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Polar Coordinates Random Test

Polar Coordinates Random Test
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2014-03-13 12:28
VectorCoordinate Geometry
This example demonstrates a random test in the polar coordinate system. Key mathematical concepts include polar coordinates, vectors, and random number generation. Using GeoGebra commands such as Random, SelectedElement, and RandomElement, a series of random polar coordinate graphics are constructed. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Random(1, R) → r
  2. SelectedElement(listAngle) → angle
  3. RandomElement(Sequence[i, i, 0*°, 359*°, angle]) → theta
  4. CountIf(x > 0, TextToUnicode[text_r]) → n_{textr}
  5. Reverse(TextToUnicode[text_r]) → listreverse_{textr}
  6. Sequence((Element[listreverse_{textr}, i] - 48) * 10^(i - 1), i, 1, n_{textr}) → listdigit_r
  7. Sum(listdigit_r) → r'
  8. CountIf(x > 0, TextToUnicode[text_θ]) → n_{textθ}
  9. If(n_{textr} * n_{textθ} ≟ 0, true, false) → empty
  10. Reverse(TextToUnicode[text_θ]) → listreverse_{textθ}
  11. Sequence((Element[listreverse_{textθ}, i] - 48) * 10^(i - 1), i, 1, n_{textθ}) → listdigit_θ
  12. Sum(listdigit_θ) → theta'
  13. Sequence(Circle[(0, 0), r], r, 1, R) → listCircle
  14. Text("90°", (-0.3, R + 0.5)) → text2
  15. Vector((R + 1, 0)) → u
  16. Text("180°", (-R - 1.8, -0.2)) → text3
  17. Text("0°", (R + 1.2, -0.2)) → text1
  18. Text("270°", (-0.5, -R - 1.2)) → text4
  19. Sequence(Text[r, (r - 0.2, -0.7)], r, 1, R) → listTextAxis
  20. Sequence(Text[(theta / π * 180)°, ((R + 0.5) * cos(theta), (R + 0.5) * sin(theta))], theta, angle, 89*°, angle) → listTextQ1
  21. Sequence(Text[(theta / π * 180)°, ((R + 0.4) * cos(theta) - 1, (R + 0.4) * sin(theta))], theta, 90° + angle, 179*°, angle) → listTextQ2
  22. Sequence(Text[(theta / π * 180)°, ((R + 0.4) * cos(theta) - 1, (R + 0.4) * sin(theta) - 0.6)], theta, 180° + angle, 269*°, angle) → listTextQ3
  23. Sequence(Text[(theta / π * 180)°, ((R + 0.4) * cos(theta), (R + 0.4) * sin(theta) - 0.6)], theta, 270° + angle, 359*°, angle) → listTextQ4
  24. Sequence(Segment[(0, 0), (R * cos(theta), R * sin(theta))], theta, 0*°, 360*°, angle) → listRadiusThick
  25. Textfield(text_r) → inputBox1
  26. Textfield(text_θ) → inputBox2

AI Drawing Prompt Reference

Draw a series of randomly generated polar coordinate graphics in the polar coordinate system to demonstrate key mathematical concepts like vectors and random number generation. Include concentric circles, angle markers (0°, 90°, 180°, 270°), axis labels, and random polar coordinate points, with their polar radii and angles calculated and displayed.
The prompt above was compiled from the original drawing commands and is for reference only.