GeoGebra for Figures, Interactive Simulations, andRandomized Problem-solving

Lenore Horner7 Hills, Cincinnati, OH

Lenore.Horner@7hills.org

ISAAPT April 11, 2015Principia College

Abstract

GeoGebra is freeware designed for interactive two and three-dimensional mathematics: alge-bra, geometry, calculus, and statistics. It has a very friendly learning curve yet under the hoodhas an astonishing amount of power. Applets can be uploaded to GeoGebraTube.org where stu-dents can access them on laptops or tablets.

This workshop will illustrate various ways in which GeoGebra is useful to a physics teacher.Participants will be walked through setting up some of their own GeoGebra applets to acquaintthem with the possibilities available. Participants should bring a laptop with a recent versionof GeoGebra already installed from http://www.geogebra.org/download. No prior knowledgeof GeoGebra is expected. The goal is to acquaint users both with the possibilities and with thebasic tools available.

Contents1 Geogebra 2

1.1 Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 What it runs on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Creating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Using - GeoGebraTube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Obtaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Examples 32.1 Static Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Dynamic Illustrations of Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Randomized Problems with Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Exercises 43.1 Basic Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2 Useful Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3 Modifying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.4 Working in 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.5 Simple Ray Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

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3.5.1 Cleaning Things Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.5.2 Learning from the Ray Diagram . . . . . . . . . . . . . . . . . . . . . . . . 123.5.3 Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.5.4 Working with Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.5.5 Using the Spreadsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.6 Do Something Often - Make a New Tool . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Resources 164.1 instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.2 learning from other peoples’ work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.1 Applets in GeoGebraTube can be downloaded, opened, and modified orused to learn how to do something. . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.2 A selection of people to learn from . . . . . . . . . . . . . . . . . . . . . . . 17

5 Sharing 18

1 Geogebra1.1 Capabilities

• interactive interface

• point-and-click toolbar (with tooltips en-abled by default)

• can type commands as an alternative

• gentle learning curve (quick demo of userinterface)

• pretty powerful (one of the Walch appletsand a Riemann’s sum to show advancedfeatures)

• create and load to GeoGebraTube tohave html5 materials for students (If you

just need pre-made stuff, there are a cou-ple of nice collections of html5 appletsgrowing at http://www.walter-fendt.de/html5/phen/ and http://www.tandftechnology.com/index.html.)

• geometry• algebra• spreadsheets• graphing• statistics• calculus

See http://www.geogebra.org/about for a little more detail and an impressive list ofawards.

Started by Markus Hohenwarter at the University of Linz (Austria) in 2005(?).

1.2 What it runs on1.2.1 Creatingdesktop / laptop operating systems

• Linux• Windows• OS Xtablets (phones says coming soon)• Windows tablet• iOS

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• AndroidIt’s really a lot easier to create on a desktop / laptop.

1.2.2 Using - GeoGebraTubeIn principle, anything that has a web browser that uses html5 correctly works with GeoGe-braTube (http://tube.geogebra.org/). In practice, a bigger window is often helpful and theiPad at least can be slow.

1.3 ObtainingGeoGebra is open-source software freely available for non-commercial users. Download fromhttp://www.geogebra.org/download.

2 Examples2.1 Static DrawingsT04-spring.ggb at http://tube.geogebra.org/material/show/id/984705

2.2 Dynamic Illustrations of Concepts• ray diagram: DoubleLenses.ggb at http://tube.geogebra.org/student/b871227#

material/977919

• image formation: Mirror-spherical-multiray.ggb at http://tube.geogebra.org/student/b871227#material/817161

• wave optics: Interference.ggb at http://tube.geogebra.org/student/b871311#material/871535

• projectile motion with drag: Projectile.ggb at• 3D: RHR-hand.ggb at http://tube.geogebra.org/student/b977927#material/718975• 3D: solenoids.ggb at http://tube.geogebra.org/student/m988531

2.3 Randomized Problems with SolutionslogPractice1.ggb at http://tube.geogebra.org/student/b871311#material/613613

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3 Exercises3.1 Basic Navigation

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Tips:• The esc key changes your tool to the arrow (for moving or selecting).• Zooming and panning can also be done with mouse and control keys

– mouse scroll up and down zooms in and out– shift drag anywhere but an axis pans– shift drag on an axis rescales that axis

• Control-click or right-click or two-finger-tap on objects to access a contextual menu includ-ing Object Properties. I’m going to call this ctrl-click even though that may not be whatyou actually do (and isn’t what I actually do on my laptop the way I have my trakcpadconfigured).

