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Segmented Bird

Segmented Bird
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2020-05-21 15:45
CircleFunctionSequenceCalculusParametric Equation
This example demonstrates the creation of a bird-like figure composed of segmented parametric curves. It involves core mathematical concepts such as parametric equations, incircle or inscribed circle, quadratic functions, and integral calculus. The construction utilizes GeoGebra commands like Sequence and Rotate, along with objects like a, dx, l1, l2, l3, l4, l2b, lseg1, c, lseg1', l1c, l2c, lseg2, lseg2', l5, A, B, l6, Speed, C, texte2, texte1, D, E, and image1. It is suitable for high school and above students to learn about parametric curves, geometric transformations, and applications of calculus.

GeoGebra Commands & Parameters

  1. Sequence(((3 * sin(((2 * π) * i / 2000))^(3)), (-cos(((8 * π) * i / 2000)))), i, 870, 1130, dx) → l1
  2. Sequence(((3 / 2 * sin(((2 * π) * i / 2000))^(3)), (-1 / 2 * cos(((6 * π) * i / 2000)))), i, 850, 1150, dx) → l2
  3. Sequence(Segment[Element[l1, i], Element[l2, i]], i, 1, Length[l1]) → l3
  4. Sequence(((3 * sin(((2 * π) * i / 2000))^(3)), (-cos(((8 * π) * i / 2000)))), i, 0, 950, dx) → l4
  5. Sequence(((3 / 2 * sin(((2 * π) * i / 2000))^(3)), (-1 / 2 * cos(((6 * π) * i / 2000)))), i, 0, 850, dx) → l2b
  6. Sequence(Segment[Element[l4, i], Element[l2b, i]], i, 1, Length[l4]) → lseg1
  7. Rotate(lseg1, c, yAxis) → lseg1'
  8. Sequence(((3 * sin(((2 * π) * i / 2000))^(3)), (-cos(((8 * π) * i / 2000)))), i, 1050, 2000, dx) → l1c
  9. Sequence(((3 / 2 * sin(((2 * π) * i / 2000))^(3)), (-1 / 2 * cos(((6 * π) * i / 2000)))), i, 1150, 2000, dx) → l2c
  10. Sequence(Segment[Element[l1c, i], Element[l2c, i]], i, 1, Length[l1c]) → lseg2
  11. Rotate(lseg2, (-c), yAxis) → lseg2'
  12. Sequence(Segment[Element[l1, i], Element[l2, i]], i, 1, Length[l2]) → l5
  13. Sequence(Translate[B, Vector[(i * Vector[B, A])]], i, 0, 1, 1 / Length[l1]) → l6