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Crystallography

Crystallography
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2016-02-22 10:09
CirclePolygonFunctionInequality
This example demonstrates crystallography focusing on symmetry and geometric constructions. It involves core math concepts like polygons, symmetry, functions, unit circle, inequalities, and angles. The construction uses GeoGebra commands: Sequence, Distance, Dilate, Element, Point, Rotate; objects include B, M, vang, N, A, list1, list3, edge, E, list2, D, D', E', list4, list6, list6', a, b, button1. Suitable for high school students and educators.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[B, ((i * 360) * ° / N), A], i, 1, N + 1) → list1
  2. Sequence(sidevx[Element[list1, i + 1], Element[list1, i], vang], i, 1, N) → list3
  3. Distance(Element[list1, 1], Element[list3, 1]) → edge
  4. Dilate(Element[list3, 1], 1 + edge / Length[Vector[A, Element[list3, 1]]], A) → E
  5. Sequence(diamond[Element[list1, i], Element[list1, i + 1], vang], i, 1, N) → list2
  6. Element(list3, 1) → D
  7. Point(Ray[D, (2 * D) - A]) → D'
  8. Point(Ray[E, (2 * E) - A]) → E'
  9. Sequence(Rotate[Translate[Sequence[Rotate[Element[list2, 1], ((j * 360) * ° / M), D], j, 1, M], Vector[D, D']], ((i * 360) * ° / N), A], i, 1, N) → list4
  10. Sequence(Mirror[list4, Rotate[E', ((i * 360) * ° / N), A]], i, 0, N - 1) → list6
  11. Rotate(list6, (180 * ° / N), A) → list6'