According to the geometric point of view an ellipse has two focuses and two axes (the bigger axis and the smaller axis). We can define an ellipse as being the set of plane points so that the addition of their distances to the focuses is always the same. One of the features is that any luminous ray that comes from one of the focuses is reflected by the ellipse to another focus.

## Is a circumference different from an ellipse?

Yes and no, because every circumference is an ellipse but not every ellipse is a circumference. So as to give you a better explanation, I will tell you that a circumference is a special kind of ellipse in which two focuses meet each other in the same place.

## Can I draw an ellipse with a compass?

No, you can’t. The compass is only useful to draw circumferences since all the points are at the same distance from the centre. It does not happen with the ellipse whose distance from the points to the centre changes. The best method to draw an ellipse is shown in the following animation and it requires fixing a string to two points (the focuses of the ellipse).

## What is an ellipse useful for?

During many years the circumference was believed to represent the “perfection” of a geometric figure. Astronomers tried in vain to describe the stars orbit through the use of the circumference. All the attempts showed some margin of error. It was Johannes Kepler who, about 1610, after a hard study of Mars Planet Orbit, found it was an ellipse. He went further when he found that the Planet raises its speed when it comes closer to the sun and it slows down when it moves away. From then on Kepler checked the orbit of the other Planets belonging to the solar system and he found that all of them move themselves according to an elliptic orbit around the sun, having attention to the fact that the sun occupied one of the focuses of the ellipse. However, Kepler did not find the ellipse since this geometric figure was already known for some hundreds of years before the birth of Christ. There are references to the ellipse in the ancient manuscripts coming from the famous library of Alexandria!

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