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Cross Sections of a Rectangular Pyramid

Cross Sections of a Rectangular Pyramid
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2012-11-28 23:37
PolygonCoordinate GeometrySolid Geometry
In collections Geometry Constructions truncated pyramid
This example explores the cross sections of a rectangular pyramid, helping students understand the concept of cross sections in solid geometry. Key mathematical concepts include polygons and solid geometry. Using GeoGebra commands such as Vector, Polygon, Translate, etc., students can dynamically observe the changes in cross sections. Suitable for middle school and above students to learn geometric construction and solid geometry.

GeoGebra Commands & Parameters

  1. Vector(O, Z) → w
  2. Vector(O, Y) → v
  3. Vector(O, X) → u
  4. Dilate(D, 0.6, O') → D'_3
  5. Dilate(C, 0.6, O') → C'_3
  6. Dilate(B, 0.6, O') → B'_3
  7. Dilate(A, 0.6, O') → A'_3
  8. Polygon(A, B, C, D) → poly1, a, b_1, c_1, d_1
  9. Translate(A, Vector[hauteur * u]) → A'
  10. Translate(B, Vector[hauteur * u]) → B'
  11. Translate(C, Vector[hauteur * u]) → C'
  12. Translate(D, Vector[hauteur * u]) → D'
  13. Polygon(A', B', C', D') → poly1', a', b', c', d'
  14. PointIn(poly1') → S
  15. Translate(B, Vector[(1 - hauteur3) * hauteur * u]) → B'_2
  16. Translate(C, Vector[(1 - hauteur3) * hauteur * u]) → C'_2
  17. Translate(D, Vector[(1 - hauteur3) * hauteur * u]) → D'_2
  18. Translate(A, Vector[(1 - hauteur3) * hauteur * u]) → A'_2
  19. Polygon(A'_2, B'_2, C'_2, D'_2) → poly1'', a'_2, b'_2, c'_2, d'_2
  20. Translate(A, Vector[(1 - hauteur3) * u]) → A'_1
  21. Translate(B, Vector[(1 - hauteur3) * u]) → B'_1
  22. Translate(C, Vector[(1 - hauteur3) * u]) → C'_1
  23. Translate(D, Vector[(1 - hauteur3) * u]) → D'_1
  24. Translate(S, Vector[-hauteur * u]) → S'
  25. Segment(S', S) → j
  26. Sequence(O' + b * v * cos((k * 360 / Sommets)° + i°) + b * w * sin((k * 360 / Sommets)° + i°), k, 0, Sommets) → liste1
  27. Sequence(Segment[Element[liste1, l], S], l, 0, Sommets) → liste4
  28. Polygon(liste1) → poly2, , , , ,
  29. Dilate(poly2, hauteur3, S) → poly2'
  30. Sequence(Polygon[Element[liste1, k], Element[liste1, k + 1], S], k, 0, Sommets) → liste9