The connection between mathematics and
art goes back thousands of years. Mathematics has been
used in the design of Gothic cathedrals, Rose windows,
oriental rugs, mosaics and tilings. Geometric forms were
fundamental to the cubists and many abstract expressionists,
and award-winning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius ands, tessellations, deformations,
reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.
Mathematicians and artists continue to
create stunning works in all media and to explore the
visualization of mathematics--origami, computer-generated
landscapes, tesselations, fractals, anamorphic art, and
more.
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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.
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.
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.
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.
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.
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.