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Lampshade Designer

Lampshade Designer
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2018-01-22 10:49
TrigonometrySolid GeometryGeometric Construction
This example demonstrates how to generate the geometric shape of a lampshade by rotating a cone. It involves core mathematical concepts such as cones, cylinders, solid geometry, conditional probability, and expected value. The construction uses GeoGebra commands/objects like Intersect, Point, Segment, Circle, Ray, Rotate, CircleArc, and Angle. Suitable for high school and above students to learn and understand the construction of three-dimensional shapes and their related mathematical principles.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(Circle[A, botrad]) → B
  3. Segment(A, B) → f
  4. Circle(A, height) → c
  5. Intersect(c, yAxis, 2) → C
  6. Point(Circle[C, toprad]) → D
  7. Segment(C, D) → g
  8. Ray(B, D) → h
  9. Segment(B, D) → i
  10. Intersect(h, yAxis) → E
  11. Circle(E, A) → d
  12. Point(d) → F
  13. Rotate(F, α, E) → F'
  14. Rotate(F, (-α), E) → F'_1
  15. CircleArc(E, F'_1, F') → e
  16. Segment(E, F'_1) → j
  17. Segment(E, F') → k
  18. Circle(E, inrad) → p
  19. Intersect(p, j, 1) → H
  20. Intersect(p, k, 1) → I
  21. Angle(F'_1, E, F') → β
  22. Rotate(F'_1, γ, E) → G
  23. Rotate(G, γ, E) → G'
  24. Segment(E, G) → l
  25. Segment(E, G') → m
  26. Intersect(p, l, 1) → J
  27. Intersect(p, m, 1) → K
  28. Rotate(F'_1, -2°, E) → L
  29. Segment(C, A) → n

AI Drawing Prompt Reference

Draw the geometric shape of a lampshade by rotating a cone. Start by marking the intersection of the x-axis and y-axis as point A, then draw a circle centered at A, intersecting the y-axis at point B and connecting AB. Next, draw a circle centered at A with the height as the radius, intersecting the y-axis at point C, and draw a circle centered at C, intersecting the y-axis at point D and connecting CD. Draw a ray h from B through D, and line segment BD. Find the intersection of h with the y-axis at point E, then draw a circle centered at E with the inner radius, intersecting the arc at H and I. Calculate the angle between F' and E, rotate F' to get G and G', and connect E to G and G'. Finally, rotate F'_1 to get point L, and connect C to A.
The prompt above was compiled from the original drawing commands and is for reference only.