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Occurrence of the Conics
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"
OCCURRENCE
OF
THE CONICS
Mathematicians have a habit of studying, just for the fun of it, things
that seem utterly useless; then centuries later their studies turn out
to have enormous scientific value.
There is no better example of this than the work done by the ancient
Greeks on the curves known as the conics: the ellipse, the parabola, and
the hyperbola. They were first studied by one of Plato's pupils. No important
scientific applications were found for them until the 17th century, when
Kepler discovered that planets move in ellipses and Galileo proved that
projectiles travel in parabolas.
Appolonious of Perga, a 3rd century B.C. Greek geometer, wrote the greatest
treatise on the curves. His work "Conics" was the first to show how all
three curves, along with the circle, could be obtained by slicing the same
right circular cone at continuously varying angles.
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THE ELLIPSE
Though not so simple as the circle, the ellipse is nevertheless the
curve most often "seen" in everyday life. The reason is that every circle,
viewed obliquely, appears elliptical.
Any cylinder sliced on an angle will reveal an ellipse in cross-section
(as seen in the Tycho Brahe Planetarium in Copenhage"
....
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