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Points Visible from Origin

Points Visible from Origin
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2023-03-05 03:18
VectorFunctionCoordinate GeometryCalculusOptimization
In collections Pi Approximations
This example demonstrates the set of points visible from the origin, exploring their relationship with various geometric shapes. It involves core mathematical concepts such as coordinate systems, vectors, function graphs, inequalities, limits, and calculus. Key GeoGebra commands and objects used include RemoveUndefined, Length, Join, Point, Vector, and Min to dynamically generate and display points satisfying specific conditions. Suitable for high school and above students learning spatial geometry, analytical geometry, and calculus applications.

GeoGebra Commands & Parameters

  1. RemoveUndefined(Flatten[Sequence[Sequence[If[GCD[a, b] ≟ 1, (a, b), NaN], a, 1, n], b, 1, n]]) → L_1
  2. RemoveUndefined(Flatten[Sequence[Sequence[If[GCD[a, b] ≠ 1, (a, b), NaN], a, 1, n], b, 1, n]]) → L_2
  3. Length(L_1) → a
  4. Length(L_2) → d
  5. Join({L_1, L_2}) → L_3
  6. Point(L_3) → B
  7. Vector(B) → u
  8. Min(6, floor(200 / n)) → c

AI Drawing Prompt Reference

Describe a set of points visible from the origin, showing their relationship with geometric shapes. Use coordinate systems, vectors, function graphs, and inequalities to explore these points. Key objects include points, vectors, and minimum values, used to dynamically generate and display points satisfying specific conditions. Suitable for high school and above students learning spatial geometry and analytical geometry.
The prompt above was compiled from the original drawing commands and is for reference only.