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Exercise on Hyperbolic Surface Construction

Exercise on Hyperbolic Surface Construction
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2017-01-24 22:56
Solid GeometryTransformationGeometric Construction
In collections LINEAR FUNCTIONS
This example demonstrates the geometric construction of a hyperbolic surface, involving concepts such as surfaces, transformations, and loci. Using GeoGebra commands like Random, RandomElement, and Textfield, users can dynamically explore the properties of the hyperbolic surface. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Random(-10, 10) → d_2
  2. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → c_1
  3. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → c
  4. Random(-10, 10) → a
  5. Random(-10, 10) → b
  6. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → a_1
  7. Textfield(h) → InputBox1
  8. Random(-10, 10) → b_1
  9. Random(-10, 10) → d_1
  10. Textfield(m) → InputBox2
  11. Textfield(f) → InputBox4
  12. TableText({{A1_1, B_1, C_1, D_1}, {-3, g(-3), h(-3), f(-3)}, {-2, g(-2), h(-2), f(-2)}, {-1, g(-1), h(-1), f(-1)}, {0, g(0), h(0), f(0)}, {1, g(1), h(1), f(1)}, {2, g(2), h(2), f(2)}, {3, g(3), h(3), f(3)}, {1, e, l, k}}, "|_r") → text3_1

AI Drawing Prompt Reference

Draw a geometric construction of a hyperbolic surface with randomly generated parameters and axes, showing how transformations and loci form the surface, and label key parameters and function relationships, first determine the basic parameters, then generate points on the surface, and finally display the relationship between parameters and function values in a table.
The prompt above was compiled from the original drawing commands and is for reference only.