• In the Algebra View, click on the circle left of each object to toggle between visible (circleis blue) and hidden (circle is empty).

• Capitalization matters. Agecoefficient̸=agecoefficient.• If you create an object and can’t find it in either the Graphics or the Algebra view, ctrl-

click any object and select Object Properties. Then find your missing object in that controlpanel. It may be off-screen, buried, or hidden.

• The different views can be resized by dragging on boundaries marked with a dot in themiddle.

• The different views can be rearranged by clicking on the view title bar and dragging it. Anoutline shows where the view will land if you let go at any particular mouse location.

3.2 Useful Tools• point - A point placed in empty space will be moveable. These points are (usually)

bright blue. A point placed on an axis, line, function, or conic section will move only alongthat axis, line,.... These points are (usually) light blue. Points which cannot be moved(usually) default to dark gray.

• intersection - Click the two objects that intersect. If they intersect twice, you will gettwo points. Hide the one you don’t want. When there are infinitely many intersections (sinand cos for instance), a nearby intersection is picked; there may be a delay while GeoGebrafigures out which intersection is closest. If the one you want doesn’t get picked, undo andtry a different location.

• midpoint - Select this tool and then select two points or a line segment and GeoGe-bra will create a point in the middle.

• line - Select the line tool and then select any two points to define that line. If eitheror both of the points move, the line will follow. The line will always run off the edges ofthe screen to indicate that it is infinite.

• line segment - works the same way a line does except that the ends are defined by thepoints.

• ray - A ray starts at the first point chosen and pass through and beyond the secondpoint chosen. Does not have an arrowhead on it. If we want arrowheads, we need to usethe vector tool .

• circular arc - Click the center of the circle the arc is a piece of first. Then click twomore points to define the ends of the arc. The second point defines the radius of the circle.

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3.3 Modifying1. Go to http://tube.geogebra.org/material/show/id/984705.2. Click the download button.3. Double-click the file wherever download put it on your computer or open GeoGebra and

then use File -> Open to find the file and open it. (Details will depend on operating sys-tem.)

4. You should have something like .

5. Go to View -> Algebra and click. You should end up

with something like .

6. Well that’s not very helpful. Let’s make the window bigger so we can see enough to func-tion. On a Mac I just click and drag the bottom-right corner or click and drag the rightside and then the bottom, or option click the green button. Enlarging the window is anoperating system function so what you have to do to get a bigger window will dependwhich operating system you use.

7. If your Algebra view looks like then click the triangle to the left of Algebra

.

8. Sort the elements by object type because we want to find all the point objects quickly.

9. You should be able to find the points A through K in a list (in two shades of blue and ashade of dark gray).

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• Either click in the open circle to the left of each point to show the point in the graph-ics view,

• or click the top point and then shift-click (or whatever your operating system’s selectfrom last mouse click to here protocol is) the bottom point.

10. Right-click, ctrl-click, or two-finger-tap (depending on your operating systemand your preferences) to call up a contextual menu and choose Show Object.

11. Try to click-drag each of the now-visible points. What happens?12. In the Algebra view find the numbers and click the radio button to make r visible. You

should see a slider appear. What does this one do?13. Right-click, ctrl-click, or two-finger-tap (depending on your operating system and your

preferences) the slider and choose Object Properties and the bottom of the pop-up menu.14. Take a look particularly at the options in the Basic, Slider, Color, Style, and Position

menus. Select other elements in the drawing in the left part of this window and notice thatthe available options change.

