (1, 3), 3x 5y = 12)

(Mac OS: Ctrl-click)

F4 : F4

XE Object:Insert:Definition in Input Bar

XE Insert:Definition in Input Bar

XE Definition, insert in Input Bar : (, A = (4, 2), c = Circle[A, B])

Alt

F3: F3

3.2. XE Input Bar

XE Direct input

GeoGebra Enter-

3.2.1.

XE Number

3 GeoGebra ( r = 5.32 r).

GeoGebra . XE Decimal point

e

ee GeoGebra

XE Angle

radpi

Alt-O (MacOS: Ctrl-O)

Alt-P (MacOS: Ctrl-P) pi

: (,= 60) (= pi/3)

: GeoGebra /180

XE Degree to radians, Convert

XE Radians to degree, Convert

a = 30 = a a = 30

b = / b = 30

XE Slider

XE Arrow keys

()()

XE Angle, Limit value XE Number, Limit value XE Limit, Value of number

XE "Limit, Value of angle"

[min, max]( )

:

3.2.2. XE Point

XE Vector

()

:,

PvP = (1, 0) or v = (0, 5)

P P = (1; 0) v = (5; 90) GeoGebra

GeoGebra

:

ABMM = (A + B) / 2

v length = sqrt(v * v)

3.2.3. XE Line

XE Axis

, ()

:(:)

:

g : 3x + 4y = 2 g

t (t = 3)g : X = (-5, 5) + t (4, -3)

m = 2 b = -1 g: y = m x + b

XE Axes, xAxis and yAxis

xAxis yAxis

: Perpendicular[A, xAxis] A x

3.2.4. XE Conic section

x y ()

XE Conic section, Name

XE Name, Conic section

ell: 9 x^2 + 16 y^2 = 144

hyp: 9 x^2 16 y^2 = 144

par: y^2 = 4 x

c1c1: x^2 + y^2 = 25

c2c2: (x5)^2 + (y+2)^2 = 25

a = 4 b = 3 ell: b^2 x^2 + a^2 y^2 = a^2 b^2

3.2.5. x XE Function

()

f

f(x) = 3 x^3 x^2

g

g(x) = tan(f(x))

sin(3 x) + tan(x)

: (, sin, cos, tan) XE Trigonometric functions

GeoGebra

f(x) f(x),f(x)

f(x) = 3 x^3 x^2g(x) = cos(f(x + 2))g

, ( )

XE Function, Limit to interval

XE Limit, Function to interval

[a,b],

3.2.6. XE Arithmetic operations

XE Pre-defined functions

()

XE "Addition"

+

-

XE "Multiplication"

* or

XE Scalar product

* or

XE "Complex multiplication"

XE "Multiplication, Complex"

XE "Division"

/

XE "Exponentiation"

^ or 2

XE "Factorial"

!

Gamma XE "Gamma function"

gamma( )

XE "Parentheses"

( )

x- XE "x-coordinate "

XE "Coordinates, x-coordinate"

x( )

y- XE "y-coordinate "

XE "Coordinates, y-coordinate"

y( )

XE "Absolute value"

abs( )

XE "Sign"

sgn( )

sqrt( )

XE "Cubic root"

cbrt( )

01 XE "Random"

random( )

exp( ) or x

ln( ) or log( )

(2) XE "Logarithm"

ld( )

(10) XE "Logarithm"

lg( )

XE "Cosine"

XE " Trigonometric function, Cosine"

cos( )

sin( )

XE "Tangent"

XE " Trigonometric function, Tangent"

tan( )

XE "Trigonometric function, Arc cosine"

acos( )

XE "Trigonometric function, Arc sine"

asin( )

XE "Trigonometric function, Arc tangent"

atan( )

XE "Trigonometric function, Hyperbolic cosine"

cosh( )

XE "Trigonometric function, Hyperbolic sine"

sinh( )

XE "Trigonometric function, Hyperbolic tangent"

tanh( )

XE "Trigonometric function, Antihyperbolic cosine"

acosh( )

XE "Trigonometric function, Antihyperbolic sine"

asinh( )

XE "Trigonometric function, Antihyperbolic tangent"

atanh( )

XE "Floor"

floor( )

