Naming Objects
You can assign a certain name to an object when you create it using the //Input Bar//:

Points: In GeoGebra, points are always named using upper case letters. Just type in the name (e. g., A, P) and an equal sign in front of the coordinates or commands.Examples: C = (2, 4), P = (1; 180°), Complex = 2 + i

Vectors: In order to distinguish between points and vectors, vectors need to have a lower case name in GeoGebra. Again, type in the name (e. g., v, u) and an equal sign in front of the coordinates or commands.Examples: v = (1, 3), u = (3; 90°), complex = 1 – 2i

Lines, circles, and conic sections: These objects can be named by typing in the name and a colon in front of their equations or commands.Examples: g: y = x + 3, c: (x-1)^2 + (y – 2)^2 = 4, hyp: x^2 – y^2 = 2

Functions: You can name functions by typing, for example, f(x) = or g(x)= in front of the function’s equation or commands. Examples: h(x) = 2 x + 4, q(x) = x^2, trig(x) = sin(x)

Display Input Bar History

After placing the cursor in the //Input Bar// you can use the ↑ up and ↓ down arrow keys of your keyboard in order to navigate through prior input step by step. Note: Click on the little question mark to the left of the Input Bar in order to display the help feature for theInput Bar.

Statistics Commands

BarChart[Start Value, End Value, List of Heights]: Creates a bar chart over the given interval where the number of bars is determined by the length of the list whose elements are the heights of the bars. Example: BarChart[10, 20, {1,2,3,4,5} ] gives you a bar chart with five bars of specified height in the interval [10, 20].

BarChart[Start Value a, End Value b, Expression, Variable k, From Number c, To Number d]: Creates a bar chart over the given interval [a, b], that calculates the bars’ heights using the expression whose variable k runs from number c to number d. Example: If p = 0.1, q = 0.9, and n = 10 are numbers, then BarChart[ -0.5, n + 0.5, BinomialCoefficient[n,k]*p^k*q^(n-k), k, 0, n ] gives you a bar chart in the interval [-0.5, n+0.5]. The heights of the bars depend on the probabilities calculated using the given expression. BarChart[Start Value a, End Value b, Expression, Variable k, From Number c, To Number d, Step Width s]: Creates a bar chart over the given interval [a, b], that calculates the bars’ heights using the expression whose variable k runs from number c to number d using step width s. BarChart[List of Raw Data, Width of Bars]: Creates a bar chart using the given raw data whose bars have the given width.Example: BarChart[ {1,1,1,2,2,2,2,2,3,3,3,5,5,5,5}, 1] BarChart[List of Data, List of Frequencies]: Creates a bar chart using the list of data with corresponding frequencies. Note: The List of data must be a list where the numbers go up by a constant amount.Examples:

BarChart[{10,11,12,13,14}, {5,8,12,0,1}]

BarChart[{5, 6, 7, 8, 9}, {1, 0, 12, 43, 3}]

BarChart[{0.3, 0.4, 0.5, 0.6}, {12, 33, 13, 4}]

BarChart[List of Data , List of Frequencies, Width of Bars w]: Creates a bar chart using the list of data and corresponding frequencies whose bars are of width w. Note: The List of data must be a list where the numbers go up by a constant amountExamples:

BarChart[{10,11,12,13,14}, {5,8,12,0,1}, 0.5] leaves gaps between bars.

BarChart[{10,11,12,13,14}, {5,8,12,0,1}, 0] produces a line graph.

BoxPlot

BoxPlot[yOffset, yScale, List of Raw Data]: Creates a box plot using the given raw data and whose vertical position in the coordinate system is controlled by variable yOffset and whose height is influenced by factor yScale.Example: BoxPlot[0, 1, {2,2,3,4,5,5,6,7,7,8,8,8,9}] BoxPlot[yOffset, yScale, Start Value a, Q1, Median, Q3, End Value b]: Creates a box plot for the given statistical data in interval [a, b].

CorrelationCoefficient

CorrelationCoefficient[List of x-Coordinates, List of y-Coordinates]: Calculates the product moment correlation coefficient using the given x- and y-coordinates. CorrelationCoefficient[List of Points]: Calculates the product moment correlation coefficient using the coordinates of the given points.

Covariance

Covariance[List 1 of Numbers, List 2 of Numbers]: Calculates the covariance using the elements of both lists. Covariance[List of Points]: Calculates the covariance using the x- and y-coordinates of the points.

