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Modular Arithmetic Rolling Demonstration

Modular Arithmetic Rolling Demonstration
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2015-03-24 01:49
VectorFunctionTransformation
This example demonstrates the application of modular arithmetic in geometric shapes. Key mathematical concepts include modular arithmetic and vectors. Using GeoGebra commands such as Intersect, Circle, Sequence, Vector, Translate, and Rotate, the example dynamically shows how modular arithmetic affects the transformation of shapes. Suitable for students in middle school and above to learn geometric transformations and modular arithmetic.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → B
  2. Circle(A, B) → c
  3. Sequence(((r * cos(((-π)) / 2 + (((2 * π) * k)) / Modulus)), r + (r * sin(((-π)) / 2 + (((2 * π) * k)) / Modulus))), k, 0, Modulus - 1) → list1
  4. Vector(B, C) → u
  5. Translate(A, Vector[(s * u)]) → A'
  6. Translate(Rotate[list1, (((2 * π) * s)) / Modulus, A'], Vector[(s * u)]) → list2
  7. Rotate(list1, (((2 * π) * s)) / Modulus, A') → list1'
  8. Rotate(Element[Sequence[(x(A') + (r * cos(((-π)) / 2 + (((2 * π) * k)) / Modulus)), r + (r * sin(((-π)) / 2 + (((2 * π) * k)) / Modulus))), k, 0, Modulus - 1], 1], (((2 * π) * s)) / Modulus, A) → E
  9. Rotate(Element[Sequence[((r * cos(((-π)) / 2 + (((2 * π) * k)) / Modulus)), r + (r * sin(((-π)) / 2 + (((2 * π) * k)) / Modulus))), k, 0, Modulus - 1], 1], (((2 * π) * s)) / Modulus, A) → D
  10. Sequence(Rotate[Element[Sequence[((r * cos(((-1.5) * π) + (((2 * π) * k)) / Modulus)), r - (r * sin(((-1.5) * π) + (((2 * π) * k)) / Modulus))), k, 0, Modulus - 1], l], ((-(((2 * π) * s)))) / Modulus, A], l, 1, Modulus) → list3
  11. Sequence(Element[y(list3), k], k, 1, Modulus) → yPts
  12. Sequence((Element[xPts, k], Element[yPts, k]), k, 1, Length[xPts]) → Pts
  13. Element(Pts, 1) → F
  14. Circle(A', F) → d
  15. Sequence(Text[k - 1, Element[Pts, Modulus - k + 2]], k, 1, Modulus) → list4