XE "Ceiling"

ceil( )

XE "Round"

round( )

3.2.7. XE "Boolean, Variables"

GeoGebra true false a = true b = false Enter

XE "Boolean, Show variable"

() ()

: (0 1)

XE "Boolean, Operations"

GeoGebra

ab

==

a b a == b

!=

a b a != b

p class=""/pp class=""a < b/pp class=""/p

p class=""/pp class=""/pp class="">

a > b

= b

&&

a b

||

a b

!

a !a

a b

a b

3.2.8. XE "Lists"

XE "List Operations"

( )

L = {A, B, C} A, B, C

L = {(0, 0), (1, 1), (2, 2)}

XE "Lists, Compare"

list1 == list2 true false

list1 != list2 true false

XE "Lists, Apply functions"

XE "Lists, Apply arithmetic operations"

List1 + List2

List + Number

List1 List2

List Number

List1 * List2

List * Number

List1 / List2

List / Number

Number / List

List^2

sin(List) sin

3.2.9. XE "Matrices"

XE "Matrix operations"

GeoGebra

GeoGebra, {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}

XE "Matrices, Apply arithmetic operations"

Matrix1 + Matrix2

Matrix1 Matrix2

Matrix * Number

Matrix1 * Matrix2{{1, 2}, {3, 4}, {5, 6}} * {{1, 2, 3}, {4, 5, 6}} {{9, 12, 15}, {19, 26, 33}, {29, 40, 51}}

2x2 Matrix * Point():

{{1, 2}, {3, 4}} * (3, 4) A = (11, 25).

3x3 Matrix * Point(): {{1, 2, 3}, {4, 5, 6}, {0, 0, 1}} * (1, 2) A = (8, 20)(affine transformations)(homogenous coordinates): (x, y, 1) (x, y, 0): {{1, 2, 3}, {4, 5, 6}, {0, 0, 1}} * {1, 2, 1}.

( ):

Determinant[Matrix]

Invert[Matrix]

Transpose[Matrix]

3.2.10. XE "Complex numbers"

XE "Complex number operations"

GeoGebra

3 + 4i (3, 4) 3 + 4i

:

i i = (0, 1) 0 + 1i i ( q = 3 + 4i)

/(MacOS: Ctrl-click)

(2, 1) + (1, -2) (2 + 1i) + (1 2i) (3, -1) 3 1i.

(2, 1) - (1, -2) (2 + 1i) + (1 2i) (1, 3) 1 3i.

(2, 1) * (1, -2) (2 + 1i) * (1 2i) (4, -3) 4 3i.

(2, 1) / (1, -2) (2 + 1i) / (1 2i) (0, 1) 0 + 1i.

: (2, 1)*(1, -2)

GeoGebra

3 + (4, 5) 3 + (4 + 5i) (7, 5) 7 + 5i.

3 - (4, 5) 3 - (4 + 5i) (-1, -5) -1 - 5i.

3 / (0, 1) 3 / (0 + 1i) (0, -3) 0 -3i.

3 * (1, 2) 3 * (1 + 2i) (3, 6) 3 -6i.

3.3. XE " Commands "

: S

: g h S = Intersect[g, h] ( ).

: XE " Index " : A_1A1 S_{AB} SAB.

XE " Command, Automatic completion "

GeoGebraGeoGebra

Enter

GeoGebra

3.3.1. XE "General commands"

XE "ConstructionStep, Command"

ConstructionStep[]: Construction Protocol

ConstructionStep[Object]: Construction Protocol

XE "Delete, Command"

Delete[Object]:

XE "Relation, Command"

Relation[Object a, Object b]: Object a Object b

: ,

3.3.2. XE "Boolean, Commands"

If XE "If, Command"

If[Condition, Object]: Objectundefined Object.

If[Condition, Object a, Object b]: Object aObject b

IsDefined XE "IsDefined, Command"

IsDefined[Object]: ( true or false)

IsInteger XE "IsInteger, Command"

IsInteger[Number]: ( true or false)

3.3.3. XE "Numbers, Commands"

XE "Affine ratio, Command"

AffineRatio[Point A, Point B, Point C]: A, B, C C = A + * AB

XE "Area, Command"

Area[Point A, Point B, Point C, ...]: A, B, C,

Area[Conic c]: c ()

: XE "Area, Definite integral"

XE "AxisStep, Command"

AxisStepX[]: X

AxisStepY[]: Y

: Corner Sequence (AxisStep) (Customizing Coordinate Axes and Grid).

