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Modifiable Solid with Isosceles Right Triangles Parallel to yAxis

Modifiable Solid with Isosceles Right Triangles Parallel to yAxis
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2019-04-03 21:15
TriangleSolid GeometryCalculus
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources Cross Sectional Specials (Calculus)
This example demonstrates creating a modifiable solid with isosceles right triangle cross sections parallel to the yAxis. Key mathematical concepts include properties of isosceles right triangles, function graphs, and solid geometry. Commands used include Segment, Intersect, Line, Polygon, Textfield, Angle, CurveCartesian, Surface, etc. Suitable for high school mathematics education and calculus lessons on solid geometry.

GeoGebra Commands & Parameters

  1. Segment(H, I) → s_1
  2. Midpoint(s_1) → A_1
  3. Segment(J, K) → q_1
  4. Midpoint(q_1) → Z
  5. Midpoint(s_1) → E
  6. Midpoint(q_1) → F
  7. Intersect(upper, h, (0, 9)) → B
  8. Intersect(lower, h, (0, -9)) → C
  9. Segment(C, B) → q
  10. Intersect(upper, q, (0, 9)) → G
  11. Midpoint(C, G) → T
  12. Line(B, D) → i
  13. Sphere(B, d) → e
  14. Segment(C, B) → p
  15. Polygon(C, G, U) → q1, f_1, g_1, n_1
  16. Polygon(K, J, B_1) → q2, l, m, n
  17. Polygon(Q, P, C_1) → q3, r, s, t
  18. Textfield(upper) → InputBox1
  19. Textfield(lower) → InputBox2
  20. Textfield(a) → InputBox3
  21. Textfield(b) → InputBox4
  22. Segment(C, U) → i_1
  23. Segment(U, G) → j_1
  24. Segment(C, G) → k_1
  25. Segment(K, B_1) → f
  26. Segment(B_1, J) → g
  27. Segment(H, C_1) → l_1
  28. Segment(C_1, I) → m_1
  29. Angle(C, U, G) → α
  30. CurveCartesian(t, (0.5 * (upper(t) + lower(t))), (1 / 2 * (upper(t) - lower(t))), t, a, b) → c
  31. Surface(u, ((1 - v) * lower(u)) + ((0.5 * v) * (lower(u) + upper(u))), ((1 / 2 * v) * (upper(u) - lower(u))), u, a, b, v, 0, 1) → o
  32. Surface(u, (v * upper(u)) + (((1 - v) * 0.5) * (lower(u) + upper(u))), ((0.5 * (1 - v)) * (upper(u) - lower(u))), u, a, b, v, 0, 1) → u