# parabola

## Definitions

• WordNet 3.6
• n parabola a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve
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Webster's Revised Unabridged Dictionary
• n Parabola (Geom) A kind of curve; one of the conic sections formed by the intersection of the surface of a cone with a plane parallel to one of its sides. It is a curve, any point of which is equally distant from a fixed point, called the focus, and a fixed straight line, called the directrix. See Focus.
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Century Dictionary and Cyclopedia
• n parabola Same as parabole.
• n parabola A curve commonly defined as the intersection of a cone with a Plane parallel with its side. The name is derived from the following property. Let the figure represent the cone. Let ABG be the triangle through the axis of the cone. Let DE be a line perpendicular to this triangle, cutting BG in H. Let the cone be cut by a plane through DE parallel to AG, so that the intersection with the cone will be the curve called the parabola. Let Z be the point where this curve cuts AB. Then the line ZH is called by Apollonius the diameter of the parabola, or the principal diameter, or the diameter from generation; it is now called the axis. From Z draw ZT at right angles to ZH and in the plane of ZH and AB, of such a length as to make ZT: ZA: BG: A B. AG. This line ZT is called the latus rectum; it is now also called the parameter. Now take any point whatever, as K, on the curve. From it draw KL parallel to DE meeting the diameter in L. ZL is called the abscissa. If now, on ZL as a base, we erect a rectangle equal in area to the square on KL, the other side of this rectangle may be precisely superposed upon the latus rectum, ZT. This property constitutes the best practical definition of the parabola. If a similar construction were made in the case of the ellipse, the side of the rectangle would fall short of the latus rectum; in the case of the hyperbola, would surpass it. The modern scientific definition of the parabola is that it is that plane curve of the second order which is tangent to the line at infinity. The parabola is also frequently defined as the curve which is everywhere equally distant from a fixed point called its focus, and from a fixed line called its directrix. The normal to a parabola at every point on the curve bisects the angle between the line parallel to the axis and the line to the focus. See also cuts under conic.
• n parabola By extension, any algebraical curve, or branch of a curve, having the line at infinity as a real tangent. Such a curve runs off to infinity without approximating to an asymptote. If the branch has an asymptote at one end but not at the other, it is not commonly termed a parabola.
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Chambers's Twentieth Century Dictionary
• n Parabola par-ab′o-la (geom.) a curve or conic section, formed by cutting a cone with a plane parallel to its slope (for illustration, see Cone)
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## Etymology

Webster's Revised Unabridged Dictionary
[NL., fr. Gr. ; -- so called because its axis is parallel to the side of the cone. See Parable, and cf. Parabole
Chambers's Twentieth Century Dictionary
Gr. parabolē; cf. Parable.

## Usage

### In literature:

As she spoke, a shot rose high in air and ended its parabola in the heart of the doomed city.
"The New England Magazine, Volume 1, No. 1, January 1886" by Various
He reached the height of the 'parabola,' and is now about to descend.
"Debts of Honor" by Maurus Jókai
At any convenient distance above J fasten a straight-edge A B, setting it parallel to the base C D of the parabola.
"Mechanical Drawing Self-Taught" by Joshua Rose
I can make it mighty tight though, if I make my surface a perfect parabola.
"The Ultimate Weapon" by John Wood Campbell
"Talents, Incorporated" by William Fitzgerald Jenkins
Is the orbit that of an ellipse, or a circle, or a parabola?
"Aether and Gravitation" by William George Hooper
Some shooting stars slipped suddenly, describing on the sky, as it were, the parabola of an enormous rocket.
"Bouvard and Pécuchet" by Gustave Flaubert
He sees them coming from afar, and, suspended like stones in a sling, describing their orbits and pushing forward their parabolas.
"The Temptation of St. Antony" by Gustave Flaubert
The parabola of a comet was perhaps a yet better illustration of the career of humanity.
"Looking Backward" by Edward Bellamy
At the age of 19, in 1657, he gave the first rectification of the semicubical parabola.
"A Budget of Paradoxes, Volume II (of II)" by Augustus de Morgan
You will remember that a Republican State is represented by a parabola.
"The Romance of Mathematics" by P. Hampson
It will here be only necessary to point to the connection which exists between the parabola and the ellipse.
"The Story of the Heavens" by Robert Stawell Ball
The next time, he flew to the peak in a zipping parabola that was as the course of a rocket.
"The Trimming of Goosie" by James Hopper
Well, to-morrow we must begin polishing, or rather I must, to turn our glass from a spherical-curved mirror into a parabola.
"The Vast Abyss" by George Manville Fenn
The human race seemed destined to an ambiguous future; the parabola of progress would one day reach its summit, and the fall begin.
"Religion and Science" by John Charlton Hardwick
FALL OF BODIES IN A PARABOLA.
"Conversations on Natural Philosophy, in which the Elements of that Science are Familiarly Explained" by Jane Haldimand Marcet and Thomas P. Jones
Hamlet darted the bus at the curves; then softly padded round like an angel: then off again for the next parabola.
"Sea and Sardinia" by D. H. Lawrence
In the most improved form these were made to that peculiar curve known as a parabola.
"Marvels of Scientific Invention" by Thomas W. Corbin
The flying gentleman soared softly into a parabola, coming down with a crash, while a pistol fell from his hand.
"Parson Kelly" by A. E. W. (Alfred Edward Woodley) Mason
While resembling the parabola in extending to infinity, the curve has closest affinities to the ellipse.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 2" by Various
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### In poetry:

