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Algebraic Puzzle: Development

Algebraic Puzzle: Development
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2019-12-29 16:21
FunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Algebraic puzzles for binomial formula
This example demonstrates the graphical solution of an algebraic puzzle, visualizing the solutions of equations through dynamic geometry. It involves core math concepts like Algebra, Expected Value, Conic Sections, Piecewise Functions, Special Points, and Logarithms. Construction highlights the use of commands such as Line, Point, Segment, Vector, Translate, Sequence, Polygon, and Midpoint in GeoGebra. Suitable for high school and above, it illustrates the integration of algebra and geometry.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → a
  2. Point(a) → F
  3. Segment(A, F) → c
  4. Point(c) → C
  5. Point(c) → B
  6. Line(A, yAxis) → b
  7. Point(b) → G
  8. Segment(A, G) → d
  9. Point(d) → E
  10. Point(d) → D
  11. Vector(H, V) → v
  12. Translate(I, Vector[(Animation * v)]) → I'
  13. Segment(A, D) → f
  14. Segment(A, B) → e
  15. Sequence(A + (i, 0), i, 0, e, e / e1) → liste1
  16. Sequence(D + (i, 0), i, 0, e, e / e1) → liste2
  17. Sequence(A - (0, i), i, 0, f, f / f1) → liste4
  18. Sequence(Segment[Element[liste1, i], Element[liste2, i]], i, 1, Length[liste1]) → liste3
  19. Sequence(B - (0, i), i, 0, f, f / f1) → liste5
  20. Sequence(Segment[Element[liste4, i], Element[liste5, i]], i, 1, Length[liste5]) → liste6
  21. Polygon(A, B, H, D) → poly1, a_1, b_1, h, d_1
  22. Segment(B, C) → g
  23. Sequence(B + (i, (0 * i)), i, 0, g, g / g1) → liste7
  24. Sequence(H + (i, (0 * i)), i, 0, g, g / g1) → liste8
  25. Sequence(Segment[Element[liste7, i], Element[liste8, i]], i, 1, Length[liste7]) → liste9
  26. Sequence(C - (0, i), i, 0, f, f / f1) → liste10
  27. Sequence(Segment[Element[liste10, i], Element[liste5, i]], i, 1, Length[liste5]) → liste11
  28. Polygon(B, C, I, H) → poly2, i, j, k, l
  29. Segment(D, E) → m
  30. Sequence(D - (0, i), i, 0, m, m / m1) → liste12
  31. Sequence(H - (0, i), i, 0, m, m / m1) → liste13
  32. Sequence(Segment[Element[liste12, i], Element[liste13, i]], i, 1, Length[liste12]) → liste14
  33. Sequence(E + (i, 0), i, 0, e, e / e1) → liste15
  34. Sequence(Segment[Element[liste15, i], Element[liste2, i]], i, 1, Length[liste1]) → liste16
  35. Polygon(D, H, J, E) → poly3, d_2, h_1, j_1, e_1
  36. Polygon(H, I, K, J) → poly4, h_2, i_1, k_1, j_2
  37. Sequence(J + (i, (0 * i)), i, 0, g, g / g1) → liste17
  38. Sequence(Segment[Element[liste17, i], Element[liste8, i]], i, 1, Length[liste7]) → liste18
  39. Sequence(I - (0, i), i, 0, m, m / m1) → liste19
  40. Sequence(Segment[Element[liste19, i], Element[liste13, i]], i, 1, Length[liste12]) → liste20
  41. Midpoint(A, B) → L
  42. Midpoint(B, C) → M
  43. Midpoint(A, D) → N
  44. Midpoint(D, E) → O
  45. Midpoint(B, D) → P
  46. Midpoint(I, J) → Q
  47. Midpoint(I, B) → R
  48. Midpoint(J, D) → S
  49. Vector(D, T) → u
  50. Translate(A, Vector[(Animation * u)]) → A'
  51. Translate(B, Vector[(Animation * u)]) → B'
  52. Translate(H, Vector[(Animation * u)]) → H'
  53. Translate(D, Vector[(Animation * u)]) → D'
  54. Polygon(A', B', H', D') → poly1', a', b', h', d'
  55. Vector(E, I') → w
  56. Translate(B, Vector[(Animation * v)]) → B'_1
  57. Translate(C, Vector[(Animation * v)]) → C'
  58. Translate(H, Vector[(Animation * v)]) → H'_1
  59. Polygon(B'_1, C', I', H'_1) → poly2', b'_1, c', i', h'_1
  60. Translate(D, Vector[(Animation * w)]) → D'_1
  61. Translate(H, Vector[(Animation * w)]) → H'_2
  62. Translate(J, Vector[(Animation * w)]) → J'
  63. Translate(E, Vector[(Animation * w)]) → E'
  64. Polygon(D'_1, H'_2, J', E') → poly3', d'_1, h'_2, j', e'
  65. Vector(H, W) → z
  66. Translate(H, Vector[(Animation * z)]) → H'_3
  67. Translate(I, Vector[(Animation * z)]) → I'_1
  68. Translate(K, Vector[(Animation * z)]) → K'
  69. Translate(J, Vector[(Animation * z)]) → J'_1
  70. Polygon(H'_3, I'_1, K', J'_1) → poly4', h'_3, i'_1, k', j'_1
  71. Midpoint(B', T) → Z
  72. Midpoint(D'_1, I') → C_1
  73. Segment(C', D'_1) → p
  74. Segment(D'_1, I') → q
  75. Midpoint(I'_1, J'_1) → A_1
  76. Midpoint(C', V) → B_1
  77. Midpoint(H'_2, I') → D_1
  78. Vector(B_1, I') → r
  79. Vector(D_1, I') → s