parabola object
In mathematics, the parabola (pronounced /pəˈræbələ/, plural parabolae or parabolas, from the Greek παραβολή) is a conic section, the intersection of a right circular conical surface and a
plane parallel to a generating straight line of that surface.
Given a point (the focus) and a corresponding line (the directrix) on the plane, the locus of points in that plane that are equidistant from them is a parabola. The line perpendicular to the directrix and passing through the focus (that is the line that splits the parabola through the middle)is called the "axis of symmetry". The point on the axis of symmetry that intersects the parabola is called the "vertex". The vertex is the point where the curvature is greatest. Parabolas can open up, down, left, right, or in some other arbitrary direction.
The name "parabola" is derived from a New Latin term that means something similar to "compare" or "balance".
parabola graph
The parabola has many important applications, from automobile headlight reflectors to the design of ballistic missiles. They are frequently used in physics, engineering, and many other areas.
earliest known work on conic sections was by Menaechmus in the fourth century BC. He discovered a way to solve the problem of doubling the cube using parabolae. (The solution, however, does not meet the requirements imposed by compass and straightedge construction.) The area enclosed by a parabola and a line segment, the so-called "parabola segment", was computed by Archimedes via the method of exhaustion in the third
century BC, in his The Quadrature of the Parabola. The name "parabola" is due to Apollonius, who discovered many properties of conic sections. The focus–directrix property of the parabola and other conics is due to Pappus.
Galileo showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity.
The idea that a parabolic reflector could produce an image was already well-known before the invention of the reflecting telescope. Designs were proposed in the early to mid seventeenth century by many mathematicians including René Descartes, Marin Mersenne, and James Gregory. When Isaac Newton built the first reflecting telescope in 1668 he skipped using a parabolic mirror because of the difficulty of fabrication, opting for a spherical mirror. Parabolic mirrors are used in most modern reflecting telescopes and in satellite dishes and radar.
A parabola may also be characterized as a conic section with an eccentricity of 1. As a consequence of this, all parabolae are similar, meaning that while they can be different sizes, they are all the same shape. A parabola can also be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction. In this sense, a parabola may be considered an ellipse that has one focus at infinity. The parabola is an inverse transform of a cardioid.
A parabola has a single axis of reflective symmetry, which passes through its focus and is perpendicular to its directrix. The point of intersection of this axis and the parabola is called the vertex. A parabola spun about this axis in three dimensions traces out a shape known as a paraboloid of revolution.