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Essay / Research Paper Abstract
A 12 page research paper that explores the fascinating nature of these conic sections. The writer discusses the history of conic investigation, their definitions, and then explores multiple applications and uses of these concepts. Bibliography lists 7 sources.
Page Count:
12 pages (~225 words per page)
File: D0_khhyppar.rtf
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Unformatted sample text from the term paper:
in 350 BC (Olmstead, 1998). This makes conic sections one of the oldest math subjects to be studied systematically (Lee, 2003). Conics were viewed as a possible means for solving
three famous math problems: trisecting the angle, duplicating the cube, and squaring the circle (Lee, 2003). The conics were first defined as the "intersection of a right circular cone of
varying vertex angle; a plane perpendicular to an element of the cone," (an element of a cone is any line that makes up the cone) (Lee, 2003). If the angle
with which the cone is sliced can be less than, equal to, or greater than 90 degrees, which produces an ellipse, parabola or hyperbola, respectively (Lee, 2003). To put
this another way, these curves are defined in reference to sections sliced from a cone or pair of cones (picture the cones as meeting at their points. Imagine an ice
cream cone placed upside down on a table with a second cone balanced right side up on the tip of the first.) (Hyperbola, 2000). If a pair of cones is
sliced parallel to the base, it results in a circular section. Slicing at an angle causes the section cut to become an elongated circle, an ellipse. The more the knife
cutting the cone is angled, the ellipse produced will be correspondingly more elongated, up to the point where the curve is no longer closed and an open curve is produced.
This is called a parabola. A parabola is created only at the moment when the slice of the cone is parallel to the side of the cone (Hyperbola, 2000). This
is the only shape for a parabola, because if the knife is tilted more, a new curve is produce, the hyperbola (Hyperbola, 2000). As this suggests, a hyperbola has two
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