Importance of Ellipse

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IMPORTANCE OF ELLIPSE By: Jovilyn B. Marquez

Transcript of Importance of Ellipse

Page 1: Importance of Ellipse

IMPORTANCE OF ELLIPSE

By: Jovilyn B. Marquez

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ELLIPSE• An ellipse is all points found by keeping the

sum of the distances from two points (each of which is called a focus of the ellipse) constant. The midpoint of the segment connecting the foci is the center of the ellipse. An ellipse can be formed by slicing a right circular cone with a plane traveling at an angle to the base of the cone.

• A curved planar figure, the locus of all points which have the same total distance from two fixed points called the foci.

DEFINITION

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Applications of Ellipse in our Daily Life

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If you cut a cylinder at an angle, you will get elliptical sections. This can have important applications in optics (lenses and mirrors can be elliptical in shape), or in the kitchen (where one might cut vegetables or sausage along a "bias cut" in order to obtain pieces that have the same thickness, but have more surface area exposed.

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Some tanks are in fact elliptical (not circular) in cross section. This gives them a high capacity, but with a lower center-of-gravity, so that they are more stable when being transported. And they're shorter, so that they can pass under a low bridge. You might see these tanks transporting heating oil or gasoline on the highway.

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The ellipse is found in art and architecture, and you may be familiar with the Ellipse, part of a President's Park South (a National Park in Washington, DC, just south of the White House).

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Ellipses (or half-ellipses) are sometimes used as fins, or airfoils in structures that move through the air.

The elliptical shape reduces drag.

FIN(water)

AIRFOIL(air)

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On a bicycle, you might find a chain wheel (the gear that is connected to the pedal cranks) that is approximately elliptical in shape. Here the difference between the major and minor axes of the ellipse is used to account for differences in the speed and force applied, because your legs push and pull more effectively when the pedals are arranged so that one pedal is in front and one is in back, than when the pedals are in the "dead zone" (when one pedal is up and one pedal is down).

CHAIN WHEEL/ CHAIN RING

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• 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.

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

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• 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.

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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. 

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

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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.

Lithotripsy machine

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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. 

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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.

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The ability of the ellipse to rebound an object starting from one focus to the other focus can be demonstrated with an elliptical billiard 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 billiard table is live enough, the ball will continue passing through each focus and rebound to the other.

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THANK YOU |m|

-joba \m/