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Sections of Rectangular Pyramids by Anthony OR 柯志明

Sections of Rectangular Pyramids by Anthony OR 柯志明
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2014-11-03 23:29
Coordinate GeometrySolid GeometryGeometric Construction
In collections Area, Surface Area, Volume, Cross Section, 3D 3D Geometry & Cross Sections Geometry - Areas and Volumes Sections of 3D Shapes Cross Sections Cross sections
This example demonstrates different sections of a rectangular pyramid. Key mathematical concepts include solid geometry. Using GeoGebra commands such as Polygon, PointIn, Translate, Rotate, Pyramid, Plane, IntersectPath, etc., one can construct a rectangular pyramid and its sections. Suitable for high school students or teachers.

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[(-1.5, -1.25, 0), (1.5, -1.25, 0), (1.5, 1.25, 0), (-1.5, 1.25, 0)], (0, 0, 4)) → 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

AI Drawing Prompt Reference

Draw a rectangular pyramid and show its different sections. Start by creating a rectangular base, then extend it vertically to form the pyramid. Next, draw three parallelograms on the sides of the pyramid to represent different sections. Finally, use rotation and intersection to show the lines where the pyramid intersects with planes, creating complex section shapes.
The prompt above was compiled from the original drawing commands and is for reference only.