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Prism Cross-section Construction: Geometry and Calculus Integration

Prism Cross-section Construction: Geometry and Calculus Integration
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2018-10-01 03:48
Solid GeometryCalculusGeometric Construction
This example demonstrates the construction of a prism cross-section, involving concepts from geometry (plane intersection) and calculus (indefinite integral). The construction uses GeoGebra commands such as Polygon, Prism, Plane, IntersectPath, etc. It is suitable for high school students or college freshmen learning solid geometry and calculus fundamentals.

GeoGebra Commands & Parameters

  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