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Translate Dots Pattern

Translate Dots Pattern
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2014-08-03 22:52
VectorSequence
In collections Symmetry, Transformation and Tessellation
This example demonstrates the creation of geometric patterns through repeated translations of points. It involves core mathematical concepts like vectors, sequences, and geometric transformations. The construction utilizes GeoGebra commands and objects such as Vector, Sequence, and Translate. It is suitable for high school mathematics education, helping students understand geometric transformations and the generation of spatial figures.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(C, D) → v
  3. Sequence(Translate[Sequence[Translate[E, Vector[(n * u)]], n, -5, 5], Vector[(m * v)]], m, -5, 5) → pattern
  4. Sequence(Translate[F, Vector[(n * u)]], n, -5, 5) → dots
  5. Translate(dots, v) → dots1
  6. Translate(dots, Vector[(2 * v)]) → dots2
  7. Translate(dots, Vector[(3 * v)]) → dots3
  8. Translate(dots, Vector[(4 * v)]) → dots4
  9. Translate(dots, Vector[(5 * v)]) → dots5
  10. Translate(dots, Vector[(-v)]) → dots1'
  11. Translate(dots, Vector[((-2) * v)]) → dots2'
  12. Translate(dots, Vector[((-3) * v)]) → dots3'
  13. Translate(dots, Vector[((-4) * v)]) → dots4'
  14. Translate(dots, Vector[((-5) * v)]) → dots5'