15. Move the Object Properties window so that you can also see the drawing. The move yourmouse over the list of objects in the Object Properties window (don’t click, just hover).Notice that the drawing highlights what you are hovering over (or have selected) providedthe object is currently visible.

16. If you need to modify something that isn’t showing up in the Algebra view - buttons forinstance, go to Object Properties for anything else and then choose the hidden object fromwithin the Object Properties window.

3.4 Working in 3D1. Select View → 3D Graphics.

2. Select the point tool. or

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3. Move the mouse to the 3D Graphics view. You should see something like

which indicates that your mouse movements will only change

the x and y coordinates of the point.4. Click to place a point somewhere in the 3D Graphics view.5. Now hold your mouse over the point you just created. You should see something like

which indicates that if you click and drag you can now change

the z coordinate of the point. You can switch back and forth between the two modes byclicking on the point without dragging.

6. Make 3 more points in the 3D Graphics view. Note that as soon as you move points out ofthe z = 0 plane, the points disappear from the 2D graphics view.

7. Select the vector tool.8. Click on one of your points and then move your mouse to click on another of your points.

Connect the remaining two points the same way.9. In the input bar

(a) type the name of one of your vectors that you just create,(b) click the letter alpha at the far right of the input bar,(c) click on the character that looks like a circled multiplication sign,(d) type the name of your other vector.

10. (Notice that if you’ve typed the name of an existing object, the name turns light blue.)11. Play with your view of the results.

(a) Use the scrolling up/down motion to zoom in and out.(b) Use shift-click-drag to move the origin within the viewing window.

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(c) Or use the tools. . The top tool in this

list is the only way to rotate the figure.

3.5 Simple Ray Diagram• If the axes aren’t showing, show them.

– method 1: Click the icon under the window label “Graphics” that looks like axes. Ifthe icon isn’t visible, click the triangle next to the window label “Graphics”.

– method 2: Ctrl-click on the graphics window somewhere in the middle (not a borderor the title bar) and select the axes icon in the resulting pop-up menu.

– method 3: Click the gear-like icon in the group of 4 icons on the right side of the win-dow and then choose graphics.

• Draw a mirror.– For aesthetic purposes, set the mirror so it crosses the x-axis at the origin. To do so,

create a point at the origin. To make a point that will definitely stick at the origin,typeIntersect[xAxis,yAxis] in the Input bar and hit the return key. You can also dothis by selecting the point tool and then clicking the intersection of the axes. If youtype (0,0) in the Input bar, the point is a moveable point because it is just two co-ordinates. Notice that GeoGebra names the points in alphabetical order with Capitolletters. If you don’t like the default name, ctrl-click and choose rename. You can alsoname the point when you create it HOWEVER, if the name you choose when you cre-ate the object starts with a lowercase letter, you will get a vector instead of a point.

– Create another point on the x-axis to be the center of curvature of your mirror.– Select the arc tool. Select your center of curvature point. Select the point at the ori-

gin. Create a third point above the axis. Notices that the arc draws as you move themouse so you have a sense of how much arc you are creating. For me, this third pointis called C.

– We’d like the mirror to be symmetric above and below the optical axis which will co-incides with the x-axis. To accomplish this, do ONE of the following things.* In the input bar type (x(C),-y(C)) and then hit return.

* Select the reflection tool . Click point C and then click the x-axis.* In the input bar type ref at which point command completion will offer you three

options. Use arrow keys or the mouse to select \reflect[<Object>,<Line>]and hit return to put that in the Input bar for you to fill in the <> pieces. Then<Object> should be highlighted. Type C. Then hit the tab key. Now <Line>should be highlighted. Type xAxis. Hit return.

