Apollonius' problem is a challenge in Euclidean plane geometry to construct circles that are tangent to three given circles in a plane. Apollonius of Perga posed and solved this famous problem in his work Επαφαι ("Tangencies"); this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them and each solution circle encloses or excludes the three given circles in a different way. François Viète found such a solution by exploiting limiting cases: any of the three given circles can be shrunk to zero radius (a point) or expanded to infinite radius (a line). Viète's approach, which uses simpler limiting cases to solve more complicated ones, is considered a plausible reconstruction of Apollonius' method. The method of van Roomen was simplified by Isaac Newton, who showed that Apollonius' problem is equivalent to finding a position from the differences of its distances to three known points. This has applications to navigation and positioning systems such as GPS. Later mathematicians introduced algebraic methods, which transform a geometric problem into algebraic equations.
Read the rest of this article:
_________________________
Today's selected anniversaries:
1869:
1831:
1967:
1975:
2004:
Orange Revolution: Massive protests started in cities across Ukraine, resulting from allegations that the Ukrainian presidential election between sitting Prime Minister Viktor Yanukovych and leader of the opposition coalition Viktor Yushchenko was rigged.
(
http://en.wikipedia.org/wiki/Orange_Revolution)
_______________________
Wiktionary's word of the day:
______________________
Wikiquote quote of the day: