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Rectangular Prism and Cross Sections

Rectangular Prism and Cross Sections
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2018-06-26 21:37
Solid GeometryTransformationGeometric Construction
This example demonstrates the construction of a rectangular prism and its cross sections. Key mathematical concepts include solid geometry, specifically the rectangular prism and cross sections. Using GeoGebra commands such as Polygon, PointIn, Translate, Rotate, etc., the example dynamically shows the faces and cross sections of the prism. Suitable for middle school and above students or teachers for teaching or self-study.

GeoGebra Commands & Parameters

  1. Polygon(B + (-2, -2), B + (2, -2), B + (2, 2), B + (-2, 2)) → poly3, e, f, g, i
  2. PointIn(poly3) → C
  3. Translate((0, 0, 0), Vector[B, C]) → A
  4. Polygon(A + (-4, -4), A + (4, -4), A + (4, 4), A + (-4, 4)) → poly1, a, b, c, d
  5. Rotate(Rotate[Translate[poly1, Vector[A, A + (0, 0, h)]], (90° * s), A + (0, 0, h), yAxis], (90° * t), A, zAxis) → poly2
  6. Rotate(D, 120°, (0, 0, 0)) → E
  7. Prism(Polygon[(-1.5, -1.25, 0), (1.5, -1.25, 0), (1.5, 1.25, 0), (-1.5, 1.25, 0)], (-1.5, -1.25, 4)) → m, M, edge2, edge3, edge4, edge5, edge6, edge7, edge8, N, Q, face1, face2, face3, face4, face5, edge1
  8. Polygon(D, E, 3, xOyPlane) → poly4, j, k, l, F
  9. PointIn(poly2) → G
  10. PointIn(poly2) → H
  11. PointIn(poly2) → I
  12. Plane(G, I, H) → n
  13. IntersectPath(n, m) → poly6, poly5, r, a_1, b_1, c_1, K, L_1, O, P, J, L, p, q
  14. Rotate(m, 0, zAxis) → m'
  15. Rotate(m, 0, zAxis) → m'_1
  16. OrthogonalLine(A, n) → d_1