– Use the arc tool again to draw a second arc. Note that if you pick your points in thewrong order, you will get the complement of the arc you wanted. Undo and try againif you make this mistake. This looks fine but being in two pieces may cause troublelatter (points attached to one half can’t jump to the the other half). Delete both arcsbut don’t delete the points that define the ends of the arc. Now use the arc tool tocreate a single arc from C to C ′. (Don’t click on A as you pass by.)

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• Create the focal point.– Select the midpoint tool and then click on the center of curvature of the mirror and

the origin (in any order). This is the focal point.– Since this point depends entirely on other things for its location, it is gray. You can

move it only by changing the center of curvature.• Create the object. We’ll use the traditional upright arrow for now.

– Create a point somewhere above the x-axis. This will be a free point so we can movethe object and change the object’s height. This will be the top of the object.

– We want the base of the object to be directly below the tip and on the optical axis.Assuming the point at the top of your object is called E, type (x(E),0) in the Inputbar and hit return. This creates a point with the same x-coordinate as point E and 0for the y-coordinate.

– Use the Vector tool to draw an arrow starting at F on the axis and going up to E.• Create the first ray.

– We’ll do the parallel ray. We need a line through E and parallel to the horizontal axis.Do ONE of the following.* From the right-hand collection of line tools, select the Perpendicular Line tool

. Then click on point E and after that click on the y-axis.

* From the right-hand collection of line tools, select the Parallel Line tool .The click on point E and after that click on the x-axis.

* In the Input bar, type lin command completion will supply four options. Arrowdown to Line[ <Point>, <Parallel Line> ] and hit return. Then type E, hitthe tab key, and type xAxis (note capitalization), then hit return.

– Select the Intersect Two Objects tool and then click on the mirror and the horizontalline you just drew (in either order). This point is gray because we can’t move it in-dependently. You can accomplish the same thing in the Input bar after noticing thatthe horizontal line we added has been named a by GeoGebra and that the mirror wascalled c by typingIntersect[a,c] and then hit return.

– Light coming in parallel to the optical axis reflects through (or nearly so) the focalpoint so make a line connecting the point we just created on the mirror with the focalpoint. Use the Line tool rather than the Segment tool.

• Use similar techniques to draw at least one more ray.• Create the tip of the image as the intersection of two rays.• Create the image arrow the same way we created the object arrow.• The final result should look something like this.

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You can drag both the center of curvature and the top of the object to test different sce-narios.

• Notice that when the object crosses the focal point, the ray diagram breaks. This is be-cause the other intersection of the line with the mirror comes into play and we didn’t drawa parallel line through that point. Do that and create a new image arrow.

3.5.1 Cleaning Things UpThis diagram works, but feels rather cluttered. We can do a few things to help.

• Hide points A, C ′, F , G, H, I, J , K, M , and L by clicking their blue radio buttons in thealgebra view. Notice that the points can’t be hidden when they are undefined but thatonce hidden, they stay hidden as the switch back and forth from defined to undefined.Likewise if you show them.

• To hide names of points, or to rename them, ctrl-click on the point either in the Algebra orthe Graphics view and choose the appropriate option.

• Other improvements include turning Lines into Rays when we know where they start butnot where they end or into Segments when we know both beginning and ending.

• Finally, we can color-code the rays and other things. Ctrl-click on an object (either in theAlgebra or the Graphics view) and choose Object Properties. Using the various tabs, youcan change colors and line thicknesses among other things.

• Hide the y-axis by ctrl-clicking on a blank space in the Graphics window and then select-ing Graphics. (the last option). Select the y-axis tab.

• Use an actual image instead of the arrow. Choose the Image tool from the insertionscollections. Click in the Graphics window and use the resulting dialog box to navigate to asuitable image file on your computer. Then ctrl-click the image, choose Object Properties,choose the Position tab. Set corner 1 to be F (the base of the object vector) and corner 4to be E (the top of the object vector). Execute similar steps for both image vectors. Youcan hide the vectors.

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• If you compare this to http://tube.geogebra.org/student/b871227#material/11893,you will see that If statements can be used to differentiate the path light follows from vir-tual rays.

