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Nautile Spiral

Nautile Spiral
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2020-07-22 18:45
FunctionTrigonometryCoordinate GeometryProbability & StatisticsParametric Equation
This example demonstrates the construction and properties of the Nautile spiral curve. It involves core mathematical concepts such as parametric equations, coordinate geometry, and probability & statistics (normal distribution). Key GeoGebra commands used include CurveCartesian, Angle, Distance, and Fit. Suitable for high school students and math enthusiasts learning geometric representations of parametric curves and probability distributions.

GeoGebra Commands & Parameters

  1. CurveCartesian((r(t) * cos(t)), (r(t) * sin(t)), t, -20, 10) → a
  2. Angle((1, 0), C, A1) → B1
  3. Distance(C, A1) → C1
  4. Distance(C, A2) → C2
  5. Distance(C, A3) → C3
  6. Distance(C, A4) → C4
  7. Distance(C, A5) → C5
  8. Distance(C, A6) → C6
  9. Distance(C, A7) → C7
  10. Distance(C, A8) → C8
  11. Distance(C, A9) → C9
  12. Distance(C, A10) → C10
  13. Distance(C, A11) → C11
  14. Distance(C, A12) → C12
  15. Distance(C, A13) → C13
  16. Distance(C, A14) → C14
  17. Distance(C, A15) → C15
  18. Distance(C, A16) → C16
  19. Distance(C, A17) → C17
  20. Distance(C, A18) → C18
  21. Distance(C, A19) → C19
  22. Distance(C, A20) → C20
  23. Distance(C, A21) → C21
  24. Distance(C, A22) → C22
  25. Distance(C, A23) → C23
  26. Distance(C, A24) → C24
  27. Distance(C, A25) → C25
  28. Distance(C, A26) → C26
  29. Distance(C, A27) → C27
  30. Distance(C, A28) → C28
  31. Distance(C, A29) → C29
  32. Distance(C, A30) → C30
  33. Distance(C, A31) → C31
  34. Distance(C, A32) → C32
  35. Distance(C, A33) → C33
  36. Distance(C, A34) → C34
  37. Distance(C, A35) → C35
  38. Distance(C, A36) → C36
  39. Distance(C, A37) → C37
  40. Distance(C, A38) → C38
  41. Distance(C, A39) → C39
  42. Distance(C, A40) → C40
  43. Distance(C, A41) → C41
  44. Distance(C, A42) → C42
  45. Distance(C, A43) → C43
  46. Distance(C, A44) → C44
  47. Distance(C, A45) → C45
  48. Distance(C, A46) → C46
  49. Distance(C, A47) → C47
  50. Distance(C, A48) → C48
  51. Distance(C, A49) → C49
  52. Distance(C, A50) → C50
  53. Fit(D4:D50, {1, x}) → f
  54. CurveCartesian((ℯ^(f(t)) * cos(t)), (ℯ^(f(t)) * sin(t)), t, 8, 30) → b

AI Drawing Prompt Reference

Draw a nautilus spiral curve defined by a parametric equation where the radius is a function of the angle, with the angle ranging from -20 to 10. Place a fixed center point and mark a series of points along the curve. Measure and display the distances from the center to each of these points, and also show an angle formed by the center, a reference point, and the curve's starting point. The distances should vary progressively along the spiral, suggesting a pattern that can be fitted to a normal distribution. The illustration should clearly show the spiral's expanding coils, the center, the measurement segments, and the angle marker, combining geometric and statistical elements.
The prompt above was compiled from the original drawing commands and is for reference only.