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Intersection of Three Cylinders

Intersection of Three Cylinders
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2016-08-05 03:02
Coordinate GeometrySolid GeometryGeometric Construction
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the geometric intersection of three cylinders and its cross-sectional shapes. Key math concepts include solid geometry, intersection calculations, surface area, and coordinate geometry. Construction involves commands like Cylinder, CurveCartesian, Point, Sphere, PointIn, Surface, and Cube, highlighting spatial relationships and calculations. Suitable for high school students and math enthusiasts exploring 3D geometry.

GeoGebra Commands & Parameters

  1. Cylinder(A, B, r) → d, e, f, g
  2. Cylinder(C, D, r) → h, h_2, h_3, h_4
  3. Cylinder(E, F, r) → j, j_2, j_3, j_4
  4. CurveCartesian((cos(t) * r), (cos(t) * r), (sin(t) * r), t, (-π), π) → m
  5. CurveCartesian((cos(t) * r), ((-cos(t)) * r), (sin(t) * r), t, (-π), π) → b
  6. CurveCartesian((sin(t) * r), (cos(t) * r), (cos(t) * r), t, (-π), π) → c
  7. CurveCartesian((sin(t) * r), (cos(t) * r), ((-cos(t)) * r), t, (-π), π) → i
  8. CurveCartesian((cos(t) * r), (sin(t) * r), (cos(t) * r), t, (-π), π) → k
  9. CurveCartesian((cos(t) * r), (sin(t) * r), ((-cos(t)) * r), t, (-π), π) → l
  10. Point(c) → G
  11. Point(b) → H
  12. Point(i) → I
  13. Point(m) → J
  14. Point(k) → K
  15. Point(m) → L
  16. Point(b) → M
  17. Point(k) → N
  18. Sphere(O, J) → n
  19. PointIn(h_4) → Bodh4
  20. Surface((cos(t) * r), ((cos(t) * r) * s), (sin(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → r_1
  21. Surface((cos(t) * r), ((cos(t) * r) * s), ((-sin(t)) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → s
  22. Surface((sin(t) * r), ((s * cos(t)) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → t
  23. Surface(((-sin(t)) * r), ((s * cos(t)) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → u
  24. Surface((sin(t) * r), (cos(t) * r), (((-cos(t)) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → v
  25. Surface(((-sin(t)) * r), (cos(t) * r), ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → w
  26. Surface(((cos(t) * r) * s), (cos(t) * r), ((-sin(t)) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → b_1
  27. Surface(((cos(t) * r) * s), (sin(t) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → c_1
  28. Surface((cos(t) * r), (sin(t) * r), ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → d_1
  29. Surface((cos(t) * r), ((-sin(t)) * r), ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → e_1
  30. Surface(((cos(t) * r) * s), ((-sin(t)) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → f_1
  31. Surface(((cos(t) * r) * s), (cos(t) * r), (sin(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → a_1
  32. Cube(A_1, B_1, o_1) → p_1, P, stena4, stenaPQUT, stenaRSTU, hrana2, hrana1, hrana4, hranaPQ, hrana3, hranaQU, hranaRU, Q, hranaRS, hrana5, hranaST, hranaPT, hranaTU, R, S, T, U, stena1, stena3, stena2
  33. Cylinder(A, B, r) → q_1, s_1, t_1, u_1
  34. Cylinder(C, D, r) → v_1, c_2, d_2, w_1
  35. Cylinder(E, F, r) → a_2, e_2, f_2, b_2
  36. Surface((cos(t) * r), ((-sin(t)) * r) - g_2, ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → g_1
  37. Surface(((cos(t) * r) * s), ((-sin(t)) * r) - g_2, (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → h_1
  38. Surface((cos(t) * r), ((cos(t) * r) * s), (sin(t) * r) + g_2, s, -1, 1, t, π / 4, (3 * π / 4)) → i_1
  39. Surface((cos(t) * r), ((cos(t) * r) * s), ((-sin(t)) * r) - g_2, s, -1, 1, t, π / 4, (3 * π / 4)) → j_1
  40. Surface((sin(t) * r) + g_2, ((s * cos(t)) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → k_1
  41. Surface(((-sin(t)) * r) - g_2, ((s * cos(t)) * r), (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → l_1
  42. Surface((sin(t) * r) + g_2, (cos(t) * r), (((-cos(t)) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → m_1
  43. Surface(((-sin(t)) * r) - g_2, (cos(t) * r), ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → n_1
  44. Surface(((cos(t) * r) * s), (cos(t) * r), ((-sin(t)) * r) - g_2, s, -1, 1, t, π / 4, (3 * π / 4)) → o
  45. Surface(((cos(t) * r) * s), (sin(t) * r) + g_2, (cos(t) * r), s, -1, 1, t, π / 4, (3 * π / 4)) → p
  46. Surface((cos(t) * r), (sin(t) * r) + g_2, ((cos(t) * r) * s), s, -1, 1, t, π / 4, (3 * π / 4)) → q
  47. Surface(((cos(t) * r) * s), (cos(t) * r), (sin(t) * r) + g_2, s, -1, 1, t, π / 4, (3 * π / 4)) → a