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A parabola (; plural ''parabolas'' or ''parabolae'', adjective ''parabolic'', from (ギリシア語:παραβολή)) is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram below, but which can be in any orientation in its plane. It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape. One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane which is parallel to another plane which is tangential to the conical surface. A third description is algebraic. A parabola is a graph of a quadratic function, , for example. 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 parabola that intersects the axis of symmetry is called the "vertex", and is the point where the parabola is most sharply curved. The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola which is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola — that is, all parabolas are geometrically similar. Parabolas have the property that, if they are made of material that reflects light, then light which 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. 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. The same effects occur with sound and other forms of energy. This reflective property is the basis of many practical uses of parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors to the design of ballistic missiles. They are frequently used in physics, engineering, and many other areas. Strictly, the adjective ''parabolic'' should be applied only to things that are shaped as a parabola, which is a two-dimensional shape. However, as shown in the last paragraph, the same adjective is commonly used for three-dimensional objects, such as parabolic reflectors, which are really paraboloids. Sometimes, the noun ''parabola'' is also used to refer to these objects. Though not perfectly correct, this usage is generally understood. ==History== The 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 parabolas. (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. It means "application", referring to "application of areas" concept, that has a connection with this curve, as Apollonius had proved.〔(Apollonius' Derivation of the Parabola ) at (Convergence )〕 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.〔, (Extract of page 3 ) 〕 Designs were proposed in the early to mid seventeenth century by many mathematicians including René Descartes, Marin Mersenne,〔''Stargazer'', (p. 115 ).〕 and James Gregory.〔''Stargazer'', (pp. 123 and 132 )〕 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 receivers. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「parabola」の詳細全文を読む スポンサード リンク
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