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Sections of Rectangular Prisms (Cuboids) by Anthony OR 柯志明

Sections of Rectangular Prisms (Cuboids) by Anthony OR 柯志明
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2014-11-03 22:08
Coordinate GeometrySolid GeometryGeometric Construction
In collections Area, Surface Area, Volume, Cross Section, 3D 3D Geometry & Cross Sections Sections of 3D Shapes Cross Sections Cross sections
This example demonstrates how to investigate different sections of a rectangular prism (cuboid) by intersecting it with various planes. Key math concepts include solid geometry, cross-section geometry, and 3D shape representation. Construction highlights the use of GeoGebra commands and objects such as Polygon, PointIn, Translate, Rotate, Prism, Plane, IntersectPath, OrthogonalLine to build the cuboid, section planes, and intersection lines. Suitable for high school students learning solid geometry, cross-section analysis, and spatial visualization skills.

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

AI Drawing Prompt Reference

Draw a rectangular prism (cuboid) with a square base on the horizontal plane and adjustable height. Inside or on the prism, place a movable polygon defined by three points, which determines a cutting plane. Intersect this plane with the prism to show the cross-section polygon. Additionally, draw an equilateral triangle outside the prism, rotated around the origin. Finally, from one vertex of the prism, draw a perpendicular line to the cutting plane, showing the foot of the perpendicular. The scene illustrates the geometry of plane sections of a prism in 3D space.
The prompt above was compiled from the original drawing commands and is for reference only.