The Problem

Solution

Original Discussion

Pedagogy

Demonstrations

Bibliography

To launch the demonstration, click on the large button in the top-right corner of this page labelled "Demo". After a little while, two windows should appear; one will be labelled "Controls" and the other "Triangles".

In the "Triangles" window, you will see a triangle and it's corresponding midpoint triangle. You can drag the blue vertex of the triangle around; the areas of the two triangles and their ratio will automatically be calculated and displayed in the "Controls" window.

In addition, it is possible to move the other two points of the triangle by typing in their coordinates (in the boxes labelled "A" and "B") in the "Controls" window.

You may notice that the areas are sometimes negative. This is because we are calculating the oriented area. If you are not familiar with this concept, you may want to read the introduction to oriented area.