Varignon 3D Action: REVAMPED!
- Tim Brzezinski
Creation of this applet was initially inspired by a Twitter conversation among Patrick Honner, Eddie Woo, Chris Bolognese, and Steven Strogatz. Here's the Twitter link. It is a revamped version of this previously created GeoGebra resource. Before playing with the applet below, recall the theorem you've already discovered and proven in class and also illustrated here on this animation. (For a quick, informal investigation of this theorem, refer here.) Notice how on either resource, all 4 vertices of the original quadrilateral were coplanar. But what happens when we have 4 non-coplanar points? Check it out below: Feel free to move the ORANGE VERTICES of this original "quadrilateral" anywhere you'd like! How can we formally prove what is dynamically illustrated here?
To Explore in GeoGebra Augmented Reality:1) To explore in GeoGebra Augmented Reality, you need a device that has ARCore by Google already installed on it. Here's the link to install it (if you have not yet done so). 2) Also be sure GeoGebra 3D Graphing Calculator is installed on your device. If you have not yet installed it, you can download it here. 3) Open up GeoGebra 3D Graphing Calculator on your device. 4) Go to the MENU (horizontal bars) in the upper left corner. Select OPEN. In the Search GeoGebra Resources input box, type dvubftbr (Note this is the resource ID = last 8 digits of the URL for this resource.) 5) In the resource that uploads to the GeoGebra 3D Graphing Calculator, zoom in/out if needed. Press the AR button in the lower right corner of your 3D screen. Follow the directions that appear. For more info with respect to opening GeoGebra Augmented Reality, click here. Note: The animate slider controls the animation. Note how 3 of the vertices coordinates (a, b, c), (d, o, w), and (t, u, v). Each of these coordinates has a slider so you can dynamically change its value when exploring this resource in GeoGebra Augmented Reality.