XE "BinomialCoefficient, Command"

BinomialCoefficient[Number n, Number r]: n r

XE "Circumference, Command"

Circumference[Conic]:

:

XE "CrossRatio, Command"

CrossRatio[Point A, Point B, Point C, Point D]: A, B, C, D

= AffineRatio[B, C, D] / AffineRatio[A, C, D]

XE "Curvature, Command"

Curvature[Point, Function]:

Curvature[Point, Curve]:

XE "Distance, Command"

Distance[Point A, Point B]: A B

Distance[Point, Line]:

Distance[Line g, Line h]: g h: 0

: Distance or Length

XE "FirstAxisLength, Command"

FirstAxisLength[Conic]: ()

XE "GCD, Command" XE "Greatest Common Divisor, Command"

UK English: HCF XE HCF, Tool

XE Highest Common Factor, Tool

GCD[Number a, Number b]: ab(UK-English: HCF = highest common factor)

GCD[List of numbers]: (UK-English: HCF = highest common factor)

XE "IntegerDivision, Command"

Div[Number a, Number b]: ab

XE "Integral, Command"

Integral[Function, Number a, Number b]: [a , b]l XE "Integral, Definite"

: X . XE "Area, Definite integral"

Integral[Function f, Function g, Number a, Number b]: [a, b]f(x)g(x)

: fg . XE "Area between two functions"

XE "Area, Definite integral"

: Indefinite Integral

XE "Iteration, Command"

Iteration[Function, Number x0, Number n]: x0 f n : f(x) = x^2 Iteration[f, 3, 2] (32)2 = 81

XE "LCM, Command"

LCM[Number a, Number b]: ab(UK English: LCM = lowest common multiple)

LCM[List of numbers]: (UK English: LCM = lowest common multiple)

XE "Length, Command"

Length[Vector]:

Length[Point A]: A

Length[Function, Number x1, Number x2]: fx1 x2

Length[Function, Point A, Point B]: fAB

: x

Length[Curve, Number t1, Number t2]: t1 t2

Length[Curve c, Point A, Point B]: c AB

Length[List]: L ()

: Distance or Length

XE "LinearEccentricity, Command"

LinearEccentricity[Conic]: :

XE "LowerSum, Command"

LowerSum[Function, Number a, Number b, Number n]: f [a,b] n :

XE "Minimum, Command"

XE "Maximum, Command"

Min[Number a, Number b]: a b

Max[Number a, Number b]: a b

XE "Modulo Function, Command"

XE "Remainder of division"

Mod[Integer a, Integer b]: a b

XE "Parameter, Command"

Parameter[Parabola]: p ()

XE "Perimeter, Command"

Perimeter[Polygon]:

XE "Radius, Command"

Radius[Circle]: c

XE "Random, Command"

XE "RandomBetween, Command"

XE "RandomBinomial, Command"

XE "RandomNormal, Command"

XE "RandomPoisson, Command"

RandomBetween[Min integer, Max integer]:

RandomBinomial[Number n of trials, Probability p]: (n,p)

RandomNormal[Mean, Standard deviation]: (m, s)

RandomPoisson[Mean]: (m)

XE "SecondAxisLength, Command"

SecondAxisLength[Conic]: ()

XE "Slope, Command"

Slope[Line]:

:

:

XE "TrapezoidalSum, Command"

UK English: TrapeziumSum XE "TrapeziumSum, Command"

TrapezoidalSum[Function, Number a, Number b, Number n of trapezoids]: f [a, b] n

:

XE "UpperSum, Command"

UpperSum[Function, Number a, Number b, Number n]: f [a,b] n

:

3.3.4. XE "Angles, Commands"

XE "Angle, Command"

Angle[Vector v1, Vector v2]:v1 v2( 0 and 360)

Angle[Line g, Line h]: gh( 0 and 360)

Angle[Point A, Point B, Point C]: BA BC (0 360), B

Angle[Point A, Point B, Angle ]: AB : Rotate[A, , B]

Angle[Conic]: c ()

Angle[Vector]: x- v

Angle[Point]: x-A

Angle[Number]: n (0 2pi)

Angle[Polygon]: p().

