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索玛立方体（240种解法）的GeoGebra三维演示

索玛立方体（240种解法）的GeoGebra三维演示
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2018-02-13 10:56
数列解析几何立体几何变换几何作图
该范例在GeoGebra中构建了经典的索玛立方体（Soma Cube）三维拼图，并展示了其240种解法中的一种。索玛立方体由7个不规则多连立方体（由3或4个小立方体组成）拼成一个3×3×3的大立方体，是立体几何与组合数学的经典问题。核心数学概念包括空间旋转、平移、对称以及组合计数。作图要点：使用GeoGebra的Sequence命令生成小立方体序列，通过Dilate命令控制缩放，并利用列表（listAll、list1、list2）存储各块的坐标与朝向，对象A1至A28及B1至B7分别代表不同拼块和辅助点，最终通过旋转和移动展示解法。适合中学高年级至大学低年级学生用于理解三维空间变换、培养空间想象力，也可作为数学游戏或编程算法（如回溯搜索）的直观教学工具。

GeoGebra 命令及参数

  1. Sequence((list1(i), list1(i + 1), list1(i + 2)), i, 1, Length[list1], 3) → list2
  2. Dilate(B1, explode, (1.5, 1.5, 1.5)) → C1
  3. Dilate(B5, explode, (1.5, 1.5, 1.5)) → C5
  4. Dilate(B9, explode, (1.5, 1.5, 1.5)) → C9
  5. Dilate(B13, explode, (1.5, 1.5, 1.5)) → C13
  6. Dilate(B17, explode, (1.5, 1.5, 1.5)) → C17
  7. Dilate(B21, explode, (1.5, 1.5, 1.5)) → C21
  8. Dilate(B25, explode, (1.5, 1.5, 1.5)) → C25
  9. Cube(C1, C1 + (0, 1, 0), u) → D1, E1, N1, O1, P1, Q1, R1, S1, T1, U1, V1, W1, F1, X1, Y1, Z1, AA1, AB1, G1, H1, I1, J1, K1, L1, M1
  10. Cube(C2, C2 + (0, 1, 0), u) → D2, E2, N2, O2, P2, Q2, R2, S2, T2, U2, V2, W2, F2, X2, Y2, Z2, AA2, AB2, G2, H2, I2, J2, K2, L2, M2
  11. Cube(C3, C3 + (0, 1, 0), u) → D3, E3, N3, O3, P3, Q3, R3, S3, T3, U3, V3, W3, F3, X3, Y3, Z3, AA3, AB3, G3, H3, I3, J3, K3, L3, M3
  12. Cube(C4, C4 + (0, 1, 0), u) → D4, E4, N4, O4, P4, Q4, R4, S4, T4, U4, V4, W4, F4, X4, Y4, Z4, AA4, AB4, G4, H4, I4, J4, K4, L4, M4
  13. Cube(C5, C5 + (0, 1, 0), u) → D5, E5, N5, O5, P5, Q5, R5, S5, T5, U5, V5, W5, F5, X5, Y5, Z5, AA5, AB5, G5, H5, I5, J5, K5, L5, M5
  14. Cube(C6, C6 + (0, 1, 0), u) → D6, E6, N6, O6, P6, Q6, R6, S6, T6, U6, V6, W6, F6, X6, Y6, Z6, AA6, AB6, G6, H6, I6, J6, K6, L6, M6
  15. Cube(C7, C7 + (0, 1, 0), u) → D7, E7, N7, O7, P7, Q7, R7, S7, T7, U7, V7, W7, F7, X7, Y7, Z7, AA7, AB7, G7, H7, I7, J7, K7, L7, M7
  16. Cube(C8, C8 + (0, 1, 0), u) → D8, E8, N8, O8, P8, Q8, R8, S8, T8, U8, V8, W8, F8, X8, Y8, Z8, AA8, AB8, G8, H8, I8, J8, K8, L8, M8
  17. Cube(C9, C9 + (0, 1, 0), u) → D9, E9, N9, O9, P9, Q9, R9, S9, T9, U9, V9, W9, F9, X9, Y9, Z9, AA9, AB9, G9, H9, I9, J9, K9, L9, M9
  18. Cube(C10, C10 + (0, 1, 0), u) → D10, E10, N10, O10, P10, Q10, R10, S10, T10, U10, V10, W10, F10, X10, Y10, Z10, AA10, AB10, G10, H10, I10, J10, K10, L10, M10
  19. Cube(C11, C11 + (0, 1, 0), u) → D11, E11, N11, O11, P11, Q11, R11, S11, T11, U11, V11, W11, F11, X11, Y11, Z11, AA11, AB11, G11, H11, I11, J11, K11, L11, M11
  20. Cube(C13, C13 + (0, 1, 0), u) → D13, E13, N13, O13, P13, Q13, R13, S13, T13, U13, V13, W13, F13, X13, Y13, Z13, AA13, AB13, G13, H13, I13, J13, K13, L13, M13
  21. Cube(C14, C14 + (0, 1, 0), u) → D14, E14, N14, O14, P14, Q14, R14, S14, T14, U14, V14, W14, F14, X14, Y14, Z14, AA14, AB14, G14, H14, I14, J14, K14, L14, M14
