Sum of Medians Divided by the Perimeter

It is a simple theorem that the sum of the lengths of the medians in a triangle must be between

3/4p

and

p

, where

p

is the perimeter of the triangle. By dragging the vertices of the triangle, you can confirm the theorem and discover which kinds of triangles come close to achieving the lower and upper bounds of 75% and 100% of the perimeter, respectively.

References

[1] H. S. M. Coxeter, Introduction to Geometry, New York: John Wiley & Sons, 1961.

[2] "Medians of Triangles Proof" from The Math Forum: Ask Dr. Math. (May 29, 2000) mathforum.org/library/drmath/view/55242.html.

External Links

Triangle (Wolfram MathWorld)

Triangle Inequality (Wolfram MathWorld)

Triangle Median (Wolfram MathWorld)

Permanent Citation

Jacob A. Siehler

"Sum of Medians Divided by the Perimeter"
http://demonstrations.wolfram.com/SumOfMediansDividedByThePerimeter/
Wolfram Demonstrations Project
Published: December 18, 2012