Pappus Theorem

THEOREM OF THE DAY

Pappus' Theorem Let A, B, C and a, b, c be two sets of collinear points. Let A be joined by a line to b and c; B to a and c; and C to a and b. Then the intersection points of the line pairs Ab with Ba, Ac with Ca and Bc with Cb are again collinear.

The above applet, created using David Joyce's Geometry Applet software, shows Pappus' Theorem in action. Click on one of the end points (A, C, a or c) and drag the point to move the whole diagram, including the points of intersection X, Y and Z of the line pairs.

Pappus, working in Alexandria about 600 years after Euclid, made valuable compilations of Greek mathematics, as well as contributing some theorems, such as the above, which appear to be original.

Web link: www.mathpages.com/home/kmath542/kmath542.htm

Further reading: Ancient Mathematics (Sciences of Antiquity), by Serafina Cuomo, Routledge, 2001.

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