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Critical Points of the Function Surface of the Eight-Point Model

Critical Points of the Function Surface of the Eight-Point Model
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2019-03-10 21:12
FunctionCalculusOptimization
In collections ₉Extreme Verteilung der 8 Punkten auf der Kugel
This example demonstrates the critical points of the function surface of the eight-point model. Core mathematical concepts include functions, derivatives, and optimization problems. Using GeoGebra commands such as Function, Plane, Derivative, and Polygon, the function surface of the eight-point model can be constructed, and its critical points can be found. Suitable for teaching and research in calculus and optimization problems.

GeoGebra Commands & Parameters

  1. Function(GAbstand(u, v), u, -1°, 60°, v, -1°, 90°) → m
  2. Plane(z = 1.480440157243445) → Pl_{Lö1}
  3. Plane(z = 1.481181823885057) → Pl_{Lö2}
  4. Derivative(GAbstand(x, y), x) → k_x
  5. Derivative(GAbstand(x, y), y) → k_y
  6. Plane(z = z0) → Plane0
  7. Polygon({(-1°, -1°), (60°, -1°), (60°, 90°), (-1°, 90°), (-1°, -1°)}) → Poly_{αθ}
  8. Textfield(Δθ) → InputBox1

AI Drawing Prompt Reference

Draw the function surface of an eight-point model, highlighting its critical points. Include the function graph ranging from -1° to 60° in u and -1° to 90° in v, two parallel planes at z=1.480440157243445 and z=1.481181823885057, and the partial derivatives with respect to x and y. Also, add a rectangular region covering the surface and an input box for parameter adjustments.
The prompt above was compiled from the original drawing commands and is for reference only.