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Building Surfaces with Cross Sections and Function Modeling

Building Surfaces with Cross Sections and Function Modeling
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2020-05-05 01:39
FunctionSolid GeometryCalculusIntegralGeometric Construction
In collections Cross Sectional Specials (Calculus)
This example demonstrates how to create 3D solid models by specifying cross sections, integrating concepts from calculus, geometry, and integral calculus. It involves function modeling, triangles, step functions, and the Pythagorean theorem. Key GeoGebra commands and objects used include Segment, Midpoint, Intersect, Line, Sphere, Polygon, CurveCartesian, and Surface. Suitable for high school students and math enthusiasts needing practice in solid geometry and calculus.

GeoGebra Commands & Parameters

  1. Segment(H, I) → s_1
  2. Midpoint(s_1) → E
  3. Segment(J, K) → q_1
  4. Midpoint(q_1) → F
  5. Intersect(upper, h, (-2.3, 9.25429478782328)) → B
  6. Intersect(lower, h, (-2.3, -4.471)) → C
  7. Segment(C, B) → q
  8. Intersect(upper, q, (-2.2999999999999994, 9.25429478782328)) → G
  9. Midpoint(C, G) → T
  10. Line(B, D) → i
  11. Sphere(B, d) → e
  12. Segment(C, B) → p
  13. Polygon(C, G, U) → q1, f_1, g_1, n_1
  14. Polygon(K, J, W) → q2, l, m, n
  15. Polygon(Q, P, V) → q3, r, s, t
  16. Segment(K, W) → f
  17. Segment(W, J) → g
  18. Segment(Q, V) → j
  19. Segment(V, P) → k
  20. CurveCartesian(t, (0.5 * (upper(t) + lower(t))), ((sqrt(3) * 1 / 2) * (upper(t) - lower(t))), t, a, b) → c
  21. Surface(u, ((1 - v) * lower(u)) + ((0.5 * v) * (lower(u) + upper(u))), (sqrt(3) / 2 * (v * (upper(u) - lower(u)))), u, a, b, v, 0, 1) → o
  22. Surface(u, (v * upper(u)) + (((1 - v) * 0.5) * (lower(u) + upper(u))), (((sqrt(3) * 0.5) * (1 - v)) * (upper(u) - lower(u))), u, a, b, v, 0, 1) → u
  23. Segment(C, U) → i_1
  24. Segment(U, G) → j_1
  25. Segment(C, G) → k_1