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  2. Paraboloid - Wikipedia

    en.wikipedia.org/wiki/Paraboloid

    Paraboloid of revolution. ... and R is the radius of the ... The surface area of a parabolic dish can be found using the area formula for a surface of revolution ...

  3. List of centroids - Wikipedia

    en.wikipedia.org/wiki/List_of_centroids

    r = the radius of the cone's base h = the distance is from base to the apex ... Solid paraboloid of revolution around z-axis: a = the radius of the base circle

  4. Parabolic reflector - Wikipedia

    en.wikipedia.org/wiki/Parabolic_reflector

    If the dish is symmetrical and made of uniform material of constant thickness, and if F represents the focal length of the paraboloid, this "focus-balanced" condition occurs if the depth of the dish, measured along the axis of the paraboloid from the vertex to the plane of the rim of the dish, is 1.8478 times F. The radius of the rim is 2.7187 F.

  5. Surface of revolution - Wikipedia

    en.wikipedia.org/wiki/Surface_of_revolution

    A portion of the curve x = 2 + cos(z) rotated around the z-axis A torus as a square revolved around an axis parallel to one of its diagonals.. A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints). [1]

  6. Parabola - Wikipedia

    en.wikipedia.org/wiki/Parabola

    In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...

  7. Parabolic cylindrical coordinates - Wikipedia

    en.wikipedia.org/wiki/Parabolic_cylindrical...

    The radius r has a simple formula as well r = x 2 + y 2 = 1 2 ( σ 2 + τ 2 ) {\displaystyle r={\sqrt {x^{2}+y^{2}}}={\frac {1}{2}}\left(\sigma ^{2}+\tau ^{2}\right)} that proves useful in solving the Hamilton–Jacobi equation in parabolic coordinates for the inverse-square central force problem of mechanics ; for further details, see the ...

  8. Parabolic antenna - Wikipedia

    en.wikipedia.org/wiki/Parabolic_antenna

    Parabolic antennas are based on the geometrical property of the paraboloid that the paths FP 1 Q 1, FP 2 Q 2, FP 3 Q 3 are all the same length. Thus, a spherical wavefront emitted by a feed antenna at the dish's focus F will be reflected into an outgoing plane wave L travelling parallel to the dish's axis VF.

  9. Tree volume measurement - Wikipedia

    en.wikipedia.org/wiki/Tree_volume_measurement

    The formula for the volume of a frustum of a paraboloid [23] [24] is: V = (π h/2)(r 1 2 + r 2 2), where h = height of the frustum, r 1 is the radius of the base of the frustum, and r 2 is the radius of the top of the frustum. This allows us to use a paraboloid frustum where that form appears more appropriate than a cone.