# Applications of the Ellipse

Ellipses are conic sections formed by a plane that intersects a cone. Ellipses are characterized by the fact that the sum of the distances from any point on the ellipse to two fixed points is equal to a constant. The fixed points are called the foci of the ellipse. The shape of the ellipse and its properties make it useful in several areas.

For example, ellipses are used in architecture to design buildings and rooms, in carpentry to design tables and shelf pieces. Ellipses even have their application in the Kepler orbits of planets and satellites.

##### PRECALCULUS

Relevant for

Learning about the various applications of an ellipse.

See applications

##### PRECALCULUS

Relevant for

Learning about the various applications of an ellipse.

See applications

## Planetary orbits

The orbits of the planets follow an elliptical path. Kepler’s first law of planetary motion says: The path of each planet is an ellipse with the sun at one focus.

This means that the different parameters and the different formulas of the ellipses can be used to perform calculations on the trajectory of planets or satellites. This is very useful in astronomy and aerospace engineering.

## 3D objects formed from ellipses

Ellipses can form different shapes and three-dimensional objects when rotated. For example, if we rotate an ellipse with respect to its major axis, we get a football.

It is also possible to form elliptical shapes of food. This results in a refined touch for meals that could be simple. For example, cutting carrots, cucumbers, or other similar foods at an angle to their main axis, results in elliptical slices.

## Architecture

Various elliptical shapes can be used in architecture to enhance building design and produce unique properties. An example of this is the National Statuary Hall in the United States. This building is elliptical and has a very interesting acoustic phenomenon.

John Quincy Adams was the one who discovered this phenomenon. He placed his desk at a focal point of the elliptical ceiling and this allowed him to hear private conversations from other members of the representative house who were located near the other focal point.

Rooms or buildings that have acoustic properties are called whispering galleries. These rooms have a special construction that allows conversations to be heard at a specific point, even in a low voice, that take place at any other point of the building.

This property stems from the design of the roof and the shape of the walls. The sound waves that start from a point are reflected when they encounter an obstacle, so in an elliptical ceiling, the sounds produced in one of the foci are reflected in another of the foci of the ellipse.

## Carpentry

Elliptical shapes can enhance the design of various pieces of woodwork such as tables, shelving parts, and bookcases. Additionally, the reflective property of ellipses is useful in elliptical pool tables. As the name implies, the elliptical pool tables is shaped like an ellipse.

When you hit the ball so that it passes through one focus, it will reflect off the ellipse and go into the hole that is located at the other focus.