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Solids Formed by Prism Stacking

Solids Formed by Prism Stacking
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2017-10-01 09:16
Solid GeometryGeometric Construction
In collections Cross Sectional Specials (Calculus)
This example illustrates the formation of various solids through prism stacking. Key mathematical concepts include solid geometry and geometric construction. It utilizes GeoGebra commands such as Plane, Segment, Intersect, Polygon, Midpoint, Sphere, Sequence, Line, and Textfield. Suitable for high school students learning solid geometry and dynamic geometry.

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