Ovals upon ovals!

A circle has a center c and a radius r. The points on the circle are all a distance of exactly r units from c. What if we start with two fixed center points? The set of points on an ellipse have a fixed sum-distance to two center points c1 and c2 (called foci). An ellipse has kind of an oval shape. Ellipses occur in nature – the Earth’s orbit is not a perfect circle but rather an ellipse, with the Sun being just one of the two foci.

In this activity we investigated how to draw ellipses using pushpins and string. We also asked whether it is possible to have more than two fixed center points.

Some questions we investigated

  • How can you use two push-pins and a string to draw an ellipse?
  • What happens when the push-pins are close together? What happens when they are far apart?
  • How can you describe the set of points on an ellipse algebraically?
  • What is the area of an ellipse? We did this by drawing a big ellipse and cutting up the paper.
  • What happens if you have three push-pins? Can you arrange your string properly to create a shape with three foci?

Pictures

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