MathPlotAI Logo MathPlotAI

Animation 119: Geometry and Functions Demo

Animation 119: Geometry and Functions Demo
Loading the math board and drawing, please wait…
2016-10-07 22:34
VectorCoordinate GeometryCalculusGeometric Construction
This example demonstrates the integration of parallel quadrilaterals, linear functions, and coordinate geometry through animation. Key math concepts include coordinate geometry, vectors, and integral (upper and lower sums or Riemann sums). GeoGebra commands used in construction are Rotate, Line, Point, Segment, Polygon, etc. Suitable for high school mathematics education to understand the dynamic relationship between function graphs and geometric shapes.

GeoGebra Commands & Parameters

  1. Rotate(B, (a * π / 180), A) → B'
  2. Angle(B, A, B') → α
  3. Ray(A, B') → g
  4. Line(A, B') → h
  5. Point(h) → C
  6. Ray(B', C) → i
  7. Point(i) → D
  8. Line(E, h) → j
  9. Circle(D, b) → c
  10. Intersect(c, k, 2) → F
  11. Intersect(h, l) → G
  12. Segment(G, F) → m
  13. Segment(F, D) → n
  14. Min(m, n) → d
  15. Circle(F, (0.3 * d)) → e
  16. Intersect(e, k, 2) → H
  17. Intersect(e, m, 1) → I
  18. CircleSector(F, H, I) → p
  19. Polygon(D, F, G) → poly1, g_1, d_1, f_1
  20. CircleSector(F, I, H) → q
  21. Ray(F, H) → t
  22. Dilate(G, If[0 < o ≤ 1, 1 - o, 0], F) → G'
  23. Segment(G, G') → r
  24. Dilate(F, If[1 < o ≤ 2, 2 - o, 0], D) → F'
  25. Segment(F, F') → s
  26. Rotate(p, If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], F) → p'
  27. Rotate(q, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], F) → q'
  28. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], E) → D'
  29. Vector(D, D') → u
  30. Translate(D, u) → D'_1
  31. Translate(F, u) → F'_1
  32. Translate(G, u) → G'_1
  33. Polygon(D'_1, F'_1, G'_1) → poly1', g'_1, d'_1, f'_1
  34. Translate(G, u) → G'_2
  35. Translate(G', u) → G''
  36. Segment(G'_2, G'') → r'
  37. Translate(F, u) → F'_2
  38. Translate(F', u) → F''
  39. Segment(F'_2, F'') → s'
  40. Translate(p', u) → p''
  41. Segment(D'_1, G'_1) → h_1
  42. Translate(q', u) → q''