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Interactive Demo of Linear Functions and Probability Distributions

Interactive Demo of Linear Functions and Probability Distributions
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2018-03-20 09:49
FunctionProbability & StatisticsGeometric ConstructionSlider AnimationGraphing
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This example demonstrates the geometric relationship between linear functions and Poisson/Binomial distributions through interactive graphics. Key math concepts include linear functions, Poisson distribution, binomial distribution, rational numbers, and perimeter. GeoGebra commands/objects used in construction are Vector, Point, Intersect, Segment, Sequence, DynamicCoordinates, Polygon, If, and Angle. Suitable for high school and above students to visualize function and probability distribution graphs and understand parameter effects.

GeoGebra Commands & Parameters

  1. Vector(A, C1) → u
  2. Point(Ray[A + (1, 0), A + (2, 0)]) → B
  3. Vector(B, C2) → v
  4. Intersect(Ray[D, Rotate[D + (1, 0), 45°, D]], Ray[E, Rotate[E - (1, 0), (-(60°)), E]]) → F
  5. Segment(F, D) → k
  6. Sequence((x(A) + (Length[u] * cos(t°)), y(A) + (Length[u] * sin(t°))), t, 0, 355, 5) → VPoints
  7. Segment(E, F) → j
  8. DynamicCoordinates(C1, x(ClosestPoint[VPoints, C1]), y(ClosestPoint[VPoints, C1])) → C
  9. Segment(A, C) → f
  10. Segment(A, B) → g
  11. Sequence((x(B) + (Length[v] * cos(t°)), y(B) + (Length[v] * sin(t°))), t, 0, 355, 5) → UPoints
  12. DynamicCoordinates(C2, x(ClosestPoint[UPoints, C2]), y(ClosestPoint[UPoints, C2])) → C'
  13. Segment(C', B) → h
  14. Intersect(Ray[A, C], Ray[B, C']) → G
  15. Polygon({A, B, G}) → t1
  16. If(C ≟ G ∧ C' ≟ G, true, false) → closed1
  17. Segment(D, E) → i
  18. Polygon(D, E, F) → t3, l, m, n
  19. Angle(E, D, F) → α
  20. Angle(F, E, D) → β
  21. Angle(D, F, E) → γ
  22. Angle(B, A, C) → δ
  23. Angle(C', B, A) → ε
  24. Angle(A, C, B) → ζ

AI Drawing Prompt Reference

Create an interactive graphic showing the geometric relationship between linear functions and Poisson/Binomial distributions. Include two vectors and an intersection point, generating rays from the vectors, and connecting the intersection to form a triangle. Display the trajectories of the vector endpoints with dynamic coordinates and draw line segments connecting these points. Finally, combine the triangle with the line segments to illustrate the relationship between functions and distributions, labeling key angles.
The prompt above was compiled from the original drawing commands and is for reference only.