THE ELLIPSE

Though not so simple as the circle, the ellipse is nevertheless the curve most often "seen" in everyday life. The reason is that every circle, viewed obliquely, appears elliptical


Any cylinder sliced on an angle will reveal an ellipse in cross-section (as seen in the Tycho Brahe Planetarium inCopenhagen).

Tilt a glass of water and the surface of the liquid acquires an elliptical outline. Salami is often cut obliquely to obtain elliptical slices which are larger.

The early Greek astronomers thought that the planets moved in circular orbits about an unmoving earth, since the circle is the simplest mathematical curve. In the 17th century, Johannes Kepler eventually discovered that each planet travels around the sun in an elliptical orbit with the sun at one of its foci.

The orbits of  the moon and of artificial satellites of the earth are also elliptical as are the paths of comets in permanent orbit around the sun

Halley's Comet takes about 76 years to travel abound our sun. Edmund Halley saw the comet in 1682 and correctly predicted its return in 1759. Although he did not live long enough to see his prediction come true, the comet is named in his honour.

On a far smaller scale, the electrons of an atom move in an approximately elliptical orbit with the nucleus at one focus.

The ellipse has an important property that is used in the reflection of light and sound waves. Any light or signal that starts at one focus will be reflected to the other focus. This principle is used in lithotripsy, a medical procedure for treating kidney stones. The patient is placed in a elliptical tank of water, with the kidney stone at one focus. High-energy shock waves generated at the other focus are concentrated on the stone, pulverizing it.

The principle is also used in the construction of "whispering galleries" such as in St. Paul's Cathedral in London. If a person whispers near one focus, he can be heard at the other focus, although he cannot be heard at many places in between.

Statuary Hall in the U.S. Capital building is elliptic. It was in this room that John Quincy Adams, while a member of the House of Representatives, discovered this acoustical phenomenon. He situated his desk at a focal point of the elliptical ceiling, easily eavesdropping on the private conversations of other House members located near the other focal point.

The ability of the ellipse to rebound an object starting from one focus to the other focus can be demonstrated with an elliptical pool table. When a ball is placed at one focus and is thrust with a cue stick, it will rebound to the other focus. If the pool table is live enough, the ball will continue passing through each focus and rebound to the other.