FitLine

FitLine[List of Points]: Calculates the y on x regression line of the points. FitLineX[List of Points]: Calculates the x on y regression line of the points. Note: Also see tool //Best Fit Line//

Other Fit Commands

FitExp[List of Points]: Calculates the exponential regression curve. FitLog[List of Points]: Calculates the logarithmic regression curve. FitLogistic[List of Points]: Calculates the regression curve in the form a/(1+b e^(-kx)). Note: The first and last data point should be fairly close to the curve. The list should have at least 3 points, preferably more. FitPoly[List of Points, Degree n of Polynomial]: Calculates the regression polynomial of degree n. FitPow[List of Points]: Calculates the regression curve in the form a xb. Note: All points used need to be in the first quadrant of the coordinate system. FitSin[List of Points]: Calculates the regression curve in the form a + b sin(cx + d). Note: The list should have at least 4 points, preferably more. The list should cover at least two extremal points. The first two local extremal points should not be too different from the absolute extremal points of the curve.

Histogram

Histogram[List of Class Boundaries, List of Heights]: Creates a histogram with bars of the given heights. The class boundaries determine the width and position of each bar of the histogram. Example: Histogram[{0, 1, 2, 3, 4, 5}, {2, 6, 8, 3, 1}] creates a histogram with 5 bars of the given heights. The first bar is positioned at the interval [0, 1], the second bar is positioned at the interval [1, 2], and so on. Histogram[List of Class Boundaries, List of Raw Data]: Creates a histogram using the raw data. The class boundaries determine the width and position of each bar of the histogram and are used to determine how many data elements lie in each class. Example: Histogram[{1, 2, 3, 4},{1.0, 1.1, 1.1, 1.2, 1.7, 2.2, 2.5, 4.0}] creates a histogram with 3 bars, with the heights 5 (first bar), 2 (second bar), and 1 (third bar).

InverseNormal

InverseNormal[Mean μ, Standard Deviation σ, Probability P]: Calculates the function Φ-1(P) * σ + μ where Φ -1 is the inverse of the probability density function Φ for N(0,1). Note: Returns the x-coordinate with the given probability to the left under the normal distribution curve.

Mean commands

Mean[List of Numbers]: Calculates the mean of the list elements. MeanX[List of Points]: Calculates the mean of the x-coordinates of the points in the list. MeanY[List of Points]: Calculates the mean of the y-coordinates of the points in the list.

Median

Median[List of Numbers]: Determines the median of the list elements.

Mode

Mode[List of Numbers]: Determines the mode(s) of the list elements. Examples:

Mode[{1,2,3,4}] returns an empty list {}.

Mode[{1,1,1,2,3,4}] returns the list {1} .

Mode[{1,1,2,2,3,3,4}] returns the list {1, 2, 3}.

Normal

Normal[Mean μ, Standard Deviation σ, Variable Value x]: Calculates the function Φ((x – μ) / σ) where Φ is the probability density function for N(0,1) . Note: Returns the probability for a given x-coordinate value (or area under the normal distribution curve to the left of the given x-coordinate).

Quartile commands

Q1[List of Numbers]: Determines the lower quartile of the list elements. Q3[List of Numbers]: Determines the upper quartile of the list elements.

SD

SD[List of Numbers]: Calculates the standard deviation of the numbers in the list.

Sigma commands

SigmaXX[List of Numbers]: Calculates the sum of squares of the given numbers. Example: In order to work out the variance of a list you may use SigmaXX[list]/Length[list] - Mean[list]^2. SigmaXX[List of Points]: Calculates the sum of squares of the x-coordinates of the given points. SigmaXY[List of x-Coordinates, List of y-Coordinates]: Calculates the sum of the products of the x- and y-coordinates. SigmaXY[List of Points]: Calculates the sum of the products of the x- and y-coordinates. Example: You can work out the covariance of a list of points using SigmaXY[list]/Length[list] - MeanX[list] * MeanY[list]. SigmaYY[List of Points]: Calculates the sum of squares of y-coordinates of the given points.

Commands for statistic quantities

Sxx[List of Numbers]: Calculates the statistic Σ(x2) -Σ(x) * Σ(x)/n. Sxx[List of Points]: Calculates the statistic Σ(x2) -Σ(x) * Σ(x)/n using the x-coordinates of the given points. Sxy[List of Numbers, List of Numbers]: Calculates the statistic Σ(xy) -Σ(x) * Σ(y)/n. Sxy[List of Points]: Calculates the statistic Σ(xy) -Σ(x) * Σ(y)/n. Syy[List of Points]: Calculates the statistic Σ(y2) -Σ(y) * Σ(y)/n using the y-coordinates of the given points.

