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棱柱截面构造：几何与微积分结合

棱柱截面构造：几何与微积分结合
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2018-10-01 03:48
立体几何微积分几何作图
该范例展示了棱柱的截面构造，涉及几何中的平面截交与微积分中的不定积分概念。作图要点包括使用GeoGebra命令如Polygon、Prism、Plane、IntersectPath等来构建棱柱和截面。适合高中生或大学低年级学生用于学习立体几何和微积分基础。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Prism(q1, 5.838265672597288) → e, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  3. Plane(I, xOyPlane) → f
  4. IntersectPath(f, faceBCGF) → g
  5. Intersect(f, faceBCGF) → J, K
  6. IntersectPath(f, faceCDHG) → h
  7. Intersect(f, faceCDHG) → L, M
  8. IntersectPath(f, faceADHE) → i
  9. Intersect(f, faceADHE) → N, O
  10. IntersectPath(f, faceABFE) → j
  11. Intersect(f, faceABFE) → P, Q
  12. Polygon(N, P, Q, L) → q2, n, p, q, l
  13. Circle(R, 2, xOyPlane) → k
  14. Point(Circle[S, 1.433875866314794]) → T
  15. Polygon(S, T, U, V, W, Z, A_1, B_1) → poly1, s, t, u, v, w, z_1, a_1, b_1
  16. Polygon(C_1, D_1, E_1) → t1, e_1, c_1, d_1
  17. Cylinder(k, 5.988461600068064) → m, r, o
  18. Prism(t1, 6.604452887287681) → f_1, F_1, edge3, edge4, edge6, edge5, G_1, H_1, face2, face4, face3, face1, edge1, edge2
  19. IntersectPath(f, m) → g_1
  20. IntersectPath(f, face2) → h_1
  21. Intersect(f, face2) → I_1, J_1
  22. IntersectPath(f, face3) → i_1
  23. Intersect(f, face3) → K_1, L_1
  24. IntersectPath(f, face4) → j_1
  25. Intersect(f, face4) → M_1, N_1
  26. Polygon(M_1, N_1, L_1) → t2, l_1, m_1, n_1