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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