Note: These quantities are simply unnormalized forms of the variances and covariance of X and Y given by Sxx = N var(X), Syy = N var(Y), and Sxy = N cov(X, Y). Example: You can work out the correlation coefficient for a list of points using Sxy[list] / sqrt(Sxx[list] Syy[list]).

Variance

Variance[List of Numbers]: Calculates the variance of list elements. www.geogebra.org

Creating a User Defined Tool

First, create the construction your tool should be able to create later on. In the //Tools// menu, click on //Create New Tool// in order to open the corresponding dialog box. Now you need to fill in the three tabs Output Objects, Input Objects, and Name and Icon in order to create your custom tool.

Example:
Create a Square-tool that creates a square whenever you click on two existing points or on two empty spots in the //Graphics View//.

Construct a square starting with two points A and B. Construct the other vertices and connect them with the tool Polygon to get the square poly1.

Specify the Output Objects: Click on the square or select it from the drop down menu. Also, specify the edges of the square as Output Objects.

Specify the Input Objects: GeoGebra automatically specifies the Input Objects for you (here: points A and B). You can also modify the selection of input objects using the drop down menu or by clicking on them in your construction.

Specify the Tool Name and Command Name for your new tool.Note: The Tool Name will appear in GeoGebra’s Toolbar, while the Command Name can be used in GeoGebra’s Input Bar.

You may also enter text to be shown in the Toolbar Help.

You can also choose an image from you computer for the Toolbar icon. GeoGebra resizes your image automatically to fit on a Toolbar button.

Saving a User Defined Tool

You can save your custom tools so you can reuse them in other GeoGebra constructions. In the //Tools// menu, select [[http://www.geogebra.org/help/docuen/topics/137.html#_Manage_Tools…|Manage Tools]]. Then, select the custom tool you want to save from the appearing list. Click on button Save As… in order to save your custom tool on your computer. Note: User defined tools are saved as files with the file name extension GGT so you can distinguish custom tool files from usual GeoGebra files (GGB).

Accessing a User Defined Tool

If you open a new GeoGebra interface using item //New// from the //File// menu, after you created a custom tool, it will still be part of the GeoGebra Toolbar. However, if you open a new GeoGebra window (item //New Window// from the File menu), or open GeoGebra on another day, your custom tools won’t be part of the Toolbar any more.

There are different ways of making sure that your user defined tools are displayed in the Toolbar of a new GeoGebra window:

After creating a new user defined tool you can save your settings using item //Save Settings// from the //Options// menu. From now on, your customized tool will be part of the GeoGebra Toolbar. Note: You can remove the custom tool from the Toolbar after opening item [[http://www.geogebra.org/help/docuen/topics/138.html#_Customize_Toolbar…|Customize Toolbar…]] from the //Tools// menu. Then, select your custom tool from the list of tools on the left hand side of the appearing dialog window and click button Remove >. Don’t forget to save your settings after removing the custom tool.

After saving your custom tool on your computer (as a GGT file), you can import it into a new GeoGebra window at any time. Just select item [[http://www.geogebra.org/help/docuen/topics/87.html#_/_Open…|Open]] from the //File// menu and open the file of your custom tool. Note: Opening a GeoGebra tool file (GGT) in GeoGebra doesn’t affect your current construction. It only makes this tool part of the current GeoGebra Toolbar.

TableText - may relate to sequences etc - worth looking at.

Element Element[List, Number n]: Yields the nth element of the list. Note: The list can contain only elements of one object type (e. g., only numbers or only points).

First First[List] Returns the first element of the list. First[List, Number n of elements] Returns a new list that contains just the first n elements of the list.

Sequence Sequence[Expression, Variable i, Number a, Number b]: Yields a list of objects created using the given expression and the index i that ranges from number a to number b Example: L = Sequence[(2, i), i, 1, 5] creates a list of points whose y coordinates range from 1 to 5:L = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5)} Sequence[Expression, Variable i, Number a, Number b, Increment]: Yields a list of objects created using the given expression and the index i that ranges from number a to number b with given increment. Example: L = Sequence[(2, i), i, 1, 3, 0.5] creates a list of points whose 61 y coordinates range from 1 to 3 with an increment of 0.5: L = {(2, 1), (2, 1.5), (2, 2), (2, 2.5), (2, 3)}.
Note: Since the parameters a and b are dynamic you could use slider variables as well.

