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1) Compare this with the parabola x 2 = 4 f y , {\displaystyle x^{2}=4fy,} (2) which has its vertex at the origin, opens upward, and has focal length f (see preceding sections of this article). Equations (1) and (2) are equivalent if R = 2 f . Therefore, this is the condition for the circle and parabola to coincide at and extremely close to the origin. The radius of curvature at the origin ...
In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form. (with a ≠ 0) in some Cartesian coordinate system . Solving for y leads to the explicit form. which imply that every real point satisfies x ≥ 0. The exponent explains the term semicubical parabola.
A parabolic segment. Quadrature of the Parabola ( Greek: Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC and addressed to his Alexandrian acquaintance Dositheus. It contains 24 propositions regarding parabolas, culminating in two proofs showing that the area of a parabolic ...
The line of thrust. Unlike a catenary arch, the parabolic arch employs the principle that when weight is uniformly applied above, the internal compression (see line of thrust) resulting from that weight will follow a parabolic curve. Of all arch types, the parabolic arch produces the most thrust at the base. Also, it can span the widest area.
Paraboloid. In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plane section of a paraboloid by a plane parallel to the axis of symmetry is a parabola.
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Parabola of safety. In classical mechanics and ballistics, the parabola of safety or safety parabola is the envelope of the parabolic trajectories of projectiles shot from a certain point with a given speed at different angles to horizon in a fixed vertical plane. The fact that this envelope is a parabola had been first established by ...
Parabolic reflector. A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface generated by a parabola revolving around its axis. The parabolic reflector transforms an ...