Thursday, March 4, 2010

The Complete Quadrilateral

John Wentworth Clawson
Last year, I found this relatively short article from 1919 by John Wentworth Clawson called The Complete Quadrilateral  in The Annals of Mathematics, Vol. 20, No. 4. I used this article as a basis for a presentation illustrating some of the amazing things that happen when, essentially, four pieces of spaghetti are thrown onto a table.

What is a complete quadrilateral? Four lines, no three concurrent, intersect in six distinct points, creating what is known as the COMPLETE QUADRILATERAL. Why worry about this? There are a number of concurrency, collinearity, cyclic, and harmonic relationships lurking in this rather ordinary configuration. Over the next couple of posts, we will begin to explore these relationships.

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