Jun 10, 2010

Posted by in Math

Parabola

parabolaIn mathematics, the parabola is a conic, the intersection of a right circular conical surface and a plane for a production line right of this region. Given a point (center) and a corresponding line (the director) on the plan, the location of points in this plan, which is equal distance between them is a parabola.

The parabola has many applications in the automotive headlight reflectors in the design of ballistic missiles. They are often used in physics, engineering and many other areas.

The similarity was studied by Menaechmus in an attempt to achieve doubling of the cube. Menaechmus solve the problem of finding the intersection of two parabolas x ^ 2 = y ^ 2 and y = 2x. Euclid wrote about the resemblance, and got its present name by Apollonius. Pascal has the parabola as a projection of a circle, and Galileo showed that projectiles fall by gravity parabolic trajectories to follow uniform.

The pedal of the parabola whose apex is closed with a Cissoid. The pedal of the parabola with focus as a highlight is a straight line. At the foot of the director when it comes to a climax Strophoid law (an oblique Strophoid another point in the Directive). The pedal of the curve, when the pedal is the image of the object in the directive is a Trisectrix Maclaurin.

The evolute of the parabola is a parabola Neil. From a point above the three normal development can be learned from the parable, while only one normal can be drawn from the parable of a point below the evolute.

As the center of the dish is considered the center of the inversion, the inverse parabola with a cardioid. If the top of the dish is considered the center of the inversion, the opposite of a parabolic Cissoid Diocles.

The caustic of the dish with the spokes perpendicular to the axis of the parabola is cubic Tschirnhaus.

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