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Interactive Demonstration of Cutting a Cylinder with a Plane

Interactive Demonstration of Cutting a Cylinder with a Plane
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2020-04-13 23:57
Solid GeometryTransformationGeometric Construction
In collections Cutting solids by a plane
This example demonstrates how to use an interactive plane to cut a cylinder. Key mathematical concepts include the intersection of a plane and a cylinder in solid geometry. Using GeoGebra commands such as Point, Cube, Line, Circle, and Plane, a dynamic graphical representation of the cutting process is constructed. Suitable for middle school and above students or teachers for teaching and learning.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, arêteAD, arêteAB, arêteBC, arêteCD, arêteAE, arêteDH, arêteEH, arêteEF, E, arêteBF, arêteFG, arêteCG, arêteGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Midpoint(C, A) → I
  4. Midpoint(F, H) → J
  5. Line(J, I) → f
  6. Circle(I, Distance[A, B], f) → c
  7. Point(c) → K
  8. Midpoint(F, C) → M
  9. Mirror(K, I) → K'
  10. Line(K', K) → g
  11. Circle(I, (1.2 * Distance[A, B]), g) → d
  12. Point(d) → L
  13. Plane(L, K, K') → p
  14. Circle(K', L, K) → e
  15. Center(e) → N
  16. OrthogonalLine(N, p) → h
  17. Point(h) → O
  18. Vector(I, O) → u
  19. Translate(p, u) → p'
  20. Segment(K', K) → b
  21. Line(L, b) → f_1
  22. Point(arêteEF) → D_1
  23. OrthogonalLine(K, p) → h_1
  24. Plane(K', h_1) → p_1
  25. OrthogonalLine(K, p_1) → k_1
  26. Line(K', k_1) → l_1
  27. Intersect(f_1, l_1) → E_1
  28. Intersect(k_1, f_1) → F_1
  29. Mirror(F_1, K) → G_1
  30. Mirror(E_1, K') → H_1
  31. Polygon(F_1, E_1, H_1, G_1) → q2, m_1, e_1, n_1, q_1
  32. Translate(q2, u) → q2'
  33. Circle(I, Distance[I, A], f) → q
  34. Point(f) → S
  35. Segment(A, I) → i
  36. Segment(I, S) → j
  37. Cylinder(q, (-Distance[I, S])) → l, t, m
  38. IntersectPath(p', l) → k

AI Drawing Prompt Reference

Draw a cylinder and use an interactive plane to cut it, showing the changing shape of the cross-section. Start by constructing the cylinder, then create a circle that includes the midpoint of the cylinder. Generate another auxiliary circle through mirroring and rotation. Define a plane and find its intersection with the cylinder to determine the cutting position. Finally, translate the plane along a specific direction to observe the cutting effect.
The prompt above was compiled from the original drawing commands and is for reference only.