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Custom Solid: Cross Sections Parallel to yAxis are Quadrilaterals Always Similar

Custom Solid: Cross Sections Parallel to yAxis are Quadrilaterals Always Similar
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2019-12-23 09:17
PolygonCoordinate GeometrySolid GeometryCalculus
In collections Cross Sectional Specials (Calculus)
This example demonstrates a custom solid where cross sections parallel to the yAxis are always similar quadrilaterals to the base. It involves core math concepts like solid geometry, polygons, similarity, and coordinate geometry. Constructed using GeoGebra commands like PointIn, Polygon, FitPoly, Segment, CurveCartesian. Suitable for high school students and above for learning and exploring solid geometry and cross-section properties, ideal for classroom demonstrations and exploratory learning.

GeoGebra Commands & Parameters

  1. PointIn(x < 0) → A
  2. PointIn(x > 0) → B
  3. Polygon(A, B, D, C) → q1, a, b, d, c
  4. FitPoly({A, B}) → g
  5. Segment(E, F) → h
  6. CurveCartesian(t, 0, (g(t) * c / d), t, x(C), x(D)) → i
  7. CurveCartesian(t, g(t), (g(t) * b / d), t, x(C), x(D)) → j
  8. Polygon(E, G, H, F) → q2, e_1, g_1, h_1, f_1
  9. Polygon(C, I, J, D) → q3, c_1, i_1, j_1, d_1
  10. Polygon(I, K, L, J) → q4, i_2, k, l_1, j_2
  11. Polygon(A, K, L, B) → q5, a_1, k_1, l_2, b_1
  12. Polygon(J, L, B, D) → q6, j_3, l_3, b_2, d_2
  13. Segment(I, K) → n
  14. Segment(C, A) → p
  15. Segment(A, K) → q
  16. Segment(C, I) → r
  17. Segment(D, J) → s
  18. Segment(J, L) → t
  19. Segment(L, B) → m_1
  20. Segment(B, D) → n_1
  21. Segment(D, C) → p_1
  22. Segment(E, G) → q_1
  23. Segment(G, H) → r_1
  24. Segment(H, F) → s_1
  25. Segment(A, B) → t_1
  26. Polygon(A, C, I, K) → q7, a_2, c_2, i_3, k_2