3.5.2 Learning from the Ray DiagramThe object can be moved around to show what locations result in real/imaginary images etc.

Notice that if they object is too tall relative to the size of the mirror and you have morethan two rays that the rays don’t all intersect at a single point. This is a real problem withspherical mirrors not an artifact of our rays or GeoGebra. Try replacing the mirror with aparabola (challenging in this orientation).

3.5.3 Projectile MotionLet’s simulate throwing a rock from a variable location, at a variable angle, with a variablespeed, on various planets.

• If the axes aren’t showing, show them.– method 1: Click the icon under the window label “Graphics” that looks like axes. If

the icon isn’t visible, click the triangle next to the window label “Graphics”.– method 2: Ctrl-click on the graphics window somewhere in the middle (not a border

or the title bar) and select the axes icon in the resulting pop-up menu.– method 3: Click the gear-like icon in the group of 4 icons on the right side of the win-

dow and then choose graphics.• Create the variables.

– Create a movable launch point by using the Point tool and clicking anywhere but anaxis in the Graphics view.

– Create a way to set the launch angle by selecting the slider tool and then clickingsomewhere out of the way in the Graphics view. (You can move sliders by ctrl-clickingthem and then unchecking the Fixed option.) Select the angle option. Click Apply. Ifyou like θ better then the default α as the name of your angle, then before you clickApply, click on the box at the right end of the name bar to pull up a symbol tableand from that table select θ.

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– Create a way to set the launch speed.* In the Input bar type v_0=2. The value doesn’t matter; we can change it later,

but we need to create the speed variable.* Choose the Input Box tool and click somewhere out of the way in the Graphics

window for the box to live. The caption is the label that will show. We want tolink this input box to the variable v0. Input boxes default to very long, so ctrl-click ON THE LABEL and select the style tab and then type a smaller numberthan 20 for the size of the box.

– Create a slider or input box for the value of acceleration. Either make the accelerationa magnitude and put the minus sign for direction into your equation later (my habit)or make the acceleration negative and use a positive sign in the equation later.

• Describe the projectile’s height as a function of its horizontal position (so the path is afunction). Assuming the launch point is called A, the angle is α, and the gravitational ac-celeration is called g typef(x)=y(A)+(x-x(A))*tan()-(g/2)*((x-x(A))/(v_0*sin()))^2 in the Input bar thenput the cursor in each of the empty trig-function arguments in turn and click the box atthe far right of the input bar to select the angle. Hit return to enter the function. If yousee red parentheses, that means your parentheses are unbalanced (too many openers or toomany closers).

• This works (play with the parameters). However, we probably don’t want the part ofthe parabola before the launch point. To get rid of it, double-click the function and addif[x>=x(A), to the beginning of the function and then ] to the end.

• You should have something that looks roughly like this.

3.5.4 Working with CurvesThe function version gives us the shape very nicely, but we’ve entirely lost the sense of time inthe process. To recapture that, we need to work with parametric equations, called curves in Ge-oGebra.

You can build on top of the previous work - perhaps hiding the function - or use Save Asand then delete the function but keep the controls.

• Create a time slider.• Type Curve[x(A)+v_0*cos(�)*t,y(A)+v_0*sin(�)*t-g/2*t^2,t,0,time] in the Input

bar and then hit return. Again, use the symbol table to insert the angle name where thereare empty parentheses in the equation.

• Ctrl-click on the time slider and choose Animation On to trace the projectile’s path.

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This still leaves something to be desired because we can’t see the roll of time afterwards sowe can’t point to it and discuss it afterwards very well. We have a couple of options. The first iseasier to type (a little) but disappears every time we zoom or pan.

• In the Input bar type (x(A)+v_0*cos(�)*time,y(A)+v_0*sin(�)*time-g/2*time^2). Ac-tually, I used the up arrow key to get back the Curve typing I’d done and then modifiedthat. Then ctrl-click on the point just created and select Trace On. Reset time to zero andclick the triangle in the lower left of the Graphics view to run the animation. If you needto get rid of the dots, go to View - Refresh Views.

