IBM Educational Project

Conic Sections

When intersecting a cone with a plane, the resulting contour of the intersection is either a circle, an ellipse, a parabola, or a hyperbola. The different curves are obtained by tilting the plane. Moving the plane up or down will scale the current curve. If the plane passes through the tip of the cone, so-called degenerated conic sections (a point, a line, or two intersecting lines) are obtained.

Conic sections have been studied for over 2000 years and are still important tools for present-day investigations in science, engineering, and other areas. Some well-known examples: a planet's orbit around the sun (ellipse), the cable of a suspension bridge (parabola), a telescopic lens (hyperbola).

Our VRML model allows the user to tilt and move the intersecting plane interactively and observe the resulting contours in real-time. All types of conic sections, including the degenerated cases, can be produced. The three-dimensional cone-plane model can be rotated and inspected from all sides. This facilitates the comprehension of a specific arrangement and the understanding of the resulting contour.


Selected Links

Our Pilot VRML Model of Conic Sections

Click here to explore conic sections with our VRML 2.0 model (26K). Two viewpoints (Entry and From Above) are preset in this scene. To control the intersection of the plane with the cone, use the two sliders. The bar controls the vertical placement of the plane and the circle controls the angle of the plane with respect to the cone. Some settings are preset and can be selected by clicking on the arrows. Depending on the type of computer you are using, you may see the pointer (cursor) change when it is above the arrows, indicating that they are active. You also can click on the slider lines and drag them to change the position continuously. The spinning of the cone and plane can be turned on or off by clicking on either object.

Click here to explore conic sections with a NEW version of our VRML 2.0 model (100K). This version has a FlyRide animated viewpoint and the top of the blue cone can be "blown off" by clicking on the cone. To put the top back on, click on the word Ellipse, which describes this cone-plane intersection. The plane intersecting the center (yellow) cone still spins when you click on either the plane or cone and stops when you click again.

Last Update: April 24, 2001, kpb

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