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3D Implicit Surface Grapher: Gabriel's Horn

3D Implicit Surface Grapher: Gabriel's Horn
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2015-01-02 20:35
FunctionCoordinate GeometrySolid Geometry
This example demonstrates a 3D implicit surface graph, specifically Gabriel's Horn. It involves implicit functions, algebraic and polynomial equations. Using GeoGebra commands, complex 3D shapes can be constructed. Suitable for high school and above students to learn about 3D geometry and implicit functions.

GeoGebra Commands & Parameters

  1. Textfield(x_{min}) → Textfeld1
  2. Textfield(y_{min}) → Textfeld2
  3. Textfield(z_{min}) → Textfeld3
  4. Textfield(x_{max}) → Textfeld4
  5. Textfield(y_{max}) → Textfeld5
  6. Textfield(z_{max}) → Textfeld6
  7. Textfield(Nn) → Textfeld10
  8. Textfield(g) → Textfeld13
  9. Textfield(b) → inputBox1

AI Drawing Prompt Reference

Create a 3D implicit surface graph of Gabriel's Horn, a horn-shaped solid that narrows infinitely. The surface should be defined by an implicit algebraic equation. Display a three-dimensional coordinate system with axes. Around the graph, include several input fields: six for setting the minimum and maximum bounds of x, y, and z coordinates, one for adjusting the grid resolution (number of subdivisions), and one text box for entering the function expression. Arrange these controls neatly beside the 3D view for an educational demonstration.
The prompt above was compiled from the original drawing commands and is for reference only.