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Kries Mo GeoGebra Interpretation

Kries Mo GeoGebra Interpretation
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2015-03-11 10:41
TriangleCircleSequenceCalculusProbability & Statistics
This example demonstrates a mathematical interpretation of the painting Kries Mo by Manfred Kuttner using GeoGebra, involving concepts like rotation, triangles, hypergeometric distribution, indefinite integral, pyramid, standard deviation, and limits. It uses commands such as Point, Circle, and Sequence. Suitable for high school students and educators exploring the intersection of mathematics and art.

GeoGebra Commands & Parameters

  1. Point(Ray[A, A + (1, 0)]) → B
  2. Circle(A, B) → c
  3. Point(Ray[B, B + (1, 0)]) → C
  4. Sequence(Circle[A, B + (i * (C - B))], i, 1, N) → list1
  5. Sequence(Sequence[Polygon[Rotate[B + (j * (C - B)), ((i + (j * 0.5)) * trang), A], Rotate[B + (j * (C - B)), ((i + (j * 0.5) + 1) * trang), A], Rotate[C + (j * (C - B)), ((i + (j * 0.5) + 0.5) * trang), A]], i, 0, T - 1], j, 0, N - 1) → list2
  6. Sequence(Random[1, n], i, 1, (N * T)) → list4
  7. Sequence(Sequence[Polygon[Rotate[B + (j * (C - B)), ((i + (j * 0.5) + 1) * trang), A], Rotate[C + (j * (C - B)), ((i + (j * 0.5) + 0.5) * trang), A], Rotate[C + (j * (C - B)), ((i + (j * 0.5) + 1.5) * trang), A]], i, 0, T - 1], j, 0, N - 1) → list3
  8. Sequence(Random[1, n], i, 1, (N * T)) → list6
  9. Sequence(Sequence[Polygon[Rotate[B + (j * (C - B)), (((n * i) + Element[list4, (j * N) + i] + (j * 0.5)) * trang), A], Rotate[B + (j * (C - B)), (((n * i) + Element[list4, (j * N) + i] + (j * 0.5) + 1) * trang), A], Rotate[C + (j * (C - B)), (((n * i) + Element[list4, (j * N) + i] + (j * 0.5) + 0.5) * trang), A]], i, 0, floor(T / n)], j, 0, N - 1) → list5
  10. Sequence(Sequence[Polygon[Rotate[B + (j * (C - B)), (((n * i) + Element[list6, (j * N) + i] + (j * 0.5)) * trang), A], Rotate[B + (j * (C - B)), (((n * i) + Element[list6, (j * N) + i] + (j * 0.5) + 1) * trang), A], Rotate[C + (j * (C - B)), (((n * i) + Element[list6, (j * N) + i] + (j * 0.5) + 0.5) * trang), A]], i, 0, floor(T / n)], j, 0, N - 1) → list7

AI Drawing Prompt Reference

Create a complex pattern of rotating triangles forming a pyramid-like structure around a central point. The pattern is composed of concentric circles and rays emanating from the center, with points of intersection defining the vertices of the triangles. The rotation angles and positions of the triangles are controlled by random numbers, creating a probabilistic distribution effect. The overall structure is both orderly and random.
The prompt above was compiled from the original drawing commands and is for reference only.