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.
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Today's selected anniversaries:
The Cutty Sark, one of the last sailing clippers ever to be built, was
launched at Dumbarton in Scotland.
After a bloody battle with the military causing 600 casualties, rebellious
silkworkers seized Lyon, France, beginning the First Canut Revolt.
The United Nations Security Council unanimously adopted Resolution 242 in
the aftermath of the Six-Day War between Israel and Egypt, Jordan, and
Two days after the death of Francisco Franco, Juan Carlos was declared King
of Spain according to the law of succession promulgated by Franco.
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.
Wiktionary's word of the day:
extraneous (adj) Not belonging to, or dependent upon, a thing; not
essential or intrinsic; foreign.
Wikiquote quote of the day:
Government is too big and too important to be left to the politicians.