# ellipse

## Definitions

• Ellipse
• WordNet 3.6
• n ellipse a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it "the sums of the distances from the foci to any point on an ellipse is constant"
• ***
Webster's Revised Unabridged Dictionary
• Ellipse (Geom) An oval or oblong figure, bounded by a regular curve, which corresponds to an oblique projection of a circle, or an oblique section of a cone through its opposite sides. The greatest diameter of the ellipse is the major axis, and the least diameter is the minor axis. See Conic section, under Conic, and cf. Focus.
• Ellipse (Gram) Omission. See Ellipsis.
• Ellipse The elliptical orbit of a planet. "The Sun flies forward to his brother Sun;
The dark Earth follows wheeled in her ellipse ."
• ***
Century Dictionary and Cyclopedia
• n ellipse In geometry, a plane curve such that the sums of the distances of each point in its periphery from two fixed points, the foci, are equal. It is a conic section (see conic) formed by the intersection of a cone by a plane which cuts obliquely the axis and the opposite sides of the cone. The ellipse is a conic which does not extend to infinity, and whose intersections with the line at infinity are imaginary. Every ellipse has a center, which is a point such that it bisects every chord passing through it. Such chords are called diameters of the ellipse. A pair of conjugate diameters bisect, each of them, all chords parallel to the other. The longest diameter is called the transverse axis, also the latus transversum; it passes through the foci. The shortest diameter is called the conjugate axis. The extremities of the transverse axis are called the vertices. (See conic, eccentricity, angle.) An ellipse may also be regarded as a flattened circle—that is, as a circle all the chords of which parallel to a given chord have been shortened in a fixed ratio by cutting off equal lengths from the two extremities. The two lines from the foci to any point of an ellipse make equal angles with the tangent at that point. To construct an ellipse, assume any line whatever, AB, to be what is called the latus rectum. At its extremity erect the perpendicular AD of any length, called the latus transversum (transverse axis). Connect BD, and complete the rectangle DABK. From any point L, on the line AD, erect the perpendicular LZ, cutting BK in Z and BD in H. Draw a line HG, completing the rectangle ALHG. There are now two points, E and E′ , on the line LZ, such that the square on LE or LE′ is equal to the rectangle ALHG. The locus of all such points, found by taking L at different places on the line AD, forms an ellipse. [The name ellipse in its Greek form was given to the curve, which had been previously called the section of the acute-angled cone, by Apollonius of Perga, called by the Greeks “the great geometer.” The participle ἐλλείπων, “falling short,” had long been technically applied to a rectangle one of whose sides coincides with a part of a given line (see Euclid, VI. 27). So παραβάλλειν and ύπερβάλλειν, (Euclid, VI. 28, 29) were said of a rectangle whose side extends just as far and overlaps respectively the extremity of a given line. Apollonius first defined the conic sections by plane constructions, using the latus rectum and latus transversum (transverse axis), as above. The ellipse was so called by him because, since the point L lies between A and D, the rectangle ALHG “falls short” of the latus rectum AB. In the case of the hyperbola L lies either to the left of A or to the right of D, and the rectangle ALHG “overlaps” the latus rectum. In the case of the parabola there is no latus transversum, but the line BK extends to infinty, and the rectangle equal to the square of the ordinate has the latus rectum for one side.]
• ***
Chambers's Twentieth Century Dictionary
• n Ellipse el-lips′ an oval:
• n Ellipse el-lips′ (geom.) a figure produced by the section of a cone by a plane passing obliquely through the opposite sides
• ***

## Quotations

• Victor Hugo
“Mankind is not a circle with a single center but an ellipse with two focal points of which facts are one and ideas the other.”

## Etymology

Webster's Revised Unabridged Dictionary
Gr. 'e`lleipsis, prop., a defect, the inclination of the ellipse to the base of the cone being in defect when compared with that of the side to the base: cf. F. ellipse,. See Ellipsis
Chambers's Twentieth Century Dictionary
L.,—Gr. elleipsiselleipein, to fall short—en, in, leipein, to leave.

