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M3_L7_Cross Section Rect Pyramid

M3_L7_Cross Section Rect Pyramid
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2014-12-17 01:00
Solid GeometryCalculusParametric EquationGeometric ConstructionSlider Animation
This example demonstrates the construction of a rectangular pyramid's cross-section, involving solid geometry and calculus concepts like cross-sectional area calculation. Key mathematical concepts include three-dimensional geometric transformations, trigonometric functions, and parametric equations. Construction involves GeoGebra commands such as Vector, Dilate, Polygon, Translate, and using sliders to animate changes. Suitable for high school students or college freshmen learning solid geometry and calculus fundamentals.

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

AI Drawing Prompt Reference

Draw a cross-section of a rectangular pyramid demonstrating solid geometry and calculus concepts like cross-sectional area calculation. Use vectors, dilation, translation, and sliders to construct the base and sides of the pyramid, and parametric equations to animate changes. Key objects include the base, sides, cross-section, and animation path, starting with the basic pyramid, adjusting height with a slider, and finally drawing the cross-section and animation path.
The prompt above was compiled from the original drawing commands and is for reference only.