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Orthogonal Frame Demonstration

Orthogonal Frame Demonstration
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2018-07-06 15:00
PolygonSequenceCoordinate Geometry
This example demonstrates the geometric construction and properties of an orthogonal frame. It involves core math concepts like coordinate geometry, polygon construction, and sequence application. Key GeoGebra commands used include Cube, Polygon, and Sequence for building the frame. Suitable for high school mathematics education, illustrating the integration of spatial geometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Cube(C1, A1, B1) → D1, E1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, F1, X1, Y1, Z1, AA1, G1, H1, I1, J1, K1, L1, M1
  2. Cube(C2, A2, B2) → D2, E2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2, F2, X2, Y2, Z2, AA2, G2, H2, I2, J2, K2, L2, M2
  3. Cube(C3, A3, B3) → D3, E3, N3, O3, P3, Q3, R3, S3, T3, U3, V3, W3, F3, X3, Y3, Z3, AA3, G3, H3, I3, J3, K3, L3, M3
  4. Cube(C4, A4, B4) → D4, E4, N4, O4, P4, Q4, R4, S4, T4, U4, V4, W4, F4, X4, Y4, Z4, AA4, G4, H4, I4, J4, K4, L4, M4
  5. Cube(C5, A5, B5) → D5, E5, N5, O5, P5, Q5, R5, S5, T5, U5, V5, W5, F5, X5, Y5, Z5, AA5, G5, H5, I5, J5, K5, L5, M5
  6. Cube(C6, A6, B6) → D6, E6, N6, O6, P6, Q6, R6, S6, T6, U6, V6, W6, F6, X6, Y6, Z6, AA6, G6, H6, I6, J6, K6, L6, M6
  7. Cube(C7, A7, B7) → D7, E7, N7, O7, P7, Q7, R7, S7, T7, U7, V7, W7, F7, X7, Y7, Z7, AA7, G7, H7, I7, J7, K7, L7, M7
  8. Cube(C8, A8, B8) → D8, E8, N8, O8, P8, Q8, R8, S8, T8, U8, V8, W8, F8, X8, Y8, Z8, AA8, G8, H8, I8, J8, K8, L8, M8
  9. Polygon(C1, E1, B2, A2) → q1, c1, e1, b2, a2
  10. Polygon(C1, F1, G2, A2) → q2, c1_1, f1, g2, a2_1
  11. Polygon(F1, G2, H2, I1) → q3, f1_1, g2_1, h2, i1
  12. Polygon(E1, B2, H2, I1) → q4, e1_1, b2_1, h2_1, i1_1
  13. Sequence(PolyLine[C1 - (i, 0, 0), E1 - (i, 0, 0), I1 - (i, 0, 0), F1 - (i, 0, 0), C1 - (i, 0, 0)], i, 1, a - 3) → lista_1
  14. Polygon(F3, G4, A4, C3) → q5, f3, g4, a4, c3
  15. Polygon(F3, G4, H4, I3) → q6, f3_1, g4_1, h4, i3
  16. Polygon(E3, B4, H4, I3) → q7, e3, b4, h4_1, i3_1
  17. Polygon(C3, A4, B4, E3) → q8, c3_1, a4_1, b4_1, e3_1
  18. Sequence(PolyLine[C3 - (i, 0, 0), E3 - (i, 0, 0), I3 - (i, 0, 0), F3 - (i, 0, 0), C3 - (i, 0, 0)], i, 1, a - 3) → lista_2
  19. Polygon(C5, A6, G6, F5) → q9, c5, a6, g6, f5
  20. Polygon(F5, G6, H6, I5) → q10, f5_1, g6_1, h6, i5
  21. Polygon(E5, B6, H6, I5) → q11, e5, b6, h6_1, i5_1
  22. Polygon(C5, A6, B6, E5) → q12, c5_1, a6_1, b6_1, e5_1
  23. Polygon(C7, A8, G8, F7) → q13, c7, a8, g8, f7
  24. Polygon(F7, G8, H8, I7) → q14, f7_1, g8_1, h8, i7
  25. Polygon(E7, B8, H8, I7) → q15, e7, b8, h8_1, i7_1
  26. Polygon(C7, A8, B8, E7) → q16, c7_1, a8_1, b8_1, e7_1
  27. Sequence(PolyLine[C5 - (i, 0, 0), E5 - (i, 0, 0), I5 - (i, 0, 0), F5 - (i, 0, 0), C5 - (i, 0, 0)], i, 1, a - 3) → lista_3