Perhaps I can get random motion with sequences and these:

Translate[Point, Vector ]: Translates the point by the vector.

Vector[Point A, Point B] Creates a vector from point A to point B.

Vector[Point] Returns the position vector of the given point.

http://wiki.geogebra.org/en/Category:Commands

Below are Quotes from http://www.geogebra.org/help/docuen/ that I currently require or am investigating.Please IGNORE this learning page.Naming ObjectsYou can assign a certain name to an object when you create it using the //Input Bar//:

Points: In GeoGebra, points are always named using upper case letters. Just type in the name (e. g.,A,P) and an equal sign in front of the coordinates or commands.Examples: C = (2, 4), P = (1; 180°), Complex = 2 + iVectors: In order to distinguish between points and vectors, vectors need to have a lower case name in GeoGebra. Again, type in the name (e. g.,v,u) and an equal sign in front of the coordinates or commands.Examples: v = (1, 3), u = (3; 90°), complex = 1 – 2iLines, circles, and conic sections: These objects can be named by typing in the name and a colon in front of their equations or commands.Examples: g: y = x + 3, c: (x-1)^2 + (y – 2)^2 = 4, hyp: x^2 – y^2 = 2Functions: You can name functions by typing, for example, f(x) = or g(x)= in front of the function’s equation or commands. Examples: h(x) = 2 x + 4, q(x) = x^2, trig(x) = sin(x)## Display

After placing the cursor in the //Input Bar// you can use the ↑Input BarHistoryupand ↓downarrow keys of your keyboard in order to navigate through prior input step by step.Note: Click on the little question mark to the left of the

Input Barin order to display thehelp feature for theInput Bar.## Statistics Commands

## BarChart[Start Value, End Value, List of Heights]: Creates a bar chart over the given interval where the number of bars is determined by the length of the list whose elements are the heights of the bars. Example: BarChart[10, 20, {1,2,3,4,5} ] gives you a bar chart with five bars of specified height in the interval [

BarChart[Start Value a, End Value b, Expression, Variable k, From Number c, To Number d]: Creates a bar chart over the given interval [10, 20].a, b], that calculates the bars’ heights using the expression whose variablekruns from numbercto numberd. Example: Ifp = 0.1,q = 0.9, andn = 10are numbers, then BarChart[ -0.5, n + 0.5, BinomialCoefficient[n,k]*p^k*q^(n-k), k, 0, n ] gives you a bar chart in the interval [-0.5, n+0.5]. The heights of the bars depend on the probabilities calculated using the given expression.BarChart[Start Value a, End Value b, Expression, Variable k, From Number c, To Number d, Step Width s]: Creates a bar chart over the given interval [

a, b], that calculates the bars’ heights using the expression whose variablekruns from numbercto numberdusing step widths.BarChart[List of Raw Data, Width of Bars]: Creates a bar chart using the given raw data whose bars have the given width.Example: BarChart[ {1,1,1,2,2,2,2,2,3,3,3,5,5,5,5}, 1]

BarChart[List of Data, List of Frequencies]: Creates a bar chart using the list of data with corresponding frequencies. Note: The List of data must be a list where the numbers go up by a constant amount.Examples:

- BarChart[{10,11,12,13,14}, {5,8,12,0,1}]
- BarChart[{5, 6, 7, 8, 9}, {1, 0, 12, 43, 3}]
- BarChart[{0.3, 0.4, 0.5, 0.6}, {12, 33, 13, 4}]

BarChart[List of Data , List of Frequencies, Width of Bars w]: Creates a bar chart using the list of data and corresponding frequencies whose bars are of widthw. Note: The List of data must be a list where the numbers go up by a constant amountExamples:## BoxPlot

BoxPlot[yOffset, yScale, List of Raw Data]: Creates a box plot using the given raw data and whose vertical position in the coordinate system is controlled by variableyOffsetand whose height is influenced by factoryScale.Example: BoxPlot[0, 1, {2,2,3,4,5,5,6,7,7,8,8,8,9}]BoxPlot[yOffset, yScale, Start Value a, Q1, Median, Q3, End Value b]: Creates a box plot for the given statistical data in interval [a, b].

## CorrelationCoefficient

CorrelationCoefficient[List of x-Coordinates, List of y-Coordinates]: Calculates the product moment correlation coefficient using the givenx- andy-coordinates.CorrelationCoefficient[List of Points]: Calculates the product moment correlation coefficient using the coordinates of the given points.

