Instructional Unit
The Conics
By: Diana Brown
Introduction
There are
four mathematical curves that can be found in a cone, and these curves are
called The Conics, or The Conic Sections. The four conic sections, circle, ellipse,
parabola, hyperbola can be seen as slices of a cone.
If the cone
is sliced parallel to the base, the resulting curve is a circle.
If the cone
is sliced on a slight angle, the curve is called an ellipse.
If the slice
is made parallel to the edge of the cone, the curve formed is called a
parabola.
If the slice
is perpendicular to the base of the cone, the curve is one of two branches of a
hyperbola. Mathematicians are interested
in two branches of the hyperbola, formed by putting two cones together.
Diagram of
Conics as represented above:
Real
world representations of conics
We see cones around us every day: ice cream cones,
traffic cones, and cone-shaped sushi
Ellipse:
The orbits of the planets are elliptical and the earth
itself is an ellipsoid. A circle viewed from an angle looks like an ellipse.
Parabola:
The parabola is the path followed by a
thrown ball or by a spout of water in a fountain. Upside down parabolas are
seen in some suspension bridges.
Hyperbola:
The pattern of light cast on a wall by a lampshade is
a hyperbola.
More
real world representations of conics
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