  28. Sequence(PolyLine[C7 - (i, 0, 0), E7 - (i, 0, 0), I7 - (i, 0, 0), F7 - (i, 0, 0), C7 - (i, 0, 0)], i, 1, a - 3) → lista_4
  29. Polygon(F1, C5, E5, I1) → q17, f1_2, c5_2, e5_2, i1_2
  30. Polygon(F1, G1, A5, C5) → q18, f1_3, g1, a5, c5_3
  31. Polygon(H1, G1, A5, B5) → q19, h1, g1_1, a5_1, b5
  32. Polygon(I1, H1, B5, E5) → q20, i1_3, h1_1, b5_1, e5_3
  33. Polygon(F2, G2, A6, C6) → q21, f2, g2_2, a6_2, c6
  34. Polygon(F2, I2, E6, C6) → q22, f2_1, i2, e6, c6_1
  35. Polygon(G2, H2, B6, A6) → q23, g2_3, h2_2, b6_2, a6_3
  36. Polygon(H2, I2, E6, B6) → q24, h2_3, i2_1, e6_1, b6_3
  37. Polygon(F3, G3, A7, C7) → q25, f3_2, g3, a7, c7_2
  38. Polygon(F3, I3, E7, C7) → q26, f3_3, i3_2, e7_2, c7_3
  39. Polygon(G3, H3, B7, A7) → q27, g3_1, h3, b7, a7_1
  40. Polygon(H3, I3, E7, B7) → q28, h3_1, i3_3, e7_3, b7_1
  41. Polygon(F4, G4, A8, C8) → q29, f4, g4_2, a8_2, c8
  42. Polygon(F4, I4, E8, C8) → q30, f4_1, i4, e8, c8_1
  43. Polygon(G4, H4, B8, A8) → q31, g4_3, h4_2, b8_2, a8_3
  44. Polygon(I4, H4, B8, E8) → q32, i4_1, h4_3, b8_3, e8_1
  45. Sequence(PolyLine[A5 + (0, 0, i), C5 + (0, 0, i), E5 + (0, 0, i), B5 + (0, 0, i), A5 + (0, 0, i)], i, 1, c - 3) → lista_5
  46. Sequence(PolyLine[A6 + (0, 0, i), C6 + (0, 0, i), E6 + (0, 0, i), B6 + (0, 0, i), A6 + (0, 0, i)], i, 1, c - 3) → lista_6
  47. Sequence(PolyLine[A7 + (0, 0, i), C7 + (0, 0, i), E7 + (0, 0, i), B7 + (0, 0, i), A7 + (0, 0, i)], i, 1, c - 3) → lista_7
  48. Sequence(PolyLine[A8 + (0, 0, i), C8 + (0, 0, i), E8 + (0, 0, i), B8 + (0, 0, i), A8 + (0, 0, i)], i, 1, c - 3) → lista_8
  49. Polygon(E1, I1, F3, C3) → q33, e1_2, i1_4, f3_4, c3_2
  50. Polygon(I1, H1, G3, F3) → q34, i1_5, h1_2, g3_2, f3_5
  51. Polygon(B1, H1, G3, A3) → q35, b1, h1_3, g3_3, a3
  52. Polygon(B1, E1, C3, A3) → q36, b1_1, e1_3, c3_3, a3_1
  53. Polygon(I2, H2, G4, F4) → q37, i2_2, h2_4, g4_4, f4_2
  54. Polygon(E2, I2, F4, C4) → q38, e2, i2_3, f4_3, c4
  55. Polygon(B2, H2, G4, A4) → q39, b2_2, h2_5, g4_5, a4_2
  56. Polygon(E2, B2, A4, C4) → q40, e2_1, b2_3, a4_3, c4_1
  57. Polygon(I5, H5, G7, F7) → q41, i5_2, h5, g7, f7_2
  58. Polygon(E5, I5, F7, C7) → q42, e5_4, i5_3, f7_3, c7_4
  59. Polygon(B5, H5, G7, A7) → q43, b5_2, h5_1, g7_1, a7_2
  60. Polygon(B5, E5, C7, A7) → q44, b5_3, e5_5, c7_5, a7_3
  61. Polygon(I6, H6, G8, F8) → q45, i6, h6_2, g8_2, f8
  62. Polygon(E6, I6, F8, C8) → q46, e6_2, i6_1, f8_1, c8_2
  63. Polygon(B6, H6, G8, A8) → q47, b6_4, h6_3, g8_3, a8_4
  64. Polygon(B6, E6, C8, A8) → q48, b6_5, e6_3, c8_3, a8_5
  65. Sequence(PolyLine[A3 + (0, i, 0), C3 + (0, i, 0), F3 + (0, i, 0), G3 + (0, i, 0), A3 + (0, i, 0)], i, 1, b - 3) → lista_9
  66. Sequence(PolyLine[A4 + (0, i, 0), C4 + (0, i, 0), F4 + (0, i, 0), G4 + (0, i, 0), A4 + (0, i, 0)], i, 1, b - 3) → lista_{10}
  67. Sequence(PolyLine[A7 + (0, i, 0), C7 + (0, i, 0), F7 + (0, i, 0), G7 + (0, i, 0), A7 + (0, i, 0)], i, 1, b - 3) → lista_{11}
  68. Sequence(PolyLine[A8 + (0, i, 0), C8 + (0, i, 0), F8 + (0, i, 0), G8 + (0, i, 0), A8 + (0, i, 0)], i, 1, b - 3) → lista_{12}