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Cross Sections of a Rectangular Prism by nandrews

Cross Sections of a Rectangular Prism by nandrews
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2015-05-01 20:27
Solid GeometryParametric EquationGeometric Construction
In collections Cross Sections of Prisms
This example demonstrates the analysis of cross-sections of a rectangular prism in various positions. Key mathematical concepts include solid geometry, cross-section analysis, and parametric equations. Construction involves using GeoGebra commands like Intersect, Point, Polygon, Prism, etc. to build the prism model and analyze changes in cross-sections. Suitable for high school students or college undergraduates to understand three-dimensional geometry and cross-section relationships.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → D
  3. Polygon(A, B, C, D) → poly1, a, b, c, d
  4. Prism(poly1, 2.975831365655143) → e, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  5. Point(edgeGH) → I
  6. OrthogonalLine(I, c, space) → f
  7. Intersect(c, f) → J
  8. OrthogonalLine(I, edgeEF, space) → g
  9. Intersect(edgeEF, g) → K
  10. OrthogonalLine(K, a, space) → h
  11. Plane(I, J, K) → i
  12. IntersectPath(i, e) → poly2, L, M, N, O, j, k, l, m
  13. Point(edgeCG) → P
  14. OrthogonalLine(P, edgeBF, space) → p
  15. OrthogonalLine(P, edgeDH, space) → q
  16. Intersect(edgeBF, p) → Q
  17. Intersect(edgeDH, q) → R
  18. Plane(Q, P, R) → o
  19. IntersectPath(o, e) → poly3, S, T, U, V, r, s, t, a_1
  20. Point(edgeCG) → W
  21. OrthogonalLine(W, edgeBF, space) → b_1
  22. Point(edgeDH) → Z
  23. Intersect(edgeBF, b_1) → A_1
  24. Plane(A_1, W, Z) → v
  25. IntersectPath(v, e) → poly4, B_1, C_1, D_1, E_1, c_1, d_1, e_1, f_1
  26. Point(edgeEF) → F_1
  27. Point(edgeFG) → G_1
  28. Point(edgeBF) → H_1
  29. Plane(F_1, G_1, H_1) → g_1
  30. IntersectPath(g_1, e) → poly5, I_1, J_1, K_1, N_1, h_1, i_1, j_1, l_1
  31. IntersectPath(g_1, faceEFGH) → k_1
  32. Intersect(g_1, faceEFGH) → L_1, M_1

AI Drawing Prompt Reference

Draw a rectangular prism and analyze its cross-sections at different positions. First, build the prism, then construct plane i through point I and line c, intersecting the prism to get cross-section poly2. Next, construct plane o through point P and lines edgeBF and edgeDH, intersecting the prism to get cross-section poly3. Then, construct plane v through point W, edgeBF, and edgeDH, intersecting the prism to get cross-section poly4. Finally, construct plane g_1 through points F_1, G_1, and H_1, intersecting the prism to get cross-section poly5.
The prompt above was compiled from the original drawing commands and is for reference only.