HI everyone --

Could we consider agreeing on a color for everyone to use when adding to this page? I'm finding it hard to figure out who is who. I'll use orange. I've already edited my additions to be orange. June

Okay: I'll be red, I'll go through and change any other colors I used. Elisse

And I chose blue. Doug

What if we upload files we're thinking about "upgrading" to 4.0 here and then look at each other's stuff tonight? Elisse

Here are two of mine: Looking at tangents of inverse functions using exp and ln

Guessing the coefficients of Taylor polynomials for sin x

Here are two of mine (June):

Polar Graphing: NewPolar_JP.ggb

June: Are you going to use the two graphics windows here? I'm impressed with what you did using only one graphics view. Also, I'm not able to move the"d" slider.

Yes, I was planning to use the two graphics windows for this one. Not sure what else I'll do. Maybe I'll wait until later in the week to figure it out. I'll get started with the two graphic windows though. June

Function Transformations: Function_Transformation_total_JP.ggb

If you wanted to make an applet where you had different "original" functions, you could look at how Marc Renault made his random polynomials for some of his applets, they are at:

http://webspace.ship.edu/msrenault/GeoGebraCalculus/GeoGebraCalculusApplets.html

The ones I've looked at are graphing the derivative given the function and guessing the function given its derivative.

I have another applet where I use a slider to change the function type. I'm going to try to incorporate that here too. June

Doug: I like the Function as Integral. ....I will post it here.

Two calc ggb's, Riemann sums and the Function as integral RiemannSumDK.ggb FunctionAsIntegralDK.ggb

And two precalc ggb's: ExponentialInverseDJK.ggb

Doug: I played with this one a little, maybe we can tie it in with my tangents of inverses above.

Here's what I've done. I was trying to make a slider to move the point A on the x-axis, but that killed your locus that draws the inverse. I have to look at how the locus command works.

Loci can be driven by sliders in 4.0. Not sure that helps here, though.

EG Version of Exponential Inverse

Hi Doug - I played with this one too. I moved the controls to Graphics 2, and also had some fun with the new text editing tool. June

JP Version of Exponential Inverse

I also played with FunctionAsIntegralDK.ggb I moved the directions to Graphics 2, used the new text tool, changed the min value on the upper limit slider to the current value of the lower limit slider, and found LFS's trick for resetting traces. June

JP Version of FunctionAsIntegral And Doug's modification of June's modification FunctionAsIntegralDJK_JP_DJK40.ggb I eliminated the slider for the lower limit and instead used a TextField for that.

June: I like both of your modifications -- putting the instructions and check boxes in Graphics 2 really cleans up the appearance.

In the Functions as Integral, however, I would prefer to have the upper limit NOT have to be greater than the lower limit. One of the confusing things for kids to learn is that when you integrate "backwards" you get the opposite sign of the area.

Elise: I see what you mean, and I do know that. :-) It was basically a way to experiment to see if I could now use a variable as a limit of a slider. June

Translations_of_functionDJK.ggb Doug: I like this; I also mentioned to June that I really liked Marc Renault's applets that give students a "random" function and ask them to match it. I wonder if there is a way to adapt this applet to do that: The program picks random values for a, b, c, and d and then the user has to try to match them.

http://webspace.ship.edu/msrenault/GeoGebraCalculus/GeoGebraCalculusApplets.html

Doug: Does the Riemann Sum in 4.0 do what this applet does? I haven't checked it out completely.

General Question: Is there a way to set Mouse Coordinates off in an applet. I find it pretty distracting, and imagine a student might as well.

Yes. Control-click on the Graphics View and select Graphics … (the last option). There is a checkbox near the bottom that allows you to turn off mouse coordinates. You have to do this independently for each Graphics view though. June Could you save the Settings with mouse coordinates turned off and then all new ggb files will open that way. I think, also, that you can save different settings with names. "No MC", for example, but I haven't played with that yet. Doug (blue).

I was looking at my file with exponential and log tangents

and had an actual mathematical question inspired by this: The tangent to the exponential function at a point and the tangent to the log function at the mirror point have reciprocal slopes (what I created the file to show). However, in the file you can see that the two tangents always meet on the line y=x. In the file, I only use a base of "e", but I checked that it works with other bases. While this "makes sense", I can't come up with a solid mathematical reason for it. When I tried to prove it algebraically, it was ugly and I quit. Looking geometrically, it's clear that y=x is the perp. bisector of the segment joining the mirror points, so maybe there's an argument about the tangents forming an isosceles triangle, but I don't see that argument either. Any ideas?

Later: I played with the algebra more and got the answer to work (not attractively, but it works). It is true for any function and its inverse. But it does seem that there ought to be a simple answer as to why this is true.

I like the way GeoGebra invites discoveries like this.

I think I successfully exported the ExponentialInverse (June's final version) as an applet, that appears to run successfully. ExponentialInverseGroup.html

A work in progress: Exp and Ln Tangents40EG.ggb I've tried to make this work somewhat like the ExponentialInverse of Doug's. It's what I got done before bedtime, still needs work.

June and I added some buttons to animate the upper limit on the Functions as Integral this morning

Version of FunctionsAsIntegrals with Buttons for animation

Here is the polar graphing applet. Also a work in progress. ;-)

Polar Graphing Applet

## Comments (4)

## Tony Cron said

at 8:29 pm on Jul 12, 2011

NewPolar problem with highlight boxes not allowing use sliders and boxes, change of levels for parts that do not work. Very nice work. Tony

## June Patton said

at 10:40 pm on Jul 12, 2011

Hi Tony --

Thanks! Do you mean that I should put the highlight rectangles on Level 0? Or should I move the sliders to a higher level?

## Tony Cron said

at 6:46 am on Jul 13, 2011

I moved them back to level 0, and was able to move use the sliders and check boxes. The top level is the interactive level. I seldom use levels on my applets, I feel that I need a better explanation of when and where they are necessary. I have yet to create any that are necessary.

I would guess that if you want to use levels, you should place items that you do not want changed on the lower level. E.g., your highlighted rectangle on level 0, your slider or check box on level 1; however, I usually just fix the objects on the graphic view.

## June Patton said

at 7:40 am on Jul 13, 2011

Thanks, Tony. I built this applet a while ago. If I remember correctly, I added the rectangles after the sliders, and using layers was the only way I could see at the time to get the sliders on top.

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