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Seashell Surface

Seashell Surface
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2018-12-23 05:12
FunctionSolid GeometryParametric Equation
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources
This example demonstrates the generation of a seashell-like surface. Key mathematical concepts include piecewise functions, power functions, and volume calculations. Using the Surface command in GeoGebra, combined with LENGTHEN and FILLING objects, the shape of the seashell can be dynamically adjusted by changing parameters k and c. Suitable for high school mathematics education, particularly in coordinate geometry and solid geometry.

GeoGebra Commands & Parameters

  1. Surface((((k * (1 - v / ((2 * π)))) * cos((2 * v))) * (1 + cos(u))) + cos((2 * v)), (((k * (1 - v / ((2 * π)))) * sin((2 * v))) * (1 + cos(u))) + sin((2 * v)), (20 * v / ((2 * π))) + ((2 * (1 - v / ((2 * π)))) * sin(u)) + 15, u, 0, a, v, (-2 * π), LENGTHEN) → c