Almond-tree, beneath the terrace rail,
Black, rusted, iron trunk,
You have welded your thin stems finer,
Like steel, like sensitive steel in the air,
Grey, lavender, sensitive steel, curving thinly and brittly up
in a parabola.
"Bare Almond-Trees" by D H Lawrence

### In news:

The quadratic formula, parabolas, the Fibonacci sequence.
Scoping out Lily Hoang's Parabola.
Lily Hoang's Parabola is the kind of text that solicits a rereading, but you aren't dutifully bound to return to its beginning.
Tent tops raise like parabola sails.
Those who trace a high-arcing parabola can call themselves dominant.
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### In science:

Near H = 0, the data points can be ﬁtted very well with a parabola, the coeﬃcient of the linear term gives the zero ﬁeld susceptibility χ = dm/dH |H=0 .
Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
For the smaller sizes we performed several ﬁelds values, as shown in Fig. 4, to determine for what range of ﬁelds a parabola accurately ﬁtted the data.
Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
For each system size, we ﬁt a parabola through the three data points for the average magnetization m(Hn ).
Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
To analyze the divergence of χ, we have again ﬁtted parabolas to the data points near the peak to obtain the positions h∗ (L) and χmax(L) of the maximum.
Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations
In this case, the GP equation (11) simply gives n(r) = g−1 [µ − Vext (r)], that is, a density having the form of an inverted parabola.
Helium nanodroplets and trapped Bose-Einstein condensates as prototypes of finite quantum fluids
Then, for each system size, a ﬁt to a parabola through the four data points for the average magnetization m(Hn ) is performed.
Critical exponents of four-dimensional random-field Ising systems
To analyze the divergence of χ, again parabolas were ﬁtted to the data points near the peak to obtain the positions h∗ (L) and χmax (L) of the maximum.
Critical exponents of four-dimensional random-field Ising systems
The ln L is thus a parabola in µ of the form − N 2 (µ − ¯x)2 .
A Search for Gamma-Ray Bursts and Pulsars, and the Application of Kalman Filters to Gamma-Ray Reconstruction
A lognormal distribution reduces to a parabola in its log / log representation. The quantity δrel,I can be computed analytically.
Broad distribution effects in sums of lognormal random variables
Figure 1: The left ﬁgure shows the positive parabolic CY volume which results from using the exact non-linear background in comparison to the linearized approximation which is given as the tangent to the parabola at the location of the visible boundary.
Enlarging the Parameter Space of Heterotic M-Theory Flux Compactifications to Phenomenological Viability
We construct F by ﬁtting parabolas touching tangents, determined by chords, at the points (n, f (n)).
Measure convolution semigroups and non-infinitely divisible probability distributions
If there exists an unique - Suppose that at the initial moment the particle is outside the S.s. solution ρ of (3.2), such that ρ < ρs, then the tra jectory will look like a parabola or hyperbola and will never pass inside the S.s.
New Relativistic Equations of Motion and Their Comparison with the Equations from the General Relativity
Although we shall consider ellipses as planetary tra jectories, the obtained results are also true if the tra jectory of a planet is a hyperbola or a parabola.
New Relativistic Equations of Motion and Their Comparison with the Equations from the General Relativity
It is found to be a parabola as shown in Figure 2.
Application of Theorems on Null-Geodesics on the Solar Limb Effect
FIG. 2: (Color online) Parametric plot for solutions of (5) for N < Nc (dots) for RF, equivalent to (6) (solid line, parabola) and ﬂ ow (arrows). f parameterizes disorder and only f ≥ 0 is physical.
Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension
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