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Matha'art: Trigonometric Curves

Matha'art: Trigonometric Curves
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2020-03-06 04:52
TrigonometryCoordinate GeometryParametric Equation
This example demonstrates how to create aesthetically pleasing parametric curves using trigonometric functions. Key math concepts include parametric equations, trigonometry, and coordinate geometry. Construction highlights involve using commands like CurveCartesian for Cartesian curves, TableText and Sequence for data tables, and Segment for line segments, along with variables A, B, b, c, a, C, etc. Suitable for high school and above, focusing on understanding parametric equations and function graphing techniques.

GeoGebra Commands & Parameters

  1. CurveCartesian(x(A) + cos((b * t)) + cos((c * t))^(3), y(A) + sin((b * t)) + sin((c * t))^(3), t, 0, 6.28319) → a
  2. TableText({{"x(t)=cos(" + (If[b > 1, "" + b, ""]) + "t)+cos(" + (If[c > 1, "" + c, ""]) + "t)³"}, {"y(t)=cos(" + (If[b > 1, "" + b, ""]) + "t)+cos(" + (If[c > 1, "" + c, ""]) + "t)³"}}, "l") → texte2
  3. Sequence(Text[i, A + ((4.5 * i), 3.25)], i, 1, 6) → liste9
  4. Segment(A - (2, -2.5), A + (34, 2.5)) → e
  5. Sequence(Text[i, A + (0, 4.5 - (4.5 * i))], i, 1, 5) → liste10
  6. Segment(A + (1.75, 5), A + (1.75, -26)) → f
  7. Sequence(CurveCartesian[x(A) + (4.5 * j) + cos((j * i)) + cos(i)^(3), y(A) + sin((j * i)) + sin(i)^(3), i, 0, t], j, 1, 6) → liste1
  8. Sequence(CurveCartesian[x(A) + (4.5 * j) + cos((j * i)) + cos((2 * i))^(3), y(A) - 4.5 + sin((j * i)) + sin((2 * i))^(3), i, 0, t], j, 1, 6) → liste2
  9. Sequence(CurveCartesian[x(A) + (4.5 * j) + cos((j * i)) + cos((3 * i))^(3), y(A) - 9 + sin((j * i)) + sin((3 * i))^(3), i, 0, t], j, 1, 6) → liste3
  10. Sequence(CurveCartesian[x(A) + (4.5 * j) + cos((j * i)) + cos((4 * i))^(3), y(A) - 13.5 + sin((j * i)) + sin((4 * i))^(3), i, 0, t], j, 1, 6) → liste4
  11. Sequence(CurveCartesian[x(A) + (4.5 * j) + cos((j * i)) + cos((5 * i))^(3), y(A) - 18 + sin((j * i)) + sin((5 * i))^(3), i, 0, t], j, 1, 6) → liste5
  12. Sequence(CurveCartesian[x(A) + 31.5 + cos((b * i)) + cos((j * i))^(3), y(A) + 4.5 - (4.5 * j) + sin((b * i)) + sin((j * i))^(3), i, 0, t], j, 1, 5) → liste7
  13. Sequence(CurveCartesian[x(A) + (4.5 * j) + cos((c * i)) + cos((6 * i))^(3), y(A) - 22.5 + sin((j * i)) + sin((c * i))^(3), i, 0, t], j, 1, 6) → liste8
  14. CurveCartesian(x(C) + cos((b * i)) + cos((c * i))^(3), y(C) + sin((b * i)) + sin((c * i))^(3), i, 0, t) → d

AI Drawing Prompt Reference

Create a grid of parametric curves generated by trigonometric functions. Starting near the origin, arrange six groups horizontally, each with a main curve and five variations, forming symmetric wave patterns. Stack five groups vertically, each with six curves, creating a rectangular array. To the right, draw a single large curve, and below, another curve. All curves use combinations of cosine and sine powers, resembling petals or spirals. Add coordinate axes with tick labels, boundary segments, and numeric labels near intersections.
The prompt above was compiled from the original drawing commands and is for reference only.