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长方体展开图与水面接触面积可视化

长方体展开图与水面接触面积可视化
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2019-09-01 10:34
多边形立体几何滑块动画
①本范例通过滑块 f 和 f_w 可视化长方体的展开图及水面接触的表面积；②涉及核心数学概念：立体几何、多边形面积计算、几何变换；③构造要点：使用 Textfield, Polygon, Prism, Net 命令创建了长方体、展开图及水面接触面，通过 InputBox 控制参数，利用 edge 和 face 对象定义几何关系；④适合高中数学教学，用于理解空间几何与实际应用结合。

GeoGebra 命令及参数

  1. Textfield(l) → InputBox1
  2. Textfield(b) → InputBox2
  3. Textfield(h) → InputBox3
  4. Textfield(h_w) → InputBox4
  5. Polygon(A, B, C, D) → q1, a, b_1, c, d
  6. Prism(q1, h) → e, E, edge1, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, face1, faceBCGF, faceCDHG, face2, faceEFGH
  7. Net(e, f) → g, I, R, S, T, U, V, faceIJKL, faceIJNM, faceJKPO, faceKLRQ, faceILST, J, faceMNUV, edgeIJ, edgeJK, edgeKL, edgeIL, edgeIM, edgeMN, edgeJN, edgeJO, edgeOP, K, edgeKP, edgeKQ, edgeQR, edgeLR, edgeLS, edgeST, edgeIT, edgeNU, edgeUV, edgeMV, L, M, N, O, P, Q
  8. Polygon(W_A, W_B, W_C, W_D) → q_w, w_a, w_b, w_c, w_d
  9. Prism(q_w, h_w) → e_w, W, edge2, edge3, edge4, edge5, edgeWZ, edge7, edge8, edge6, Z, A_1, B_1, face3, face5, face6, face4, face7
  10. Net(e_w, f_w) → g_w, C_1, L_1, M_1, N_1, O_1, P_1, face8, face9, face10, face11, face12, D_1, face13, edge9, edge10, edge11, edge12, edge13, edge14, edge15, edge16, edge17, E_1, edge18, edge19, edge20, edge21, edge22, edge23, edge24, edge25, edge26, edge27, F_1, G_1, H_1, I_1, J_1, K_1