## Covariance

Covariance[List 1 of Numbers, List 2 of Numbers]: Calculates the covariance using the elements of both lists.Covariance[List of Points]: Calculates the covariance using the x- and y-coordinates of the points.

## FitLine

FitLine[List of Points]: Calculates theyonxregression line of the points.FitLineX[List of Points]: Calculates the

xonyregression line of the points.Note: Also see tool //Best Fit Line//

## Other Fit Commands

FitExp[List of Points]: Calculates the exponential regression curve.FitLog[List of Points]: Calculates the logarithmic regression curve.

FitLogistic[List of Points]: Calculates the regression curve in the form

a/(1+b e^(-kx)). Note: The first and last data point should be fairly close to the curve. The list should have at least 3 points, preferably more.FitPoly[List of Points, Degree n of Polynomial]: Calculates the regression polynomial of degree

n.FitPow[List of Points]: Calculates the regression curve in the form

a xb. Note: All points used need to be in the first quadrant of the coordinate system.FitSin[List of Points]: Calculates the regression curve in the form

a + b sin(cx + d). Note: The list should have at least 4 points, preferably more. The list should cover at least two extremal points. The first two local extremal points should not be too different from the absolute extremal points of the curve.## Histogram

Histogram[List of Class Boundaries, List of Heights]: Creates a histogram with bars of the given heights. The class boundaries determine the width and position of each bar of the histogram. Example: Histogram[{0, 1, 2, 3, 4, 5}, {2, 6, 8, 3, 1}] creates a histogram with 5 bars of the given heights. The first bar is positioned at the interval [0, 1], the second bar is positioned at the interval [1, 2], and so on.Histogram[List of Class Boundaries, List of Raw Data]: Creates a histogram using the raw data. The class boundaries determine the width and position of each bar of the histogram and are used to determine how many data elements lie in each class. Example: Histogram[{1, 2, 3, 4},{1.0, 1.1, 1.1, 1.2, 1.7, 2.2, 2.5, 4.0}] creates a histogram with 3 bars, with the heights 5 (first bar), 2 (second bar), and 1 (third bar).

## InverseNormal

InverseNormal[Mean μ, Standard Deviation σ, Probability P]: Calculates the functionΦ-1(P) * σ + μwhereΦ -1is the inverse of the probability density functionΦfor N(0,1). Note: Returns thex-coordinate with the given probability to the left under the normal distribution curve.## Mean commands

Mean[List of Numbers]: Calculates the mean of the list elements.MeanX[List of Points]: Calculates the mean of the

x-coordinates of the points in the list.MeanY[List of Points]: Calculates the mean of the

y-coordinates of the points in the list.## Median

Median[List of Numbers]: Determines the median of the list elements.## Mode

Mode[List of Numbers]: Determines the mode(s) of the list elements. Examples:{}.{1} .{1, 2, 3}.## Normal

Normal[Mean μ, Standard Deviation σ, Variable Value x]: Calculates the functionΦ((x – μ) / σ)whereΦis the probability density function for N(0,1) . Note: Returns the probability for a givenx-coordinate value (or area under the normal distribution curve to the left of the givenx-coordinate).## Quartile commands

Q1[List of Numbers]: Determines the lower quartile of the list elements.Q3[List of Numbers]: Determines the upper quartile of the list elements.

## SD

SD[List of Numbers]: Calculates the standard deviation of the numbers in the list.## Sigma commands

SigmaXX[List of Numbers]: Calculates the sum of squares of the given numbers. Example: In order to work out the variance of a list you may use SigmaXX[list]/Length[list] - Mean[list]^2.SigmaXX[List of Points]: Calculates the sum of squares of the

x-coordinates of the given points.SigmaXY[List of x-Coordinates, List of y-Coordinates]: Calculates the sum of the products of the

x- andy-coordinates.SigmaXY[List of Points]: Calculates the sum of the products of the x- and y-coordinates. Example: You can work out the covariance of a list of points using SigmaXY[list]/Length[list] - MeanX[list] * MeanY[list].

