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Cutting a Cone with an Interactive Plane

Cutting a Cone with an Interactive Plane
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2020-04-13 18:35
Solid GeometryGeometric Construction
This example demonstrates the process of slicing a cone with an interactive plane to observe the changing shape of the cross-section. It involves core mathematical concepts such as solid geometry, cross-sectional geometry, linear regression, and median values. The construction utilizes GeoGebra commands and objects like Point, Line, Circle, Plane, Cone, and Intersect. It is suitable for high school and above students learning spatial geometry and cross-sectional analysis.

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. Cone(q, (-Distance[I, S])) → n, r, o
  36. IntersectPath(p', n) → k
  37. IntersectPath(p', n) → s
  38. Segment(A, I) → i
  39. Segment(I, S) → j

AI Drawing Prompt Reference

Draw a cone and slice it with an interactive plane to observe the changing shape of the cross-section. Start by creating a circle and two points, then construct a cube using these points as vertices. Find the midpoints of the circle and the cube's diagonals, and connect them to form a line. Draw two concentric circles centered at the midpoint. Locate the intersection points of these circles and use them to create a plane. Finally, move the plane along a specific direction to see the cross-section of the cone after slicing.
The prompt above was compiled from the original drawing commands and is for reference only.