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二项式立方体模型

二项式立方体模型
几何画板及绘图内容加载中，请稍等……
2024-03-23 17:13
解析几何立体几何几何作图
所属专题 Arithmetic and Algebra
该范例演示了二项式的立方体模型，展示了二项式展开在几何中的应用。核心数学概念包括二项式、体积和立体几何。通过使用GeoGebra命令如Mirror、Polygon、Point等，构建了一个动态的立方体模型，展示了二项式展开的几何意义。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Mirror(A, yAxis) → A'
  2. Polygon(A, A', 4, xOyPlane) → poli1, LatoBase, b1, c, d, B, C
  3. Point(LatoBase) → D
  4. Circle(A', D, xOyPlane) → e
  5. Intersect(b1, e, 1) → E
  6. Mirror(E, yAxis) → E'
  7. Segment(A, D) → a
  8. Segment(D, A') → b
  9. Prism(Polygon[A, D, F, E'], a) → f, G, spigolo1, spigolo2, spigolo3, spigolo4, spigolo5, spigolo6, spigolo7, spigolo8, H, I, J, faccia1, faccia2, faccia3, faccia4, faccia5
  10. Prism(Polygon[G, H, I, J], b) → g, K, spigoloGK, spigoloHL, spigoloIM, spigoloJN, spigoloKL, spigoloLM, spigoloMN, spigoloKN, L, M, N, facciaGHLK, facciaHIML, facciaIJNM, facciaGJNK, facciaKLMN
  11. Prism(Polygon[D, A', E, F], a) → h, O, spigoloDO, spigoloA'P, spigoloEQ, spigoloFR, spigoloOP, spigoloPQ, spigoloQR, spigoloOR, P, Q, R, facciaA'DOP, facciaA'EQP, facciaEFRQ, facciaDFRO, facciaOPQR
  12. Prism(Polygon[O, P, Q, R], b) → i, S, spigoloOS, spigoloPT, spigoloQU, spigoloRV, spigoloST, spigoloTU, spigoloUV, spigoloSV, T, U, V, facciaOPTS, facciaPQUT, facciaQRVU, facciaORVS, facciaSTUV
  13. Prism(Polygon[E, B, D', F], a) → j, W, spigoloEW, spigoloBZ, spigolo9, spigolo10, spigoloWZ, spigolo12, spigolo13, spigolo11, Z, A_1, B_1, facciaBEWZ, faccia6, faccia7, faccia8, faccia9
  14. Prism(Polygon[W, Z, A_1, B_1], b) → k, C_1, spigolo14, spigolo15, spigolo16, spigolo17, spigolo18, spigolo20, spigolo21, spigolo19, D_1, E_1, F_1, faccia10, faccia12, faccia13, faccia11, faccia14
  15. Prism(Polygon[C, E', F, D'], a) → l, G_1, spigolo22, spigolo24, spigolo25, spigolo23, spigolo26, spigolo28, spigolo29, spigolo27, H_1, I_1, J_1, faccia16, faccia18, faccia17, faccia15, faccia19
  16. Prism(Polygon[G_1, H_1, I_1, J_1], b) → m, K_1, spigolo30, spigolo31, spigolo32, spigolo33, spigolo34, spigolo36, spigolo37, spigolo35, L_1, M_1, N_1, faccia20, faccia22, faccia23, faccia21, faccia24
  17. UnitVector(xAxis) → n
  18. If(aniSli < 15.5, 0, 15.5 ≤ aniSli ≤ 19.7, aniSli - 15.5, 4.2) → o
  19. If(0 ≤ aniSli ≤ 10, aniSli, 10) → p
  20. Translate(i, Vector[(n * p)]) → i'
  21. If(aniSli < 10, 0, 10 ≤ aniSli ≤ 15.5, aniSli - 10, 5.5) → q
  22. Vector((0, 0, 0), O_1) → r
  23. Translate(f, Vector[(q * r)]) → f'
  24. Translate(j, Vector[(q * r)]) → j'
  25. Translate(m, Vector[(q * r)]) → m'
  26. Mirror(r, zAxis) → r'
  27. Translate(k, Vector[(o * r')]) → k'
  28. Translate(g, Vector[(o * r')]) → g'
  29. Translate(h, Vector[(o * r')]) → h'
  30. Translate({D, A', E, F}, Vector[(o * r')]) → vertHPrime
  31. Translate({D + (0, 0, a), A' + (0, 0, a), E + (0, 0, a), F + (0, 0, a)}, Vector[(o * r')]) → vertHPrimeTop
  32. Segment(vertHPrime(2), vertHPrime(3)) → segmBaseHPrime1
  33. Segment(vertHPrime(1), vertHPrime(2)) → segmBaseHPrime2
  34. Segment(vertHPrime(2), vertHPrimeTop(2)) → segmHeighHPrime
  35. Segment(E', F) → segmEPrimeF
  36. Segment(F, D') → segmFDPrime
  37. Segment(F, F + (0, 0, a)) → segmHeighGreyCube
  38. Translate({Segment[O, P], Segment[P, Q], Segment[P, P + (0, 0, b)]}, Vector[(n * p)]) → allSegmBlueCube
  39. Translate({Segment[E, B], Segment[F, E], Segment[E, E + (0, 0, a)]}, Vector[(q * r)]) → allSegmPrism
  40. Element(allSegmPrism, 2) → horSegmPrism
  41. Translate({Segment[E, B], Segment[E, E + (0, 0, a)]}, Vector[(q * r)]) → allASegmPrism

AI 绘图提示语参考

在三维空间中构建一个二项式立方体的体积分解模型。首先在水平面上绘制一个正方形，以其一条边为基准，在相邻位置构造多个长方体，分别代表展开式中的各项体积。通过镜像和旋转操作，将不同大小的棱柱体组合成一个完整的大立方体，并添加辅助线段以标示边长关系。整体呈现为多个彩色半透明棱柱体拼接的立体几何图形，展示体积的加法原理。
以上提示语为根据原始绘图命令整理而来，仅供参考。