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Butterfly Surface

Butterfly Surface
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2015-03-24 04:48
FunctionSolid GeometryParametric EquationGraphing
In collections surface 3D surface 3D
This example demonstrates a colorful butterfly surface, created by overlaying three identical surfaces with transformations to achieve a clear visual effect. It involves core mathematical concepts such as 3D surfaces, color mapping, and transformation geometry. The construction uses commands like Surface and CurveCartesian, with parameters like Umin, UmaxB, c, e, VmaxR, UmaxR, VmaxB, VmaxY, UmaxY, Umax, Vmax, g, d, b, f. It is suitable for high school and above students exploring solid geometry and parametric surfaces.

GeoGebra Commands & Parameters

  1. Surface(((cos(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), ((sin(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), (cos(u) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), u, Umin, UmaxR, v, (-VmaxR), VmaxR) → g
  2. CurveCartesian((sin(t) * ((e * ℯ^(cos(t))) - (c * cos((4 * t))) - sin(t / 12)^(2))), (cos(t) * ((e * ℯ^(cos(t))) - (c * cos((4 * t))) - sin(t / 12)^(2))), t, Umin, Max[{Umax, UmaxR, UmaxB, UmaxY}]) → d
  3. Surface(((cos(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), ((sin(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), (cos(u) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), u, Umin, UmaxB, v, (-VmaxB), VmaxB) → b
  4. Surface(((cos(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), ((sin(v) * sin(u)) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), (cos(u) * ((e * ℯ^(cos(u))) - (c * cos((4 * u))) - sin(u / 12)^(2))), u, Umin, UmaxY, v, (-VmaxY), VmaxY) → f