Dejenie A. Lakew :: Hyper Symmetries |
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Superimposition of Polar Surfaces-1, by Dejenie A. LakewThe superimposition of two polar surfaces:
rho = 2sin4[theta]
rho = 5/3 cos4[theta] (wire-framed) with some compositions of tilts and turns.
The two polar surfaces are generated in such a way that one is a derivative surface of the other but with different polar radius.
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Superimposition of Polar Surfaces-2, by Dejenie A. LakewSuperimpositions of polar surfaces. Equations:
rho = 2cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta])),
rho = exp(sin 3(exp sin 3[theta]),
rho = -3cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta]))
with compositions of tilts and turns.
Here the first polar surface is the derivative of the second surface and the third surface is a spatial reflection of the first through the origin with wire frames, but with a larger spatial radius.
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Superimposition of Polar Surfaces-3, by Dejenie A. LakewSuperimposition of polar surfaces. Equations:
rho = 2cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta])),
rho = 3 + 2cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta]))
with several compositions of tilts and turns.
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Superimposition of Polar Surfaces-4, by Dejenie A. LakewSuperimpositions of polar surfaces. Equations:
rho = 10sin8[theta]
rho = 10cos8[theta] with a number of compositions of tilts and turns.
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Superimposition of Polar Surfaces-5, by Dejenie A. LakewSuperimposition of three polar surfaces. Equations:
rho = 2cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta])),
rho = 3 + 2cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta]))
rho = -3cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta]) followed by many compositions of tilts and turns.
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Superimposition of Polar Surfaces-6, by Dejenie A. LakewSuperimposition of three polar surfaces. Equations:
rho = 2cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta])),
rho = 3 + 2cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta]))
rho = 6*(the outer sphere wire-framed) with many compositions of tilts and turns as rigid transformations.
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