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Rotation List Demonstration

Rotation List Demonstration
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2016-04-15 05:38
FunctionSequenceGeometric Construction
This example demonstrates the dynamic process of generating a series of shapes through rotation operations. It involves core mathematical concepts such as rotation, natural numbers, logarithmic functions, pie charts/circle charts, linear functions, and fractal geometry. The construction highlights the use of GeoGebra commands and objects like Sequence, Element, CurveCartesian, Segment, and Angle. Suitable for high school and above, it aids in understanding transformations, parametrization, and data visualization in mathematics.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[CurveCartesian[sin((i * t)) + sin(((sgn(i - j) * j) * t)) + sin((n * t)) + (6 * i), cos((i * t)) + cos(((sgn(i - j) * j) * t)) + cos((n * t)) + (6 * j), t, 0, (2 * π)], i, 1, 12], j, 1, 12) → liste1
  2. Element(liste1, jj, ii) → a
  3. CurveCartesian(sin((ii * t)) + sin(((sgn(ii - jj) * jj) * t)) + sin((n * t)), cos((ii * t)) + cos(((sgn(ii - jj) * jj) * t)) + cos((n * t)), t, 0, (2 * π)) → b
  4. Segment(O, A) → c
  5. Segment(A, B) → d
  6. Segment(B, C) → e
  7. Angle(A, O, O + (0, 1)) → β
  8. Angle(B, A, A + (0, 1)) → γ
  9. Angle(C, B, B + (0, 1)) → δ