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Golden Rhombus

Golden Rhombus
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2019-10-04 01:11
PolygonVectorTransformationGeometric Construction
This example demonstrates the construction of a golden rhombus, highlighting its relationship with the golden ratio. It involves core mathematical concepts such as rhombus, vectors, rotation, symmetry, etc. The construction uses GeoGebra commands like points, orthogonal lines, intersections, circles, rotations, angles, reflections, polygons, midpoints, and segments. Suitable for high school mathematics teaching, focusing on geometric constructions and transformations.

GeoGebra Commands & Parameters

  1. TableText({{A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1}, {A2, B2, C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2, O2}, {A3, B3, C3, D3, E3, F3, G3, H3, I3, J3, K3, L3, M3, N3, O3}, {A4, B4, C4, D4, E4, F4, G4, H4, I4, J4, K4, L4, M4, N4, O4}, {A5, B5, C5, D5, E5, F5, G5, H5, I5, J5, K5, L5, M5, N5, O5}, {A6, B6, C6, D6, E6, F6, G6, H6, I6, J6, K6, L6, M6, N6, O6}, {A7, B7, C7, D7, E7, F7, G7, H7, I7, J7, K7, L7, M7, N7, O7}, {A8, B8, C8, D8, E8, F8, G8, H8, I8, J8, K8, L8, M8, N8, O8}, {A9, B9, C9, D9, E9, F9, G9, H9, I9, J9, K9, L9, M9, N9, O9}, {A10, B10, C10, D10, E10, F10, G10, H10, I10, J10, K10, L10, M10, N10, O10}, {A11, B11, C11, D11, E11, F11, G11, H11, I11, J11, K11, L11, M11, N11, O11}, {A12, B12, C12, D12, E12, F12, G12, H12, I12, J12, K12, L12, M12, N12, O12}, {A13, B13, C13, D13, E13, F13, G13, H13, I13, J13, K13, L13, M13, N13, O13}, {A14, B14, C14, D14, E14, F14, G14, H14, I14, J14, K14, L14, M14, N14, O14}}, "|_lllllllllllllll") → text1
  2. Point(xAxis) → C
  3. OrthogonalLine(C, xAxis) → i
  4. Point(xAxis) → E
  5. OrthogonalLine(E, xAxis) → k
  6. OrthogonalLine(G, xAxis) → l
  7. Intersect(xAxis, yAxis) → A
  8. Point(xAxis) → B
  9. Circle(A, B) → e
  10. Point(xAxis) → D
  11. Circle(A, D) → f
  12. Rotate(B, 36°, A) → B'_1
  13. Angle(B, A, B'_1) → β
  14. OrthogonalLine(B'_1, xAxis) → g
  15. Intersect(g, xAxis) → F
  16. Mirror(F, A) → F'
  17. Rotate(B, 144°, A) → B'_2
  18. Angle(B, A, B'_2) → α
  19. Rotate(B, 216°, A) → B'_3
  20. Angle(B, A, B'_3) → γ
  21. Rotate(B, 324°, A) → B'_4
  22. Angle(B, A, B'_4) → δ
  23. Intersect(f, yAxis, 2) → H
  24. Intersect(f, yAxis, 1) → K
  25. Polygon(F', H, F, K) → q1, f', h, f_1, k_1
  26. Angle(A, H, F) → ε
  27. Angle(H, F, A) → ζ
  28. Midpoint(H, F) → L
  29. Segment(B'_2, B'_1) → j
  30. PointIn(q1) → Pointq1_1
  31. Perimeter(q1) → perimeterq1
  32. PointIn(q1) → Pointq1
  33. Segment(B'_1, B'_4) → m
  34. Segment(B'_4, B'_3) → n
  35. Segment(B'_3, B'_2) → p
  36. Angle(H, F, K) → η
  37. Angle(F', H, F) → θ
  38. Segment(A, B'_1) → q
  39. Segment(A, B'_2) → r
  40. Segment(A, B'_3) → s
  41. Segment(A, B'_4) → t
  42. Circle(H, F) → c_1
  43. OrthogonalLine(H, yAxis) → g_1
  44. Intersect(c_1, g_1, 1) → M
  45. OrthogonalLine(M, xAxis) → h_1
  46. Intersect(e, h_1, 2) → N
  47. Angle(B, A, N) → ι
  48. Segment(A, N) → i_1
  49. Midpoint(H, F) → O
  50. Midpoint(F', K) → P
  51. Midpoint(K, F) → Q
  52. Midpoint(F', H) → R
  53. Segment(R, P) → j_1
  54. Segment(P, O) → l_1