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Sections of Triangular Pyramids by Dan Dale

Sections of Triangular Pyramids by Dan Dale
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2019-06-29 07:00
Solid GeometryTransformationGeometric Construction
This example demonstrates different sections of a triangular pyramid. Key mathematical concepts include the properties of sections in solid geometry. Using GeoGebra commands such as Polygon, PointIn, Translate, Rotate, and IntersectPath, dynamic changes in sections can be shown. Suitable for high school mathematics education.

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. Pyramid(Polygon[(-2, 0, 0), Rotate[(-2, 0, 0), 120°, zAxis], Rotate[(-2, 0, 0), -120°, zAxis]], (0, 0, 4)) → m, face1, face2, face3, edge1, edge2, edge3
  7. Rotate(D, 120°, (0, 0, 0)) → E
  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