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黄金菱形

黄金菱形
几何画板及绘图内容加载中，请稍等……
2019-10-04 01:11
多边形向量变换几何作图
①本范例演示如何构造黄金菱形，展示其与黄金比例的关系；②涉及核心数学概念包括菱形、向量、旋转、对称等；③构造过程中运用了点、正交线、交点、圆、旋转、角度、镜像、多边形、中点、线段等 GeoGebra 命令；④适合高中数学教学，用于几何作图与变换教学。

GeoGebra 命令及参数

  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