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Hélio Oiticica GeoGebra Example

Hélio Oiticica GeoGebra Example
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2017-04-10 09:15
VectorSequenceCoordinate Geometry
This example demonstrates geometric shapes and mathematical principles in the artworks of Brazilian artist Hélio Oiticica using GeoGebra. It involves core math concepts like vectors, sequences, coordinate geometry, and geometric construction. Key GeoGebra commands and objects used include Point, Join, Sequence, Textfield, and Length. Suitable for high school and above students exploring the intersection of art and mathematics.

GeoGebra Commands & Parameters

  1. Point(Segment[A, D]) → H10
  2. Point(Segment[A, D]) → H9
  3. Point(Segment[A, D]) → H8
  4. Point(Segment[A, D]) → H7
  5. Point(Segment[A, D]) → H6
  6. Point(Segment[A, D]) → H5
  7. Point(Segment[A, D]) → H4
  8. Point(Segment[A, D]) → H3
  9. Point(Segment[A, D]) → H2
  10. Point(Segment[A, D]) → H1
  11. Point(Segment[A, C]) → W1
  12. Point(Segment[A, C]) → W2
  13. Point(Segment[A, C]) → W3
  14. Point(Segment[A, C]) → W4
  15. Point(Segment[A, C]) → W5
  16. Point(Segment[A, C]) → W6
  17. Point(Segment[A, C]) → W7
  18. Point(Segment[A, C]) → W8
  19. Point(Segment[A, C]) → W9
  20. Point(Segment[A, C]) → W10
  21. Join({{A}, Sort[First[{W1, W2, W3, W4, W5, W6, W7, W8, W9, W10}, N - 1]], {C}}) → list6
  22. Sequence(x(Midpoint[Element[list6, i], Element[list6, i + 1]]), i, 1, N) → xcenters
  23. Join({{A}, Sort[First[{H1, H2, H3, H4, H5, H6, H7, H8, H9, H10}, M - 1]], {D}}) → list7
  24. Sequence(y(Midpoint[Element[list7, i], Element[list7, i + 1]]), i, 1, M) → ycenters
  25. Sequence(Random[0, 360]°, i, 1, (M * N)) → list2
  26. Sequence(Random[0, (t * 100)] / 100, i, 1, (M * N)) → list3
  27. Join(Sequence[Sequence[(Element[xcenters, i], Element[ycenters, j]), i, 1, N], j, 1, M]) → list4
  28. Sequence(shrink - 0.1 + Random[0, 100] / 1000, i, 1, (M * N)) → list1
  29. Textfield(N) → InputBox1
  30. Textfield(M) → InputBox2
  31. Textfield(t) → InputBox3
  32. Textfield(shrink) → InputBox4
  33. Textfield(d) → InputBox5
  34. Sequence(x(Element[list6, i + 1]) - x(Element[list6, i]), i, 1, N) → xslist
  35. Sequence(y(Element[list7, i + 1]) - y(Element[list7, i]), i, 1, M) → yslist
  36. Length(yslist) → b
  37. Sequence(rct[Element[list4, i], Element[xslist, Mod[i - 1, N] + 1], Element[yslist, floor((i - 0.1) / N) + 1], Element[list1, i], Element[list3, i], Element[list2, i], dlt], i, 1, (N * M)) → list5