: XE "Angles, Polygon"

XE "Polygon, Angles"

: ()

3.3.5. XE "Points, Commands"

XE "Center, Command"

UK English: Centre XE "Centre, Command"

Center[Conic]:

:

:

XE "Centroid, Command"

Centroid[Polygon]: p

Corner XE "Corner, Command"

XE "Image, Corner"

Corner[Number n of Corner]: (n = 1, 2, 3, 4)Corner[Image, Number n of corner]: (n = 1, 2, 3, 4)

Corner[Text, Number n of corner]: (n = 1, 2, 3, 4)

: n=1 n=2 n =3 n=4

XE "Extremum, Command"

UK English: TurningPoint XE "TurningPoint, Command"

Extremum[Polynomial]:

XE "Focus, Command"

Focus[Conic]: c ()

XE "InflectionPoint, Command"

InflectionPoint[Polynomial]: f .

XE "Intersect, Command"

Intersect[Line g, Line h]: g h

Intersect[Line, Conic]: g c (2 )

Intersect[Line, Conic, Number n]: g c n

Intersect[Conic c1, Conic c2]: c d (4 )

Intersect[Conic c1, Conic c2, Number n]: c d n

Intersect[Polynomial f1, Polynomial f2]: f1 f2

Intersect[Polynomial f1, Polynomial f2, Number n]: f1 f2 n

Intersect[Polynomial, Line]: f g

Intersect[Polynomial, Line, Number n]: f g n

Intersect[Function f, Function g, Point A]: f g A ()

Intersect[Function, Line, Point A]: f g A ()

:

XE "Midpoint, Command"

Midpoint[Point A, Point B]: A B

Midpoint[Segment]: s

:

XE "Point, Command"

Point[Line]:

Point[Conic]: (: )

Point[Function]: f

Point[Polygon]: p

Point[Vector ]: v

Point[Point, Vector]: Pv

:

XE "Root, Command"

Root[Polynomial]: f

Root[Function, Number a]: f a()

Root[Function, Number a, Number b]: f [a, b] (FalsePosition Method)

XE "Vertex, Command"

Vertex[Conic]: ()

3.3.6. XE "Vectors, Commands"

XE "CurvatureVector, Command"

CurvatureVector[Point, Function]: f A

CurvatureVector[Point , Curve]: c A

XE "Direction, Command"

Direction[Line]: g

: ax + by = c (b, - a)

XE "PerpendicularVector, Command"

PerpendicularVector[Line]: g

: ax + by = c (a, b)

PerpendicularVector[Vector v]: v

: (a, b)(- b, a)

XE "UnitPerpendicularVector, Command"

UnitPerpendicularVector[Line]: g

UnitPerpendicularVector[Vector]: v

XE "UnitVector, Command"

UnitVector[Line]: g

UnitVector[Vector]: v

XE "Vector, Command"

Vector[Point A, Point B]: A B

Vector[Point]: A

:

3.3.7. XE "Segments, Commands"

XE "Segment, Command"

Segment[Point A, Point B]: A B

Segment[Point A, Number a]: A a

:

3.3.8. XE "Rays, Commands"

XE "Ray, Command"

Ray[Point A, Point B]: A B

Ray[Point, Vector v]: A v

: ()

3.3.9. XE "Polygons, Commands"

XE "Polygon, Command"

Polygon[Point A, Point B, Point C,...]: A, B, C,

Polygon[Point A, Point B, Number n]: n ( A B)

:

3.3.10.

