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Variable Animation of Equilateral Triangles, Squares, and Regular Hexagons Tesse

Variable Animation of Equilateral Triangles, Squares, and Regular Hexagons Tesse
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2017-12-08 04:45
TrianglePolygonTransformationGeometric Construction
This example demonstrates how equilateral triangles, squares, and regular hexagons tessellate on a plane, with a variable animation to show dynamic changes. Key math concepts include polygon tessellation, geometric transformations, angle calculations, and vector operations. Construction highlights from the GeoGebra command summary involve commands like Point, Intersect, Polygon, Circle, Rotate, Line, Vector, Sequence, and Angle. Suitable for high school mathematics education, it visually illustrates geometric transformations and combinations, enhancing understanding of polygon properties and tessellation principles.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Intersect(xAxis, yAxis) → OO
  3. Polygon(OO, B, 6) → poly1, b, F, c, d, e, f, g, C, D, E
  4. Circle(C, B) → p
  5. Circle(OO, B) → h
  6. Intersect(p, h) → I, J, ,
  7. Rotate(I, (-rot), OO) → I'
  8. Polygon(A, OO, 3) → poly2, i, j, k, H
  9. Rotate(poly2, α, J) → poly2'
  10. Rotate(poly2', α, J) → poly2''
  11. Rotate(poly2'', α, J) → poly2'''
  12. Rotate(poly2''', α, J) → poly3
  13. Rotate(poly3, α, J) → poly3'
  14. Line(OO, B) → a
  15. Rotate(H, α, J) → H'
  16. Vector(E, A) → u
  17. Sequence(Translate[ListPoly, Vector[(n * u)]], n, (-k2), k2) → ListRow1
  18. Vector(H, C) → v
  19. Sequence(Translate[ListRow1, Vector[(n * v)]], n, (-k2), k2) → ListGrid
  20. Angle(A, OO, B) → β
  21. Angle(A, OO, B) → γ