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Duchamp's Circles

Duchamp's Circles
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2017-11-18 23:55
CircleVectorOptimizationGeometric Construction
This example demonstrates dynamic circle transformations inspired by Marcel Duchamp's rotational art. It involves core math concepts like circles, translation, random experiments, expected value, 2D vectors, equilateral triangles, and linear programming. Construction highlights include commands like Ray, If, Point, Circle, and Sequence from GeoGebra. Suitable for high school and above mathematics enthusiasts exploring geometric transformations and randomness combined visually.

GeoGebra Commands & Parameters

  1. Ray(C, C + (0, 1)) → h
  2. Ray(A, A + (0, 1)) → g
  3. If(A ≟ C, 0°, Angle[A + (0, -1), A, C]) → α
  4. If(A ≟ C, Vector[(0, 0)], Vector[A, C]) → u
  5. Point(g) → B
  6. Circle(A, B) → c
  7. Sequence(Vector[Rotate[u, (i * α), A]], i, 1, n + 1) → L_1
  8. Point(h) → D
  9. Circle(C, D) → d
  10. Sequence(Vector[Sum[L_1, i]], i, 1, n + 1) → L_2
  11. Circle(C + Element[L_2, n + 1], Radius[d] + ((n + 1) * a)) → e
  12. Sequence(Circle[C + Element[L_2, i], Radius[d] + (i * a)], i, 1, n) → L_3