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Intriguing Triangle Theorems for Everyday People

While visiting friends, I happened to stumble across a book entitled The Math Book by Clifford A. Pickover. Please allow me to share two fascinating triangle theorems with you, both of which are fairly easy to comprehend, although difficult to prove. This triangle adventure may focus more on geometry than astronomy, but it's not as if two disciplines aren't intertwined. For instance, the fabric of spacetime is in itself a geometrical concept.

Above Image of Gravity Probe B & the Relativity Mission: NASA

Morley's Trisector Theorem

Trisect each angle of a triangle on the surface of a plane, and the three points of intersection of the angle trisectors form an equilateral triangle. The image below, courtesy of Wikipedia, might be worth a thousand words!

Trisection of an Angle

Viviani's Theorem

Place a point inside an equilateral triangle. Draw a perpendicular line from the point to each side of the equilateral triangle. The three lines added together equal the altitude or height of the equilateral triangle. See image below, again courtesy of Wikipedia.

Wonderment is Its Own Reward

So what's to be gained from an introduction to these theorems? An uplifting sense of wonder - hope you enjoyed!


copyright 2014 by Bruce McClure

June 2014 Feature * August 2014 Feature