Parabola is a quarterly magazine published by The Society for the Study of Myth and Tradition. Each issue centers around one topic, such as death, and is explored philosophically using many different view points. In each issue, you will find a short story, traditional myth or essay from an Indian (as in Native American), Eastern, Orthodox Christian or Classical Greek view point as often as you will see one from a Judeo-Christian perspective. It's expensive but if the topic being discussed interests you, very much worth the money.

One of the conic sections. In this vein, its relatives are the circle, the ellipse and the hyperbola. The generating equation for a parabola centered on the origin is y=ax² for some constant a. Other parabolic shapes can be generated with the equation y=ax²ⁿ for some constant a in the real numbers and n in the natural numbers.

The defining characteristic of a parabola is that each point is equidistant from a point P and a line L which does not pass through the point. To this end, each point of a parabola is the center of a circle whose edge passes through the point P and touches the line L. The idea of a circle comes into play because each point on the edge of a circle is equidistant from the center.

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Uses: mirrors in telescopes or headlights; parabolic surfaces in sound reflection; etc. The reason for these uses is that radiated energy from the focus of the parabola always ends up travelling in one direction. For example, a headlight contains a light source and a parabolic mirror. When any particular light beam from the light source hits the sides of the parabolic mirror, that beam is then directed in one direction (and only that direction, ignoring diffusion), parallel to all the other light beams which have bounced off the mirror. This is a partial laser effect; it is not complete since most light beams are significantly diffused at production, and few mirrors are "perfect".

Useful information about parabolas:

			Vertical axis		Horizontal axis		
Standard Form:		(x-h)²=4p(y-k)		(y-k)²=4p(x-h)
Eccentricity:		e=1			e=1
Length of latus rectum:	l=|4p|			l=|4p|
Directrix:		y=k-p			x=h-p
Vertex:			(h,k)			(h,k)
Focus:			(h,k+p)			(h+p,k)
Opening direction:	p<0 down, p>0 up	p<0 left, p>0 right
Parametric Form:	x′=2pt+h		x′=2pt²+h
			y′=2pt²+k		y′=2pt+k

See also:

• Conic Section
• Ellipse
• Hyperbola
• Circle

Pa*rab"o*la (?), n.; pl. Parabolas (#). [NL., fr. Gr. ; -- so called because its axis is parallel to the side of the cone. See Parable, and cf. Parabole.] Geom.

(a) 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.

(b) One of a group of curves defined by the equation y = axⁿ where n is a positive whole number or a positive fraction. For the cubical parabola n = 3; for the semicubical parabola n = 3/2. See under Cubical, and Semicubical. The parabolas have infinite branches, but no rectilineal asymptotes.<

 

© Webster 1913.