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长方体表面积演示 by Mr BM

长方体表面积演示 by Mr BM
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2015-11-28 03:41
立体几何几何作图
该范例演示了一个长方体从平面折叠成立体的过程。核心数学概念包括长方体的表面积计算。通过使用GeoGebra命令如Vector、Polygon、Area等，可以调整长方体的尺寸并计算其表面积。适合初中及以上学生学习立体几何。

GeoGebra 命令及参数

  1. Vector(PTP_1, PB_3) → tpsb
  2. Vector(PTPF_1, PTP_1) → tpf1
  3. Vector(PTP, PB_2) → tpa1
  4. Vector(PTPF, PTP) → tpf
  5. Vector(PBK, PB) → bk1
  6. Vector(PBK_1, PB_1) → bk11
  7. Vector(PFT_1, PB_3) → ftb13
  8. Vector(PFT, PB_2) → fta1
  9. Vector(PSB_1, PB_3) → sbb13
  10. Vector(PSB, PB_1) → sbb
  11. Vector(PSF_1, PB_2) → sfa1
  12. Vector(PSF, PB) → sfb
  13. Polygon(SF_3, SF, SF_1, SF_2) → aSideFront, a, b, c, d
  14. If(dist < 100.0, PTPF + (dist * Length[tpf] / 100.0; Angle[tpf]), PTP + ((dist - 100.0) * Length[tpa1] / 100.0; Angle[tpa1])) → TP_3
  15. If(dist < 100.0, PTPF_1 + (dist * Length[tpf1] / 100.0; Angle[tpf1]), PTP_1 + ((dist - 100.0) * Length[tpsb] / 100.0; Angle[tpsb])) → TP_2
  16. Polygon(TP_3, TP_2, TP_1, TP) → aTop, a_1, b_1, c_1, d_1
  17. Polygon(BK_3, BK_2, BK_1, BK) → aBack, a_2, b_2, c_2, d_2
  18. Polygon(BT, BT_1, BT_2, BT_3) → aBottom, a_3, b_3, c_3, d_3
  19. Polygon(SB, SB_1, SB_2, SB_3) → aSideBack, a_4, b_4, c_4, d_4
  20. Polygon(FT, FT_1, FT_2, FT_3) → aFront, a_5, b_5, c_5, d_5
  21. Polygon(NA_2, NA, NA_1, NA_3) → planBottom, na_2, na, na_1, na_3
  22. Polygon(NA_2, NA_3, NFT_1, NFT) → planFront, na_4, na_5, nft_1, nft
  23. Polygon(NA, NSF, NSF_1, NA_2) → planSideFront, na_6, nsf, nsf_1, na_7
  24. Polygon(NA_1, NSB, NSB_1, NA_3) → planSideBack, na_8, nsb, nsb_1, na_9
  25. Polygon(NA, NBK, NBK_1, NA_1) → planBack, na_{10}, nbk, nbk_1, na_{11}
  26. Polygon(NBK, NTPT, NTPF_1, NBK_1) → planTop, nbk_2, ntpt, ntpf_1, nbk_3
  27. Midpoint(nft_1) → Hnf
  28. Midpoint(ntpf_1) → Hpl
  29. Midpoint(nbk_1) → Hpb
  30. Midpoint(b_1) → HXts
  31. Midpoint(d_2) → HXbs
  32. Midpoint(c_5) → HXfs
  33. Area(BK_3, BK_2, BK_1, BK) → bb