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Modeling Nature Shells

Modeling Nature Shells
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2018-12-12 16:46
Coordinate GeometryParametric EquationGeometric Construction
This example demonstrates the modeling of various shell forms found in nature. Key mathematical concepts include parametric equations and coordinate geometry. Using the Surface and CurveCartesian commands, various shell shapes are constructed. Suitable for high school students and math enthusiasts.

GeoGebra Commands & Parameters

  1. Surface(((((r * ℯ^((f * u))) * (d + (a * cos(v)))) * cos((c * u))), (((r * ℯ^((f * u))) * (d + (a * cos(v)))) * sin((c * u))), h + ((r * ℯ^((f * u))) * ((-1.4 * e) + (b * sin(v))))), u, u1, u2, v, v1, v2) → g
  2. CurveCartesian((((r * ℯ^((f * t))) * (d + (a * cos(v)))) * cos((c * t))), (((r * ℯ^((f * t))) * (d + (a * cos(v)))) * sin((c * t))), h + ((r * ℯ^((f * t))) * ((-1.4 * e) + (b * sin(v)))), v, v1, v2) → i