This page presents information about the traditional views of conic sections.
Conics from a Function Viewpoint are presented on another page.
|Think Two Cones|
The name conic refers to the cones. Think really, really, thin, infinitly big, empty ice cream cone -- just the shell, just one-point-thick.
Think thinner than a piece of paper.
Think the light blue is the outer surface of the cone one-point-thick.
Think the dark blue is the inner surface of the cone one-point-thick. Remember that a point has no thickness, so, this is really thin.
The cones are sliced or cut by a plane to create a section or part of the cone. See below.
Though cuts are drawn to show an area, remember that the cut is really only the edge -- the part of the one-point-thick empty infinite cone.
The conic section is ONLY THE BLACK STRING OF POINTS AT THE EDGE OF THE PINK SURFACE.
|All Conic Sections|
Conic section are ancient mathematical ideas. They are curves, strings of points.
To a mathematician, a curve might be straight, as in a line, or have a bend or two as in a parabola or hyperbola.
It might be closed or form a loop, as in a circle or ellipse.
A point, a line, or two intersecting lines are often called degenerate conics because they are possible to form as a plane cuts the cones, but, are not the circle, ellipse, parabola, or hyperbola usually listed as the conices.
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|Cut the Cones Perspective|
Return to the Individual Pictures shown above and click on each picture so you are better able to examine how a plane passing through one or more cones creates the black string of points called a conic.
Examine the pictures and contemplate the angle at which the plane cuts the cones.
Examine the picture and summary below for a complete analysis.
Visit Conics from A Functions, modern, calculator useful, basis.
© 2007, Agnes Azzolino