# Focal Points, Ellipses and Ovals

←Make Hyperbolic Tilings of Images | Rolling Hypocycloids and Epicycloids→ |
---|

## Interactive three-ellipse and three-pins-and-a-string blob

- Move the pins.
- l-key => longer string
- s-key => shorter string

three-pins-and-a-string-blob ↑

3-ellipse ↓

Using a pin and a string one can draw a circle.

Using two pins and a string one can draw an ellipse.

Using three pins and a string one can draw a three-pins-and-a-string-blob. The blob is a curve made from six elliptical arcs. A three-pins-and-a-string-blob is shown in the first canvas.

Another way to go from **two** to **three** is to consider the focal points. An ellipse has two focal points. For any
point on the ellipse the sum of the distances to the **two** focal points is constant.

A 3-ellipse has three focal points. For any
point on the 3-ellipse the sum of the distances to the **three** focal points is constant. A 3-ellipse is shown in the second canvas.

A circle can be seen as a 1-ellipse. It is possible to make a
`n`-ellipse for any positive integer `n`.

## Interactive tree foci variant of Cassini oval

A Cassini oval is a curve defined by two focal points, just as an ellipse is. For all points on an ellipse, the **sum
of distances** to the focal points is constant. For a Cassini oval, on the other hand, the **product
of distances** to the focal points is constant. In the canvas above the curves are defined by **three** focal points.

## Animated gifs

3-ellipse on tumblr.

Cassini swing on tumblr.