![]() ![]() Parabolic mirrors are used in most modern reflecting telescopes and in satellite dishes and radar receivers. 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. Designs were proposed in the early to mid-17th century by many mathematicians, including René Descartes, Marin Mersenne, and James Gregory. The idea that a parabolic reflector could produce an image was already well known before the invention of the reflecting telescope. Galileo showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity. The focus–directrix property of the parabola and other conic sections is due to Pappus. It means "application", referring to "application of areas" concept, that has a connection with this curve, as Apollonius had proved. The name "parabola" is due to Apollonius, who discovered many properties of conic sections. (The solution, however, does not meet the requirements of compass-and-straightedge construction.) The area enclosed by a parabola and a line segment, the so-called "parabola segment", was computed by Archimedes by the method of exhaustion in the 3rd century BC, in his The Quadrature of the Parabola. He discovered a way to solve the problem of doubling the cube using parabolas. The earliest known work on conic sections was by Menaechmus in the 4th century BC. History Parabolic compass designed by Leonardo da Vinci It is frequently used in physics, engineering, and many other areas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design of ballistic missiles. This reflective property is the basis of many practical uses of parabolas. The same effects occur with sound and other waves. Conversely, light that originates from a point source at the focus is reflected into a parallel (" collimated") beam, leaving the parabola parallel to the axis of symmetry. Parabolas have the property that, if they are made of material that reflects light, then light that travels parallel to the axis of symmetry of a parabola and strikes its concave side is reflected to its focus, regardless of where on the parabola the reflection occurs. Any parabola can be repositioned and rescaled to fit exactly on any other parabola-that is, all parabolas are geometrically similar. Parabolas can open up, down, left, right, or in some other arbitrary direction. ![]() The " latus rectum" is the chord of the parabola that is parallel to the directrix and passes through the focus. The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The point where the parabola intersects its axis of symmetry is called the " vertex" and is the point where the parabola is most sharply curved. 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". ![]() Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. One description of a parabola involves a point (the focus) and a line (the directrix). It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. The parabola is a member of the family of conic sections. In this orientation, it extends infinitely to the left, right, and upward. ![]() Part of a parabola (blue), with various features (other colours). Look up parabola in Wiktionary, the free dictionary. ![]()
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