  22. Cube(C15, C15 + (0, 1, 0), u) → D15, E15, N15, O15, P15, Q15, R15, S15, T15, U15, V15, W15, F15, X15, Y15, Z15, AA15, AB15, G15, H15, I15, J15, K15, L15, M15
  23. Cube(C16, C16 + (0, 1, 0), u) → D16, E16, N16, O16, P16, Q16, R16, S16, T16, U16, V16, W16, F16, X16, Y16, Z16, AA16, AB16, G16, H16, I16, J16, K16, L16, M16
  24. Cube(C17, C17 + (0, 1, 0), u) → D17, E17, N17, O17, P17, Q17, R17, S17, T17, U17, V17, W17, F17, X17, Y17, Z17, AA17, AB17, G17, H17, I17, J17, K17, L17, M17
  25. Cube(C18, C18 + (0, 1, 0), u) → D18, E18, N18, O18, P18, Q18, R18, S18, T18, U18, V18, W18, F18, X18, Y18, Z18, AA18, AB18, G18, H18, I18, J18, K18, L18, M18
  26. Cube(C19, C19 + (0, 1, 0), u) → D19, E19, N19, O19, P19, Q19, R19, S19, T19, U19, V19, W19, F19, X19, Y19, Z19, AA19, AB19, G19, H19, I19, J19, K19, L19, M19
  27. Cube(C20, C20 + (0, 1, 0), u) → D20, E20, N20, O20, P20, Q20, R20, S20, T20, U20, V20, W20, F20, X20, Y20, Z20, AA20, AB20, G20, H20, I20, J20, K20, L20, M20
  28. Cube(C21, C21 + (0, 1, 0), u) → D21, E21, N21, O21, P21, Q21, R21, S21, T21, U21, V21, W21, F21, X21, Y21, Z21, AA21, AB21, G21, H21, I21, J21, K21, L21, M21
  29. Cube(C22, C22 + (0, 1, 0), u) → D22, E22, N22, O22, P22, Q22, R22, S22, T22, U22, V22, W22, F22, X22, Y22, Z22, AA22, AB22, G22, H22, I22, J22, K22, L22, M22
  30. Cube(C23, C23 + (0, 1, 0), u) → D23, E23, N23, O23, P23, Q23, R23, S23, T23, U23, V23, W23, F23, X23, Y23, Z23, AA23, AB23, G23, H23, I23, J23, K23, L23, M23
  31. Cube(C24, C24 + (0, 1, 0), u) → D24, E24, N24, O24, P24, Q24, R24, S24, T24, U24, V24, W24, F24, X24, Y24, Z24, AA24, AB24, G24, H24, I24, J24, K24, L24, M24
  32. Cube(C25, C25 + (0, 1, 0), u) → D25, E25, N25, O25, P25, Q25, R25, S25, T25, U25, V25, W25, F25, X25, Y25, Z25, AA25, AB25, G25, H25, I25, J25, K25, L25, M25
  33. Cube(C26, C26 + (0, 1, 0), u) → D26, E26, N26, O26, P26, Q26, R26, S26, T26, U26, V26, W26, F26, X26, Y26, Z26, AA26, AB26, G26, H26, I26, J26, K26, L26, M26
  34. Cube(C27, C27 + (0, 1, 0), u) → D27, E27, N27, O27, P27, Q27, R27, S27, T27, U27, V27, W27, F27, X27, Y27, Z27, AA27, AB27, G27, H27, I27, J27, K27, L27, M27
  35. Cube(C28, C28 + (0, 1, 0), u) → D28, E28, N28, O28, P28, Q28, R28, S28, T28, U28, V28, W28, F28, X28, Y28, Z28, AA28, AB28, G28, H28, I28, J28, K28, L28, M28
  36. Cube(C12, C12 + (0, 1, 0), u) → D12, E12_1, N12_1, O12_1, P12_1, Q12_1, R12_1, S12_1, T12_1, U12_1, V12_1, W12_1, F12_1, X12_1, Y12_1, Z12_1, AA12_1, AB12_1, G12_1, H12_1, I12_1, J12_1, K12_1, L12_1, M12_1

AI 绘图提示语参考

请绘制一个由七个不规则多立方体组成的 3D 图形，这些多立方体由 3 或 4 个单位立方体构成，它们组合成一个 3×3×3 的立方体。图形应展示其中一个解决方案，其中每个多立方体通过空间旋转和平移排列，强调对称性和组合性。部分多立方体经过放大处理，整体结构需清晰展示，适合用于空间几何和组合数学教学。
以上提示语为根据原始绘图命令整理而来，仅供参考。