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Rotating Spotlight on Stage Edge Illumination Ratio

Rotating Spotlight on Stage Edge Illumination Ratio
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2013-04-24 19:14
CircleAngleProbability & StatisticsGeometric ConstructionSlider Animation
This example demonstrates the proportion of the dark circular edge of a stage that is lit up by a rotating spotlight on its rim. It involves core math concepts like angles, circles, rotation, statistical characteristics, and rational numbers. The construction uses GeoGebra commands: Circle, Point, Rotate, Line, Intersect, CircleSector, and CircleArc. It is suitable for middle school and above students to learn geometric constructions and probability & statistics, focusing on rotation and area ratio relationships.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Circle(C, 30) → d
  4. Point(d) → H
  5. Rotate(H, β, C) → H'
  6. Line(H', C) → a
  7. Rotate(a, α, C) → a'
  8. Intersect(d, a', 1) → D
  9. Intersect(d, a, 2) → E
  10. Intersect(d, a', 2) → F
  11. CircleSector(C, H', D) → e
  12. CircleSector(C, E, F) → f
  13. Intersect(c, a, 2) → G
  14. Rotate(G, (2 * α), A) → G'
  15. CircleArc(A, G, G') → g
  16. CircleArc(A, G', G) → h
  17. CircleSector(C, D, E) → k
  18. CircleSector(C, F, H') → p

AI Drawing Prompt Reference

Draw a circle c, then take a point C on it, draw another circle d with C as the center and a radius of 30, take a point H on d, rotate H around C, then draw a line a through H and C, rotate a around C to get a', find the intersection points D, E, and F of a', a, and d, draw two sectors e and f with H' and D as the starting points and E and F as the endpoints, find the intersection point G of a and c, rotate G around C to get G', draw two arcs g and h with A as the starting point and G and G' as the endpoints, and finally draw two sectors k and p.
The prompt above was compiled from the original drawing commands and is for reference only.