Explorations in Geometry
Here is a little tidbit that John Conway, the famous Geometrician, dropped in an E-mail one day. I think you can see the relationship for yourself if you follow these steps.
1 Create a circle and select three points on the circle to form a triangle.
2. Find the product of the three sides, and the area of the triangle
3. Divide the product of the sides by the area of the triangle.
4. Now move the triangle around without changing the size of the circle. What do you notice???
What happens when the circle radius is changed?
If you have trouble seeing the pattern, adjust the radius to a integer value, and then move the points around.
Sample sketch below