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Washers and Cylinders by Jonathan Holland

Washers and Cylinders by Jonathan Holland
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2018-01-26 21:46
CircleSolid Geometry
This example demonstrates the construction of washers and cylinders. Key mathematical concepts include the properties of circles and cylinders. Using GeoGebra commands such as Intersect, Line, and Point, the construction of washers and cylinders is illustrated. Suitable for middle school and above students for geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → I
  2. Line(I, C) → f
  3. Line(I, D) → g
  4. Point(g) → F
  5. OrthogonalLine(F, g) → h
  6. Point(d) → G
  7. Line(G, f) → i
  8. Intersect(p, i, (0.8646958274483016, 1.0708883749629394)) → H
  9. Circle(h, H) → e
  10. Rotate(G, t, h) → G'
  11. Rotate(H, t, h) → H'
  12. Point(d) → J
  13. Line(J, h) → l
  14. Intersect(c, l, 2) → K
  15. OrthogonalLine(L, yAxis) → m
  16. Segment(J, K) → segJK
  17. Rotate(J, t, m) → J'
  18. Rotate(K, t, m) → K'
  19. Circle(m, K) → q
  20. Circle(m, J) → r
  21. Point(xAxis) → M
  22. Line(M, N) → s
  23. Point(x = -1) → O
  24. OrthogonalLine(O, yAxis) → f_1
  25. Intersect(d, f_1, 2) → P
  26. Intersect(d, f_1, 1) → Q
  27. Intersect(p, f_1, (2.074351191463267, 2.190082644628087)) → R
  28. Segment(O, P) → segOP
  29. Segment(Q, R) → segQR
  30. Intersect(c, f_1, 1) → S
  31. Segment(O, S) → segOS
  32. Circle(m, O) → c_1
  33. Circle(m, Q) → d_1
  34. Circle(m, O) → p_1
  35. Circle(m, S) → q_1
  36. Rotate(J, t, m) → J'_1
  37. Rotate(K, t, m) → K'_1
  38. Segment(J'_1, K'_1) → segJK'
  39. Rotate(O, t, m) → O'
  40. Rotate(S, t, m) → S'
  41. Rotate(O, t, m) → O'_1
  42. Rotate(P, t, m) → P'
  43. Segment(O'_1, P') → segOP'
  44. Rotate(O, t, m) → O'_2
  45. Rotate(S, t, m) → S'_1
  46. Segment(O'_2, S'_1) → segOS'
  47. Rotate(Q, t, m) → Q'
  48. Rotate(R, t, m) → R'
  49. Segment(Q', R') → segQR'