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3D Implicit Surface Grapher: x^4 = y^2 + z^2

3D Implicit Surface Grapher: x^4 = y^2 + z^2
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2015-01-02 19:48
FunctionCoordinate GeometrySolid GeometryGraphing
This GeoGebra example demonstrates the three-dimensional implicit surface defined by the equation x^4 = y^2 + z^2. The core mathematical concepts involved include implicit functions, three-dimensional coordinate geometry, and surface equations. In terms of construction, it utilizes GeoGebra commands such as TextField for function input, and objects like variables y_max, z_max to control plotting ranges, along with buttons and text boxes for interactive input and formula display. This example is suitable for high school or college-level mathematics, particularly in solid geometry and function visualization.

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

Draw the 3D implicit surface defined by x^4 = y^2 + z^2, with adjustable minimum and maximum bounds for the x, y, and z axes, and include controls for a grid density parameter Nn, a scaling factor g, and an offset b so the surface can be explored interactively. The user can modify the viewing limits for each coordinate axis independently, change the resolution of the surface mesh via Nn, adjust the overall size with g, and shift the surface along the axes using b, enabling a flexible visual analysis of the quartic cone-like shape.
The prompt above was compiled from the original drawing commands and is for reference only.