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Teresa Fitz-Geraldconics
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conics: the ellipse, the parabola, and the hyperbola.
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projectiles travel in parabolas.
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every circle, viewed obliquely, appears elliptical.
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cylinder sliced on an angle
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Tilt a glass of water and the surface of the liquid acquires an elliptical outline.
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each planet travels around the sun in an elliptical orbit with the sun at one of its foci.
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approximations to parabolas is the path taken by a body projected upward and obliquely to the pull of gravity, as in the parabolic trajectory of a golf ball
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reflective properties.
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(a curved surface formed by rotating a parabola about its axis)
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Charlie HiemerBritton, Jill. November 4, 2011. Occurrence of the Conics. Retrived from http://britton.disted.camosun.bc.ca/jbconics.htm
This website explores the application of parabolas in real world situations. This would be another great tool to show students why the information we are studying is relevant and interesting. -
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THE PARABOLA One of nature's best known approximations to parabolas is the path taken by a body projected upward and obliquely to the pull of gravity, as in the parabolic trajectory of a golf ball. The friction of air and the pull of gravity will change slightly the projectile's path from that of a true parabola, but in many cases the error is insignificant.
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BTerresOCCURRENCE 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.
Las cónicas y sus aplicaciones en la vida y en la tecnología -
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