• Use the up-arrow key in the input bar to recall the point just entered and modify that in-put tosequence[(x(A)+v_0*cos(�)*t,y(A)+v_0*sin(�)*t-g/2*t^2),t,0,time,0.1]

Now we have something that clearly shows the distance traveled in a fixed time and that modi-fies nicely as we alter the various parameters.

3.5.5 Using the SpreadsheetWe can add drag to the problem (either linear or quadratic) without solving the relevant differ-ential equations by using the spreadsheet to do iterative calculations.

1. Create sliders for the size of the time step (timeStep), the drag coefficient (drag), and thepower of velocity on which the drag depends (power).

2. Show the spreadsheet view by selecting from the menus View -> Spreadsheet.3. Set up the conditions at t = 0 s.

• In cell A1 type 0 for the starting time.• In cell B1 type =x(A).• In cell C1 type =y(A).• In the View menu, select Keyboard. On the keyboard click the α to get the Greek

keyboard. In cell D1 type =v_0 cos(�) and use the keyboard to insert the angle sym-bol. Note that space works as a multiplication symbol.

• In cell E1 type =v_0 sin(�) and use the keyboard to insert the angle symbol.• In cell F1 type =-sgn(D1)*drag*(abs(D1))^power. The -sgn(D1) part makes the

acceleration point the opposite direction of the velocity as a drag must.• In cell G1 type -g - sgn(E1)*drag*abs(E1)^(power).

4. Move one step forward in time.• In cell A2 type =A1+timeStep.• In cell B2 type =B1+D1*timeStep.• In cell C2 type =C1+E1*timeStep.• In cell D2 type =D1+F1*timeStep.• In cell E2 type =E1+G1*timeStep.• Select cells F1 and G1. Go to the lower right corner of the selection and drag down

one row.5. To move forward further, highlight cells A2 through G2, go to the lower right corner of the

selection and drag down 20 or 30 rows.6. Create the points to follow the motion.

• In spreadsheet cell H1 type =(B1,C1).• Select H1 and drag down to match the other columns.

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• With the entire column highlighted, ctrl-click on the column and uncheck Labels.7. You should have something that looks like this.

3.6 Do Something Often - Make a New ToolThe spring might be a good thing to turn into a tool to save time in the future when we need aspring.

1. In GeoGebra on your computer (not GeoGebraTube on line), go to your version of themass on spring file.

2. Use whatever tool your operating system supplies to take a picture of part of your currentcomputer screen. Select an area that is as close to square as you can get, not very big, andmostly includes the spring. We’ll use this later as the icon for the new tool we’re making.

3. Select Tools → Create New Tool.

4. You should end up at specifically with Out-

put Objects selected (darker gray on my computer).5. Use the drop-down menu to select the spring. Unless you’ve changed this, it should be

called curve b and the letter b should be dark red (to match the spring in the drawing).6. Click Next.7. GeoGebra will populate the Input Objects tab with objects that curve b depends on. Ge-

oGebra will usually be right about what should go here. Click Next.8. Give the command a name and a command name (the name can have spaces but the com-

mand name can’t).9. Click the icon button and navigate to select the snapshot you made in step 2.

10. Click Finish.11. A new tool should appear in the tool bar.

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4 Resources4.1 instruction

• http://wiki.geogebra.org/en/Tutorials

• http://wiki.geogebra.org/en/Manual

• http://wiki.geogebra.org/en/Category:Commands this is what I use most often when Ineed to do something new (or that I’ve forgotten)

• search the web using “geogebra” followed by what you want to do or an object or com-mand name that’s not working as expected

• http://forum.geogebra.org/

• more advanced topics (LaTeX and speed)– http://forum.geogebra.org/viewtopic.php?f=8&t=33449– http://wiki.geogebra.org/en/Tutorial:Responsive_Applets

4.2 learning from other peoples’ work4.2.1 Applets in GeoGebraTube can be downloaded, opened, and modified orused to learn how to do something.

