help for geogebra · web view統計指令 57 3.3.20. 試算表指令 61 3.3.21. 矩陣指令 61 4....
TRANSCRIPT
Help for GeoGebra
GeoGebra 3.2
Markus Hohenwarter and Judith Hohenwarterwww.geogebra.org
GeoGebra3.2
2009-10-30
Markus Hohenwarter, [email protected]
Judith Hohenwarter, [email protected]
GeoGebra
http://www.geogebra.org
http://www.geogebra.org/help/search.html
3.2
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