Problem of Pappus

Classic Problem

The is a generalization of the Four-Line Locus problem, where the number of lines is greater than $4$.


Solution


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Proof


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Source of Name

This entry was named for Pappus of Alexandria.


Historical Note

The was originally posed by Pappus of Alexandria in Book $\text {VII}$ of his Collection.

He generalized a problem of Apollonius of Perga known as the Four-Line Locus:

Find the locus of a point $P$ such that the product of the distances from $P$ to any two of them is proportional to the product of the distances from $P$ to the other two.

This locus is in fact a conic section.

It was by considering this problem in $1631$ that René Descartes was led to invent analytic geometry.


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Problem of Pappus
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): problem of Pappus
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