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Math'art

Math'art
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2020-03-05 02:51
FunctionCoordinate GeometryProbability & Statistics
This example demonstrates the creation of artistic patterns through mathematical functions and geometric constructions. It involves core math concepts like function graphing, coordinate geometry, fractal geometry, and probability & statistics. Key GeoGebra commands and objects used include Function, CurveCartesian, Sequence, and Line, as outlined in the construction summary. Suitable for high school students and math enthusiasts exploring the intersection of math and art.

GeoGebra Commands & Parameters

  1. Function((4 * cos((2 * x))), 0, theta) → r_1
  2. CurveCartesian((a * sin(t)^(3)), (a * cos(t)^(3)), t, 0, theta) → o
  3. Sequence((x(A) + (a * sin(t)^(3)), y(A) + (a * cos(t)^(3)) + z(A)), t, 0, theta, 1 / n) → liste1
  4. Sequence(Circle[Element[liste1, i], r], i, 1, Length[liste1]) → liste2
  5. Sequence((x(B) + ((cos((2 * t)) * a) * cos(t)), y(B) + ((cos((2 * t)) * b) * sin(t))), t, 0, theta, 1 / n) → liste3
  6. Sequence(Circle[Element[liste3, i], r], i, 1, Length[liste3]) → liste4
  7. Sequence((x(C) + (a / 3 * ((2 * cos(t)) + cos((m * t)))), y(C) + (a / 3 * ((2 * sin(t)) - sin((m * t))))), t, 0, theta, 1 / n) → liste5
  8. Sequence(Circle[Element[liste5, i], r], i, 1, Length[liste5]) → liste6
  9. Sequence((x(D) + ((a / 10 * t) * cos(t)), y(D) + ((a / 10 * t) * sin(t))), t, 0, (1.5 * theta), 2 / n) → liste7
  10. Sequence(Circle[Element[liste7, i], r], i, 1, Length[liste7]) → liste8
  11. Sequence((x(E) + ((a * cos(t)) * cos((2 * t))), y(E) + ((a * sin(t)) * (1.1 + cos((2 * t))))), t, 0, theta, 1 / n) → liste9
  12. Sequence(Circle[Element[liste9, i], r], i, 1, Length[liste9]) → liste10
  13. Sequence(Segment[Element[liste5, i], Element[liste5, i + 1]], i, 1, Length[liste5]) → liste11
  14. Sequence(Segment[Element[liste1, i], Element[liste1, i + 1]], i, 1, Length[liste1]) → liste12
  15. Sequence(Segment[Element[liste3, i], Element[liste3, i + 1]], i, 1, Length[liste3]) → liste13
  16. Sequence(Segment[Element[liste9, i], Element[liste9, i + 1]], i, 1, Length[liste9]) → liste14
  17. Sequence(Segment[Element[liste7, i], Element[liste7, i + 1]], i, 1, Length[liste7]) → liste15
  18. CurveCartesian(x(F) + cos(t) + (0.5 * cos((7 * t))) + (1 / 3 * cos((-17 * t) + 3.142 / 2)), y(F) + sin(t) + (0.5 * sin((7 * t))) + (1 / 3 * sin((-17 * t) + 3.142 / 2)), t, 0, theta) → c
  19. Sequence((x(F) + (1.75 * cos(t)) + cos((5 * t)) + (1 / 6 * cos((-7 * t) + 3.142 / 2)), y(F) + (1.75 * sin(t)) + sin((5 * t)) + (1 / 6 * sin((-7 * t) + 3.142 / 2))), t, 0, theta, 1 / n) → liste16
  20. Sequence(Circle[Element[liste16, i], r], i, 1, Length[liste16]) → liste17
  21. Line(G, H) → d
  22. Line(I, yAxis) → e
  23. Line(J, yAxis) → f

AI Drawing Prompt Reference

Create an artistic pattern using mathematical functions and geometric constructions. Start with a cosine function curve and a heart-shaped curve. Then generate a series of circles based on these curves and arrange them according to specific rules. Finally, connect adjacent circles with lines to form a complex geometric structure, showcasing the intersection of math and art.
The prompt above was compiled from the original drawing commands and is for reference only.