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Circle on the 45 Degree Cone

Circle on the 45 Degree Cone
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2019-05-01 05:52
CircleCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric properties of a circle formed on the surface of a 45-degree cone. It involves core mathematical concepts such as cones, circles, linear equations, real numbers, right triangles, median lines, and translations. The construction utilizes GeoGebra commands and objects like Intersect, Circle, Line, Rotate, CircleSector, Point, and Segment. It is suitable for high school students studying solid geometry and analytical geometry, helping them understand the generation and properties of spatial geometric figures.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B_1) → c
  3. Intersect(c, yAxis, 2) → C
  4. Intersect(c, yAxis, 1) → D
  5. Intersect(c, xAxis, 1) → E
  6. Line(F, D) → f
  7. Line(E, B_1) → g
  8. Rotate(f, 45°, (0, 0)) → f'
  9. Rotate(g, 45°, (0, 0)) → g'
  10. Intersect(c, g', 2) → G
  11. CircleSector(A, B_1, G) → d
  12. CircleSector(A, G, C) → e
  13. Intersect(c, f', 1) → H
  14. CircleSector(A, C, H) → h
  15. CircleSector(A, H, E) → k
  16. Intersect(c, g', 1) → I
  17. CircleSector(A, E, I) → p
  18. CircleSector(A, I, D) → q
  19. Intersect(c, f', 2) → J
  20. CircleSector(A, D, J) → r
  21. CircleSector(A, J, B_1) → s
  22. Intersect(d, k) → K, , ,
  23. Point(e) → L
  24. Point(q) → M
  25. Segment(L, M) → i
  26. Point(k) → N
  27. Point(s) → O
  28. Segment(N, O) → j
  29. Point(h) → P
  30. Point(r) → Q
  31. Segment(P, Q) → l
  32. Point(p) → R
  33. Point(s) → S
  34. Segment(R, S) → m
  35. Point(e) → T
  36. Circle(A, T) → t
  37. Circle(B, U) → c_1
  38. Rotate(c_1, 45°, A) → d_1
  39. Rotate(c_1, 90°, A) → e_1
  40. Rotate(c_1, 135°, A) → f_1
  41. Rotate(c_1, 180°, A) → g_1
  42. Rotate(c_1, 225°, A) → h_1
  43. Rotate(c_1, 225°, A) → k_1
  44. Rotate(c_1, 270°, A) → p_1
  45. Rotate(c_1, 315°, A) → q_1

AI Drawing Prompt Reference

Draw a circle on a 45-degree cone. Start by creating the intersection point A of the x-axis and y-axis, then draw a circle c with A and B1 as centers. Find the intersection points C and D of circle c with the y-axis, and E with the x-axis. Use rotation and intersection operations to generate multiple arcs and segments, ultimately forming a complete circle.
The prompt above was compiled from the original drawing commands and is for reference only.