Conic sections
A plane cutting a cone can produce a circle, ellipse, parabola, or hyperbola, depending on its position.
07 / ANTIQUITY TO THE RENAISSANCE
Apollonius of Perga
Two pins, a piece of string, and a pencil can draw an exact ellipse. What does the string keep constant?
Explore the mathematics ↓
01 / THE ELLIPSE
Draw a curve with two pins and a string
Push two pins into a board and tie a string between them, with some slack. Pull it tight with a pencil and draw.
Gardeners still mark out oval flower beds this way.
What curve does a string on two pins draw?
Keep the string tight and drag the pencil all the way around the pins.
Pin A to pencil
=Pencil to pin B
=The whole string
THE IDEAAn ellipse keeps the total distance to its two pins constant. The pins are called its foci.
The person behind the ideas
- Born in Perga, in present-day Türkiye.
- His treatise Conics developed a systematic study of sections of cones.
- His work helped establish the names ellipse, parabola, and hyperbola.
More of the mathematics
Tangents and diameters
Conics investigates relationships within these curves, including tangent lines and diameters.