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Solids Constructed from Sections

Solids Constructed from Sections
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2017-10-15 23:03
FunctionCoordinate GeometrySolid GeometryGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates the process of constructing solid figures from specific cross-sections. It involves core mathematical concepts such as solid geometry, coordinate geometry, function graphing, and matrix operations. GeoGebra commands and objects like Plane, Segment, Polygon, Sphere, Sequence, and Textfield are used in the construction. Suitable for high school students and math enthusiasts to understand spatial geometry and function applications.

GeoGebra Commands & Parameters

  1. Plane((0, 0, 0), (0, 1, 0), (0, 1, 1)) → s
  2. Plane((a, 0, 0), (a, 1, 1), (a, 1, 2)) → c
  3. Plane((b, 0, 0), (b, 1, 1), (b, 1, 2)) → d
  4. Segment((a, f(a)), (a, g(a))) → h
  5. Segment((b, f(b)), (b, g(b))) → i
  6. Intersect(f, h) → A
  7. Intersect(g, h, (-8, -6.968074739870145)) → B
  8. Intersect(f, i) → C
  9. Intersect(g, i, (8, -1.0319252601298547)) → D
  10. Polygon(A, B, (x(B), y(B), h), (x(A), y(A), h)) → q1, a_1, b_1, t, f_1
  11. Polygon(A, B, (a, (0.5 * (y(A) + y(B))), (sqrt(3) * h / 2))) → t1, g_1, a_2, b_2
  12. Midpoint(A, B) → E
  13. Sphere(E, A) → u
  14. Sequence(Polygon[(a + (i * deltax), g(a + (i * deltax)), 0), (a + (i * deltax), f(a + (i * deltax)), 0), 4, s], i, 0, n - 1, 1) → L3
  15. Polygon(A, B, (x(B), y(B), h)) → t2, k, a_3, b_3
  16. Sequence(Polygon[(a + (i * deltax), g(a + (i * deltax)), 0), (a + (i * deltax), f(a + (i * deltax)), 0), 3, s], i, 0, n - 1, 1) → L4
  17. Sequence(Polygon[(a + (i * deltax), f(a + (i * deltax)), 0), (a + (i * deltax), g(a + (i * deltax)), 0), (a + (i * deltax), g(a + (i * deltax)), Distance[(a + (i * deltax), f(a + (i * deltax)), 0), (a + (i * deltax), g(a + (i * deltax)), 0)])], i, 0, n - 1, 1) → L7
  18. Line((0, 0, 0), (1, 0, 0)) → m
  19. Line((0, 0, 0), (0, 1, 0)) → r
  20. Textfield(f) → InputBox1
  21. Textfield(g) → InputBox2
  22. Textfield(a) → InputBox3
  23. Textfield(b) → InputBox4
  24. Textfield(n) → InputBox5
  25. Sequence(Prism[Element[L3, i], deltax], i, 1, n, 1) → L2
  26. Sequence(Prism[Element[L4, i], deltax], i, 1, n, 1) → L5
  27. Sequence(Polygon[(a + (i * deltax), g(a + (i * deltax)), 0), (a + (i * deltax), f(a + (i * deltax)), 0), 5, s], i, 0, n - 1, 1) → L6
  28. Sequence(Prism[Element[L6, i], deltax], i, 1, n, 1) → L8
  29. Sequence(Midpoint[(a + (i * deltax), f(a + (i * deltax)), 0), (a + (i * deltax), g(a + (i * deltax)), 0)], i, 0, n - 1, 1) → L9
  30. Sequence((a + (i * deltax), f(a + (i * deltax)), 0), i, 0, n - 1, 1) → L10
  31. Sequence(Segment[Element[L9, i], Element[L10, i]], i, 1, n, 1) → radii
  32. Sequence((a + (i * deltax), g(a + (i * deltax)), 0), i, 0, n - 1, 1) → L11
  33. Sequence(Midpoint[Element[L10, i], Element[L11, i]], i, 1, n, 1) → L12
  34. Sequence(CircleArc[Element[L12, i], Element[L10, i], Element[L11, i], s], i, 1, n, 1) → L13
  35. Sequence(Prism[Element[L7, i], (-deltax)], i, 1, n, 1) → L

AI Drawing Prompt Reference

Draw a solid figure constructed from specific cross-sections, demonstrating core mathematical concepts. Create three planes, define the graphs of two functions, and find their intersections with the planes. Use these intersections to build multiple polygons and a sphere, then generate a series of prisms through sequence operations, combining them into a complex solid structure that illustrates spatial geometry and function applications.
The prompt above was compiled from the original drawing commands and is for reference only.