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GeoGebra Interactive Bubbles

GeoGebra Interactive Bubbles
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2022-06-03 02:35
CircleVectorTrigonometryProbability & StatisticsGeometric Construction
This example demonstrates dynamic bubbles in 2D space, simulating a screensaver effect through mathematical calculations. Core math concepts include 2D vectors, angles, geometric reflection, trigonometry, random variables, and probability & statistics. Construction highlights use of GeoGebra commands like Corner, Polygon, PointIn, Sum, Circle, with objects such as r, r1, E1-E4, pol, f-g-h-i, t, A1-A6, v1-v20 for simulating bubble motion and collisions. Suitable for high school and above students learning vectors, geometry, probability & statistics, or for mathematical demonstrations and teaching.

GeoGebra Commands & Parameters

  1. Corner(1) → E1
  2. Corner(2) → E2
  3. Corner(3) → E3
  4. Corner(4) → E4
  5. Polygon(E1 + (r1, r1), E2 + ((-r1), r1), E3 - (r1, r1), E4 + (r1, (-r1))) → pol, f, g, h, i
  6. PointIn(pol) → A1
  7. PointIn(pol) → A2
  8. PointIn(pol) → A3
  9. PointIn(pol) → A4
  10. PointIn(pol) → A5
  11. PointIn(pol) → A6
  12. PointIn(pol) → A7
  13. PointIn(pol) → A8
  14. PointIn(pol) → A9
  15. PointIn(pol) → A10
  16. PointIn(pol) → A11
  17. PointIn(pol) → A12
  18. PointIn(pol) → A13
  19. PointIn(pol) → A14
  20. PointIn(pol) → A15
  21. PointIn(pol) → A16
  22. PointIn(pol) → A17
  23. PointIn(pol) → A18
  24. PointIn(pol) → A19
  25. PointIn(pol) → A20
  26. Sum(enerLista, n) → energía
  27. Circle(A1, r2) → B1
  28. Circle(A3, r2) → B3
  29. Circle(A4, r2) → B4
  30. Circle(A5, r2) → B5
  31. Circle(A6, r2) → B6
  32. Circle(A7, r2) → B7
  33. Circle(A8, r2) → B8
  34. Circle(A2, r2) → B2
  35. Circle(A9, r2) → B9
  36. Circle(A10, r2) → B10
  37. Circle(A11, r2) → B11
  38. Circle(A12, r2) → B12
  39. Circle(A13, r2) → B13
  40. Circle(A14, r2) → B14
  41. Circle(A15, r2) → B15
  42. Circle(A16, r2) → B16
  43. Circle(A17, r2) → B17
  44. Circle(A18, r2) → B18
  45. Circle(A19, r2) → B19
  46. Circle(A20, r2) → B20

AI Drawing Prompt Reference

Create a dynamic bubble cluster consisting of 20 randomly distributed points inside a square. Each point represents a bubble, forming a circle with radius r2 around each point. The square's four corners are E1 to E4, connected to form a square. Then, randomly generate 20 points inside the square, and draw a circle with radius r2 around each point to simulate bubbles.
The prompt above was compiled from the original drawing commands and is for reference only.