Triangle Optimization : All in One

by Ravinder Kumar

You might like to press F11 to view the Microworld in Full Screen mode.

In general, we tell the Mathematical Story above the Microworld, and place the Interaction Instructions below it.

The Story:

Equilateral triangles have some interesting properties. This 8-page Microworld provides visualization of why among triangles of fixed perimeter equilateral triangles are the ones that have maximum area. Two proofs of this fact are also discussed. The first explanation depends upon multivariable calculus. The second proof depends essentially on single variable calculus.

We believe that this latter proof is a new proof and the power of Mathwright is to make visualization of this not so straightforward proof possible.

Interaction Instructions:

This Microworld mixes interactive exploration with formal proofs. The demonstrations set the stage for the precise arguments, and each of them comes equipped with careful explanations and hints under the buttons of how to proceed.