3/5/2023 0 Comments Geogebra classic animation![]() Which should be entered for the polygon and its sides. You need to repeat this for all the grey polygon’s sides, which you can do by copy-pasting the condition in their own properties.ĩ. Finally, the indigo image should only appear when the slider is at 1. Use your slider’s name!) & is how you enter the operator “and”, which is then shown as ∧. There you can enter a Condition to Show Object. Type: This is accomplished by selecting the grey polygon, and going to Edit → Object Properties → Advanced. What remains to be done: making sure that the various parts of the figure are appropriately either visible or hidden.ħ. The vectors and the grey and indigo polygons’ vertices need not be visible ever, so you should hide them.Ĩ. The grey polygon itself should only be seen while on the way, not when the slider is at 0 or 1. Success! If you move the slider back and forth between 0 and 1, your new polygon moves from the original to the image, and back. Make a new polygon by connecting the new points in the correct order. Now, if you slide the slider from 0 to 1, you’ll see your new point moving from the pre-image to the image.ĭo this for all the vertices of the original polygon.Ħ. ![]() (Obviously, you should use the appropriate letters in your figure.) Where G is the new point we are creating, C is a vertex of the original polygon, a is the slider, and w is the vector that starts at point C. Show the Input Bar (in the View menu.) Create a new point by typing: When the slider is in between, the point is in between, traveling along its vector. Here’s how you do it:ĥ. When the slider is at 1, the point’s image will have reached the end of the vector, in other words the original point’s reflection. When the slider is at 0, the point’s image stays in place. This makes it obvious which points can be manipulated directly, and which can’t.)Īnd here is the key idea: we will translate each original vertex by its own vector, multiplied by the slider number. That is a setting in Preferences → Defaults → Point → Style, where I set the Point Size to be smaller for Dependent points. (Digression: Notice that the vertices of the original polygon are fatter than the ones in the reflection. Make vectors connecting each of the vertices of the original polygon to its image. (I usually make it indigo, a reminder it is the image.)Ĥ. Use the reflection tool to make the reflected polygon. I usually make it orange, a reminder it’s the original figure.)ģ. (When exploring transformations, it’s best to use an asymmetric figure. Make a polygon, which will be the pre-image. Make a line, which will serve as the reflection line. This is the file I created while writing this post.)Īs you work through this tutorial, you might learn some non-obvious GeoGebra features.ġ. (Note: the approach outlined below is different from and better than the one I used to create the applet cited above. ![]() I hope they would also work in other recent versions of the software. These instructions work in the current version of GeoGebra 5. If you know a better way to do any of this, please let me know! I’ll use the reflection as an example, but the same basic principle can be used for many simple animations. I am not a GeoGebra expert, far from it, but in this post I’ll explain my approach to creating. In fact, in the above animation there’s a bit of a 3D flipping illusion. Still, the animation helps, and it does illustrate how we think about transformations intuitively. Technically, each point in the original figure is an input, and a single point in the image is the output. Mathematically, this is ironic, since transformations of the plane in fact do not involve motion at all: they are functions relating two static figures. The idea was to illustrate reflection in a line and help students get a feel for the transformation. (Links to related transformations applets are on this page.) ggb file, and an interactive applet in your browser here. Here is an animation I created in GeoGebra:Īs far as I can tell, WordPress only shows you the animation once, when you open this post. You can find the actual.
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