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Animation 143: Functions & 3D Vectors Demo

Animation 143: Functions & 3D Vectors Demo
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2016-11-24 12:21
VectorFunctionProbability & StatisticsGeometric ConstructionGraphing
This example demonstrates the relationship between function graphs and 3D vectors through animation, incorporating cubes, area calculations, and binomial distribution pie charts. Core math concepts include function graphs, 3D vectors, geometric transformations, and probability statistics. Construction highlights from the summary involve commands like Point, PointIn, FitPoly, Mirror, Intersect, Dilate, Segment, Rotate, Vector, Translate, and objects A, a, B, b, etc. Suitable for high school and above mathematics learners/teachers for function, vector, and data visualization education.

GeoGebra Commands & Parameters

  1. Point(x = 0) → A
  2. PointIn(a) → B
  3. PointIn(b) → C
  4. PointIn(c) → D
  5. PointIn(d) → E
  6. FitPoly(list, 4) → f
  7. Mirror(g, x = 0) → g_1
  8. Point(g) → F
  9. Intersect(h, y = 0) → G
  10. Mirror(G, x = 0) → G'
  11. Mirror(F, x = 0) → F'
  12. Dilate(H, If[0 < e ≤ 1, 1 - e, 0], G) → H'
  13. Segment(H, H') → i
  14. Dilate(G, If[1 < e ≤ 2, 2 - e, 0], F) → G'_1
  15. Segment(G, G'_1) → j
  16. Rotate(H, If[2 < e ≤ 3, ((-(e - 2)) * π), (-π)], H) → H'_1
  17. Rotate(H', If[2 < e ≤ 3, ((-(e - 2)) * π), (-π)], H) → H''
  18. Segment(H'_1, H'') → i'
  19. Dilate(G', If[3 < e ≤ 4, 4 - e, 0], F') → G''
  20. Segment(G', G'') → k
  21. Dilate(F, If[4 < e ≤ 5, 5 - e, 0], F') → F'_1
  22. Vector(F, F'_1) → u
  23. Translate(G, u) → G'_2
  24. Translate(G'_1, u) → I
  25. Segment(G'_2, I) → j'

AI Drawing Prompt Reference

Draw a function graph and demonstrate its relationship with 3D vectors through animation. Include cubes, area calculations, and binomial distribution pie charts. Start with the origin, take points on the x-axis, fit a quartic polynomial, mirror about the x-axis, find intersections, scale and rotate, connect segments, and finally translate the shape using a vector.
The prompt above was compiled from the original drawing commands and is for reference only.