SigmaYY[List of Points]: Calculates the sum of squares of

y-coordinates of the given points.## Commands for statistic quantities

Sxx[List of Numbers]: Calculates the statisticΣ(x2) -Σ(x)*Σ(x)/n.Sxx[List of Points]: Calculates the statistic

Σ(x2) -Σ(x)*Σ(x)/nusing thex-coordinates of the given points.Sxy[List of Numbers, List of Numbers]: Calculates the statistic

Σ(xy) -Σ(x)*Σ(y)/n.Sxy[List of Points]: Calculates the statistic

Σ(xy) -Σ(x)*Σ(y)/n.Syy[List of Points]: Calculates the statistic

Σ(y2) -Σ(y)*Σ(y)/nusing they-coordinates of the given points.Note: These quantities are simply unnormalized forms of the variances and covariance of

XandYgiven bySxx = N var(X),Syy = N var(Y), andSxy = N cov(X, Y). Example: You can work out the correlation coefficient for a list of points using Sxy[list] / sqrt(Sxx[list] Syy[list]).## Variance

Variance[List of Numbers]: Calculates the variance of list elements.www.geogebra.org## Creating a User Defined Tool

First, create the construction your tool should be able to create later on. In the //Tools// menu, click on //Create New Tool// in order to open the corresponding dialog box. Now you need to fill in the three tabsOutput Objects,Input Objects, andName and Iconin order to create your custom tool.Example:

Create a Square-tool that creates a square whenever you click on two existing points or on two empty spots in the //Graphics View//.

AandB. Construct the other vertices and connect them with the tool Polygon to get the squarepoly1.Create New Tool]] in the //Tools// menu.Output Objects: Click on the square or select it from the drop down menu. Also, specify the edges of the square asOutput Objects.Input Objects: GeoGebra automatically specifies theInput Objectsfor you (here: pointsAandB). You can also modify the selection of input objects using the drop down menu or by clicking on them in your construction.Tool NameandCommand Namefor your new tool.Note: TheTool Namewill appear in GeoGebra’sToolbar, while theCommand Namecan be used in GeoGebra’sInput Bar.Toolbar Help.Toolbaricon. GeoGebra resizes your image automatically to fit on aToolbarbutton.## Saving a User Defined Tool

You can save your custom tools so you can reuse them in other GeoGebra constructions. In the //Tools// menu, select [[http://www.geogebra.org/help/docuen/topics/137.html#_Manage_Tools…|Manage Tools]]. Then, select the custom tool you want to save from the appearing list. Click on buttonSave As…in order to save your custom tool on your computer.Note: User defined tools are saved as files with the file name extension

GGTso you can distinguish custom tool files from usual GeoGebra files (GGB).## Accessing a User Defined Tool

If you open a new GeoGebra interface using item //New// from the //File// menu, after you created a custom tool, it will still be part of the GeoGebraToolbar. However, if you open a new GeoGebra window (item //New Window// from theFilemenu), or open GeoGebra on another day, your custom tools won’t be part of theToolbarany more.There are different ways of making sure that your user defined tools are displayed in the

Toolbarof a new GeoGebra window:Toolbar. Note: You can remove the custom tool from theToolbarafter opening item [[http://www.geogebra.org/help/docuen/topics/138.html#_Customize_Toolbar…|Customize Toolbar…]] from the //Tools// menu. Then, select your custom tool from the list of tools on the left hand side of the appearing dialog window and click buttonRemove >. Don’t forget to save your settings after removing the custom tool.Open]] from the //File// menu and open the file of your custom tool. Note: Opening a GeoGebra tool file (GGT) in GeoGebra doesn’t affect your current construction. It only makes this tool part of the current GeoGebraToolbar.TableText - may relate to sequences etc - worth looking at.

ElementElement[List, Number n]: Yields thenthelement of the list.Note: The list can contain only elements of one object type (e. g., only numbers or only points).FirstFirst[List]Returns the first element of the list.First[List, Number n of elements]Returns a new list that contains just the firstnelements of the list.SequenceSequence[Expression, Variable i, Number a, Number b]: Yields a list of objects created using the given expression and the index

that ranges from number aito numberbExample:

L = Sequence[(2, i), i, 1, 5] creates a list of points whosecoordinates range from 1 to 5:yL = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5)}Sequence[Expression, Variable i, Number a, Number b, Increment]: Yields a list of objects created using the given expression and the index

that ranges frominumber

with given increment.ato numberbExample:

L = Sequence[(2, i), i, 1, 3, 0.5]creates a list of points whose 61 y coordinates range from 1 to 3 with an increment of 0.5: L = {(2, 1), (2, 1.5), (2, 2), (2, 2.5), (2, 3)}.

Note: Since the parameters

variables as well.aandbare dynamic you could usesliderPerhaps I can get random motion with sequences and these:## Translate[Point, Vector ]: Translates the point by the vector.

## Vector[Point A, Point B] Creates a vector from point

Ato pointB.## Vector[Point] Returns the position vector of the given point.

Work in progress...