XE "AngleBisector, Command"

AngleBisector[Point A, Point B, Point C]: ABC

: B

AngleBisector[Line g, Line h]: gh

:

Asymptote[Hyperbola]: h

Axes[Conic]: c

Diameter[Line, Conic]: cg

Diameter[Vector, Conic]: cv

Directrix[Parabola]: p

FirstAxis[Conic]: c

Line[Point A, Point B]: AB

Line[Point, Line]: Ag

Line[Point, Vector v]: Av

:

XE "Perpendicular, Command"

Perpendicular[Point, Line]: Ag

Perpendicular[Point, Vector]: Av

:

PerpendicularBisector[Point A, Point B]: AB

PerpendicularBisector[Segment]:

:

Polar[Point, Conic]: c

:

SecondAxis[Conic]: c

XE "Tangent, Command"

Tangent[Point, Conic]: cA()

Tangent[Line, Conic]: cg

Tangent[Number a, Function]: f(x)x=a

Tangent[Point A, Function]: f(x)x=x(A)

Tangent[Point, Curve]: cA

:

3.3.11.

Circle[Point M, Number r]: Mr

Circle[Point M, Segment]: Ms

Circle[Point M, Point A]: MA

Circle[Point A, Point B, Point C]: ABC

: Compass, Circle with Center through Point, Circle with Center and Radius, and Circle through Three Points

XE "Conic, Command"

Conic[Point A, Point B, Point C, Point D, Point E]: ABCDE:

: ()

Ellipse[Point F, Point G, Number a]: F,Ga: 2aFG

Ellipse[Point F, Point G, Segment]: F,Gs

Ellipse[ Point A, Point B, Point C]: A,BC

:

Hyperbola[Point F, Point G, Number a]: F,Ga: : 0 < 2a < FG

Hyperbola[Point F, Point G, Segment]: F,Gs

Hyperbola[Point A, Point B, Point C]: A,BC

:

XE "OsculatingCircle, Command"

OsculatingCircle[Point, Function]: fA

OsculatingCircle[Point, Curve]: cA

XE "Parabola, Command"

Parabola[Point F, Line g]: Fg

:

3.3.12.

XE "Conditional functions, Command"

If(If) XE "If, command"

: derivativesintegrals

:

f(x) = If[x < 3, sin(x), x^2]

sin(x) x < 3

x2 x 3.

a 3 b 0 a3b0

: ( , , )

()

Derivative[Function]: f(x)

Derivative[Function, Number n]: f(x)n

: f'(x) Derivative[f],f''(x)Derivative[f, 2]

Expand[Function]: : Expand[(x + 3)(x - 4)] f(x) = x2 - x - 12

XE "Factor, Command"

UK English: Factorise XE "Factorise, Command"

Factor[Polynomial]: : Factor[x^2 + x - 6] f(x) = (x-2)(x+3)

Function[Function, Number a, Number b]: f [a, b]

:

: f(x) = Function[x^2, -1, 1] x2 [-1, 1] g(x) = 2 f(x), g(x) = 2 x2, [-1, 1]

XE "Integral, Command"

Integral[Function]: f(x)

: Definite integral

Polynomial[Function]: f

: Polynomial[(x - 3)^2] x2 - 6x + 9

Polynomial[List of n points]: nn-1

XE "Simplify, Command"

Simplify[Function]:

:

Simplify[x + x + x] f(x) = 3x

Simplify[sin(x) / cos(x)] f(x) = tan(x)

Simplify[-2 sin(x) cos(x)] f(x) = sin(-2 x)

TaylorPolynomial[Function, Number a, Number n]: f(x)x=an

3.3.13.

XE "Curve, Command"

Curve[Expression e1, Expression e2, Parameter t, Number a, Number b]: (e1, e2)e1e2 (tt [a, b]: c = Curve[2 cos(t), 2 sin(t), t, 0, 2 pi]

:

: c(3)t=3

: ( ).ab( ).

Curvature[Point, Curve]: XE "Curvature:Command"

XE "Command:Curvature"

CurvatureVector[Point, Curve]: XE "Curvature:Curvature Vector, command"

XE "Command:CurvatureVector"

Derivative[Function]: f(x)

Derivative[Function, Number n]: f(x)n

Length[Curve, Number t1, Number t2]: t1 t2

Length[Curve c, Point A, Point B]: c AB

OsculatingCircle[Point, Curve]: cA

Tangent[Point, Curve]: cA

3.3.14.

