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Holed Heart Surface

Holed Heart Surface
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2015-02-04 00:59
FunctionSolid GeometryCalculusGraphing
In collections surface 3D surface 3D
This example demonstrates the construction and manipulation of a 3D heart-shaped surface with a hole. Key math concepts include Integral Calculus, Expected Value, Calculus, Logarithmic Functions, and Transformations. The construction uses the Surface command with parameters Umax, d, a, b, c, e for dynamic control. Suitable for high school students and math enthusiasts exploring spatial geometry and calculus applications.

GeoGebra Commands & Parameters

  1. Surface(v, (((4 * sqrt(1 - v^(2))) * sin(u)^(u)) * sin(u)), (((-4 * sqrt(1 - v^(2))) * sin(u)^(u)) * cos(u)), u, 0, Umax, v, (-d), d) → a
  2. Surface(v, (((-4 * sqrt(1 - v^(2))) * sin(u)^(u)) * sin(u)), (((-4 * sqrt(1 - v^(2))) * sin(u)^(u)) * cos(u)), u, 0, Umax, v, (-d), d) → b
  3. Surface(v, (((4 * sqrt(1 - d^(2))) * sin(u)^(u)) * sin(u)), (((-4 * sqrt(1 - d^(2))) * sin(u)^(u)) * cos(u)), u, 0, Umax, v, (-d), d) → c
  4. Surface(v, (((-4 * sqrt(1 - d^(2))) * sin(u)^(u)) * sin(u)), (((-4 * sqrt(1 - d^(2))) * sin(u)^(u)) * cos(u)), u, 0, Umax, v, (-d), d) → e

AI Drawing Prompt Reference

Create a 3D heart-shaped surface with a hole, demonstrating integral calculus, expected value, calculus, logarithmic functions, and transformations through dynamic parameters, starting with a basic heart shape, adding a hole, and adjusting parameters for dynamic manipulation.
The prompt above was compiled from the original drawing commands and is for reference only.