1. Go to http://tube.geogebra.org/.

2. Search.

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3. There are two kinds of items: individual applets

and books (collections of applets) . Click the square pic-

ture of the resource to go to it.4. If you chose a book, click View GeoGebraBook and then click on one of the square icons

for the worksheets in the book. You may have to scroll to the bottom and click Shareor Copy. You will end up at a screen offering you options for an individual worksheet.

5. Choose View Worksheet to see the on-line version (and check that everything translated tohtml5 successfully).

6. Choose Download to be able to open in GeoGebra on your computer and make modifica-tions or learn how something was done.

4.2.2 A selection of people to learn from• Antonio di Muro http://tube.geogebra.org/student/b370209# nice collection of vari-

ous physics applets• TJ Walsh https://sites.google.com/site/geogebrasimulations/

• Possibly useful tools from José Luis Hernández Neira at http://archive.geogebra.org/en/wiki/index.php/GeoGebra_tools_for_applications_in_Physics_Version_2

• You can find what I’ve done by searching lenore on GeoGebraTube. If you then set Mate-rial Type to GeoGebraBooks, you can see the small collections I’ve have made of my ownwork.

• Y Michas http://tube.geogebra.org/material/show/id/93246 graphing of data fromspreadsheet (orbits)

• Jerome A White http://tube.geogebra.org/student/b71469# simple harmonic motion• Andreas Lindner http://tube.geogebra.org/student/b501527#material/527879 RC

circuit: differential equations, picture of circuit, graph of potential vs time• Ryan Hirst http://tube.geogebra.org/student/b143433# numerical analysis• Markus Hohenwarter http://tube.geogebra.org/material/show/id/17496 pretty plane

mirror ray tracing• ukuku http://tube.geogebra.org/student/m160066 position-velocity-acceleration

graphs (velocity graph is adjustable)• ukuku http://tube.geogebra.org/student/b162411#material/56971 nice graphics for

uniform 1D motion

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• electric field plotting http://tube.geogebra.org/student/b439927#

• Francesco Moauro tube.geogebra.org/material/show/id/50589 2D elastic collision sim-ulation

5 Sharing1. Create an account.

(a) Go to http://tube.geogebra.org/. (I usually type geogebratube.org into mybrowser and that takes me to the given url.)

(b) Click Sign in.(c) Click Create Account or choose one of the other accounts on the right.

2. Hide the Algebra view using the x button or the View window.3. Shrink your window down to trim away unneeded space - remember people may be access-

ing this on something with a smaller screen than you have.4. Save you applet (you’ve been doing that all along on a regular basis haven’t you?), and

then select file -> share.5. If you are not currently logged into geogebratube, you will be required to log in at this

point.6. Fill in the information for students box. Basic html formatting is available and there are

some formatting tools at the top of the box as well. When you are finished, copy this info.7. Fill in the optional questions below if you like. Click Continue.8. Give a title.9. Paste what you wrote before into the Description box (or write different material if you are

so inclined).10. Choose Language and reset Target Group (Age) if reasonable values don’t pop up auto-

matically. The latter has an option to set a range of ages.11. Choose some tags. The form won’t require this, but it will let other people find your work

more easily. When you start typing, potential matches will pop up. Use or not as you seefit.

12. Click Save.13. Click View Worksheet. A new tab or window will open. Check that everything works as

expected, window size isn’t bizarre, etc.14. If (when?) you find errors, edit your original .ggb file on your computer (there are other

options, but they are - in my experience - more painful) and save your modifications.15. Close the tab or window that just opened to get back to

and choose Edit.

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16. You can change other things here as well, but to correct the actual applet, click Changefile and navigate to select the file on your computer that you just saved modifications to.

17. Click Save.18. When you are happy with what you see in View Worksheet, copy the web address out of

the address bar of your browser and give that address to your students.

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