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Drawing Cross Sections of a Pyramid

Drawing Cross Sections of a Pyramid
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2018-04-17 19:28
VectorCoordinate GeometrySolid GeometryGeometric ConstructionSlider Animation
This example demonstrates how to dynamically interact and draw cross-sections of a pyramid. Key math concepts include solid geometry, vectors, the relationship between planes and polygons, and analytical geometry. Construction highlights from the summary involve commands like Polygon, PointIn, Translate, Rotate, Pyramid, Plane, IntersectPath, and OrthogonalLine, along with objects such as points, polygons, and planes. Suitable for high school and above to understand 3D shape properties and mathematical modeling.

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, 2, 0), (2, -2, 0), (-2, -2, 0), (-2, 2, 0)], -4) → m, M, face1, face2, face3, face4, edge1, edge2, edge3, edge4
  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