:

Arc[Conic, Point A, Point B]: cA,B

:

Arc[Conic, Number t1, Number t2]: ct1t2c:

: (r cos(t), r sin(t)) r

: (a cos(t), b sin(t)) ab

XE "CircularArc, Command"

CircularArc[Point M, Point A, Point B]: MAB

: B

: Circular Arc with Center between Two Points

XE "CircularSector, Command"

CircularSector[Point M, Point A, Point B]: MAB

: B

: Circular Sector with Center between Two Points

CircumcircularArc XE "CircumcircularArc, Command"

CircumcircularArc[Point A, Point B, Point C]: A,B,C

CircumcircularSector XE "CircumcircularSector, Command"

CircumcircularSector[Point A, Point B, Point C]: A,B,C

XE "Sector, Command"

Sector[Conic, Point A, Point B]:cA,B

: .

Sector[Conic, Number t1, Number t2]: ct1t2c:

: (r cos(t), r sin(t)) r

: (a cos(t), b sin(t)) ab

XE "Semicircle, Command"

Semicircle[Point A, Point B]: AB

:

3.3.15. XE "Text, Commands"

XE "FractionText, Command"

FractionText[Number]: Graphics View (LaTeX): a: y = 1.5 x + 2 , FractionText[Slope[a]] 3/2.

LaTeX XE "LaTeX, Command"

LaTeX[Object]: LaTeX: a = 2 f(x) = a x2, LaTeX[f] 2 x2 ( LaTeX text)

LaTeX[Object, Boolean]: LaTeX: a = 2 and f(x) = a x2,

LaTeX[f, true] 2 x2 (as a LaTeX text)

LaTeX[f, false] a x2 (as a LaTeX text)

XE "LetterToUnicode, Command"

LetterToUnicode["Letter"]: : : LetterToUnicode["a"] 97

XE "Name, Command"

Name[Object]: : Object

XE "Object, Command"

Object[Name of object as text]: Returns the object for a given name which is given as a text (static and/or dynamic).

: Name .

: A1, A2, ... , A20 n = 2, Object["A" + n] A2.

TableText XE "TableText, Command"

TableText[List 1, List 2, List 3,...]: :

:

TableText[{x^2, x^3, x^4}] TableText[Sequence[i^2, i, 1, 10]]

TableText[List 1, List 2, List 3,..., "Alignment of text"]: texttextAlignment of text text: "vl", "vc", "vr", "v", "h", "hl", "hc", "hr". "hl".

"v" = , i.e. lists are columns

"h" = , i.e. lists are rows

"l" =

"r" =

"c" =

:TableText[{1,2,3,4},{1,4,9,16},"v"] textTableText[{1,2,3,4},{1,4,9,16},"h"] textTableText[{11.2,123.1,32423.9,"234.0"},"r"] text

XE "Text, Command"

Text[Object]: : ,

: a = 2 c = a2, Text[c] "4".

Text[Object, Boolean]:

: a = 2 c = a2,

Text[c, true] "4".

Text[c, false] "a2"

Text[Object, Point]:

: Text["hello", (2, 3)] hello(2,3)

Text[Object, Point, Boolean]:

XE "TextToUnicode, Command"

TextToUnicode["Text"]: text

:

TextToUnicode["Some text"] {83, 111, 109, 101, 32, 116, 101, 120, 116}.

text1 "hello", TextToUnicode[text1] {104, 101, 108, 108, 111}.

XE "UnicodeToLetter, Command"

UnicodeToLetter[Integer]: Graphics View: UnicodeToText[97] text "a".

XE "UnicodeToText, Command"

UnicodeToText[List of Integers]: : UnicodeToText[{104, 101, 108, 108, 111}] text "hello".

3.3.16.

Locus[Point Q, Point P]: Q(P) : P()

3.3.17. XE "Lists, Commands"

XE "Sequences, Commands"

Append XE "Append, Command"

Append[List, Object]:

: Append[{1, 2, 3}, (5, 5)] {1, 2, 3, (5, 5)}

Append[Object, List]:

: Append[(5, 5), {1, 2, 3}] {(5, 5), 1, 2, 3}

CountIf XE "CountIf, Command"

CountIf[Condition, List]: :CountIf[x < 3, {1, 2, 3, 4, 5}] 2

CountIf[x