## Usage

### In literature:

The earth's orbit is an ellipse, one of the foci of which is occupied by the sun.
"Fragments of science, V. 1-2" by John Tyndall
In the same way, by reversing the motion, the other half of the ellipse may be completed.
"Aether and Gravitation" by William George Hooper
Its orbit is not a circle; it is an ellipse, but not very far removed from the circular path.
"Harper's New Monthly Magazine, Vol. 3, July, 1851" by Various
For the Indians were riding on in the ellipse, and another man fitted an arrow to his bowstring, and as he rode by loosed it off.
"The Peril Finders" by George Manville Fenn
The cells in the Tombs are arranged in rows in the form of an ellipse in the centre of each of the six floors.
"The Third Degree" by Charles Klein and Arthur Hornblow
Such oval figures, it will be remembered, are technically known as ellipses.
"Astronomy of To-day" by Cecil G. Dolmage
Kepler, replaced them all by a simple ellipse.
"Pioneers of Science" by Oliver Lodge
It isn't a parabola and it isn't an ellipse.
"Astounding Stories of Super-Science, March 1930" by Various
As for the alleged instances of ellipses, I maintain they are not analogous.
"Notes and Queries, Number 218, December 31, 1853" by Various
Within these was the inner ellipse of nineteen obelisks surrounding the altar-stone.
"England, Picturesque and Descriptive" by Joel Cook
***

### In poetry:

The orb that rolls in dim eclipse
Wide wheeling round its long ellipse,--
His name Urania writes with these
And stamps it on her Pleiades.
"Benjamin Peirce" by Oliver Wendell Holmes

### In news:

On July 30, 2011, thousands of public school teachers rallied on the southwest corner of the Ellipse, near the White House.
Winnebago Industries has introduced the 42JD floor plan to its lineup of 2012 Itasca Ellipse type A motorhomes.
The Ellipse 42JD is built on a Maxum chassis and is equipped with three slideouts, including a full-wall slide on the street side.
Kansas City-based Xikar has released its new Ellipse II lighter, a second generation and step up from the original design.
A lighting ceremony took place for the National Hanukkah Menorah, the world's largest, on the Ellipse, just across from the White House on the second night (first day) of the eight-day Jewish holiday.
President Obama will preside over an evening festival of star-studded carols and sparkling displays of holiday cheer on the White House Ellipse.
With a little help from Jason Mraz, Colbie Caillat, The Fray, James Taylor and a few other artists, President Obama lit the new National Christmas Tree Thursday night on the Ellipse in Washington, DC, continuing 90 years of holiday tradition.
President Obama is joined by his daughter Malia and first lady as they watch the show at official lighting of National Christmas Tree ceremony on Ellipse in Washington ( Larry Downing, Reuters ).
President Obama is joined by his daughter Malia and first lady as they watch the show at official lighting of National Christmas Tree ceremony on Ellipse in Washington.
First lady Michelle Obama (R) and their daughters Malia (C) and Sasha Obama light the 90th National Christmas Tree during the Lighting Ceremony on the Ellipse behind the White House on December 6, 2012 in Washington, DC.
The National Menorah sits in the Ellipse just south of the White House.
9, 2010: The National Christmas Tree is shown at the Ellipse across from the White House in Washington.
Johns Hopkins University will be the beneficiary of a pedestrian-friendly "ellipse" in front of the Homewood campus entrance, giving the street the feel and look of a plaza.
Ellipses Are A Red Flag .
The other day, all of us DJ's received an e-mail with blogging guidelines per corporate and they BANNED ellipses.
***

### In science:

Now let C be one of the inscribed osculating ellipses and denote its aﬃne curvature by κ.
Sextactic points on a simple closed curve
An inscribed ellipse is said to be maximal if it is not strictly contained in any other inscribed ellipse.
Sextactic points on a simple closed curve
Let Γp,q be the one dimensional family of ellipses that is tangential to γ in p and q .
Sextactic points on a simple closed curve
Since pq meets γ transversally in p and q , we have inscribed ellipses in the family.
Sextactic points on a simple closed curve
We can also deﬁne the maximal inscribed ellipse C • p,q when p = q .
Sextactic points on a simple closed curve
***