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This is sometimes called the "linear diameter", and equals the diameter of a flat, circular sheet of material, usually metal, which is the right size to be cut and bent to make the dish. Two intermediate results are useful in the calculation: P = 2 F (or the equivalent: P = R 2 / 2 D ) and Q = √ P 2 + R 2 , where F , D , and R are ...
Paraboloidal coordinates are three-dimensional orthogonal coordinates (,,) that generalize two-dimensional parabolic coordinates.They possess elliptic paraboloids as one-coordinate surfaces.
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.
The volume ratio is maintained when the height is scaled to h' = r √ π. 3. Decompose it into thin slices. 4. Using Cavalieri's principle, reshape each slice into a square of the same area. 5. The pyramid is replicated twice. 6. Combining them into a cube shows that the volume ratio is 1:3.
The red paraboloid corresponds to τ=2, the blue paraboloid corresponds to σ=1, and the yellow half-plane corresponds to φ=-60°. The three surfaces intersect at the point P (shown as a black sphere) with Cartesian coordinates roughly (1.0, -1.732, 1.5).
In 1931, a 1.7 GHz microwave relay telephone link across the English Channel was demonstrated using 3.0-meter (10 ft) diameter dishes. [17] The first large parabolic antenna, a 9 m dish, was built in 1937 by pioneering radio astronomer Grote Reber in his backyard, [ 2 ] and the sky survey he did with it was one of the events that founded the ...
The force of gravity (red), the buoyancy force (green), and the resultant centripetal force (blue) In the following discussion, represents the acceleration due to gravity, represents the angular speed of the liquid's rotation, in radians per second, is the mass of an infinitesimal parcel of liquid material on the surface of the liquid, is the distance of the parcel from the axis of rotation ...
Parabolic cylinder () function appears naturally in the Schrödinger equation for the one-dimensional quantum harmonic oscillator (a quantum particle in the oscillator potential), [+] = (), where is the reduced Planck constant, is the mass of the particle, is the coordinate of the particle, is the frequency of the oscillator, is the energy, and () is the particle's wave-function.