Threequilaterals

Demonstrating a fun fact about three equilateral triangles

[Run the Applet remotely]
Note:  The above link runs the applet on a remote server so that you do not need to have any special software installed in order to run it.
(and in fact it should also work on tablets and smart phones as well as on PCs). But performance could be laggy if you have a poor internet connection.
The applet was originally written in Java, which allows those with Java installed (and supported by their browser) to run it locally, but many browsers no longer support Java.
If you want to run the applet on your own machine, one option is to have Java installed and run it in Internet Explorer (or in some other browser with the IETab plugin)
Or you can install the CheerpJ Applet Runner (which runs applets in any browser by converting them to JavaScript). This may work more smoothly, but it may take quite a while to load.

[Run the Applet locally]

Note to Students and Teachers:
This applet explores the geometric theorem that for any three equilateral triangles which share a common vertex, the midpoints of the lines joining non-shared vertices of pairs of adjacent triangles themselves always form an equilateral triangle. The applet allows the user to quickly see that the claimed relationships are preserved, and maybe gain some intuition as to why the theorem is true before going through the proof.

Note to Developers: The applet linked to above was built with the  GeX component library which is intended to support the quick construction of demonstration tools for mathematics instruction.

GeX Homepage

About the GeX library

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Copyright 2006-2020 by Alan Cooper - page last modified on 11 April 2020