MathPlotAI Logo MathPlotAI

Tessellation of Kites and Degenerate Hexagons

Tessellation of Kites and Degenerate Hexagons
Loading the math board and drawing, please wait…
2019-09-22 16:40
PolygonTransformationGeometric Construction
This example demonstrates the tessellation transformation of kites and degenerate hexagons. It involves key mathematical concepts such as polygons, reflection, and transformation. Using GeoGebra commands like Intersect, Point, Semicircle, Polygon, Mirror, Segment, Circle, Angle, Rotate, Midpoint, Vector, Sequence, etc., it constructs tessellation patterns of kites and degenerate hexagons. Suitable for students at the junior high school level and above to learn about geometric transformations and tessellation patterns.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Semicircle(A, B) → c
  4. Point(c) → C
  5. Polygon(A, B, C) → t1, ch, a, b
  6. Mirror(C, ch) → C'
  7. Segment(C', B) → g
  8. Circle(C', b) → e
  9. Intersect(e, g, 1) → F
  10. Circle(B, b) → d
  11. Point(d) → E
  12. Intersect(d, a, 1) → D
  13. Angle(E, B, D) → α
  14. Rotate(F, (-α), C') → G_1
  15. Segment(A, C') → f
  16. Polygon(A, C, E, B, G, C') → poly1, a_1, c_2, e_1, b_1, g_1, c'
  17. Midpoint(b_1) → H
  18. Mirror(A, H) → A'
  19. Mirror(C, H) → C'_1
  20. Mirror(E, H) → E'
  21. Mirror(B, H) → B'
  22. Mirror(G, H) → G'
  23. Mirror(C', H) → C''
  24. Polygon(A', C'_1, E', B', G', C'') → poly1', a', c'_1, e', b', g', c''
  25. Rotate(Translate[Polygon[Mirror[A, ch], Mirror[C, ch], Mirror[E, ch], Mirror[B, ch], Mirror[G, ch], Mirror[C', ch]], B - A], 90° - α, B) → poly2
  26. Mirror(poly2, H) → poly2'
  27. Angle(G, C', F) → β
  28. Rotate(Translate[B, B - A], 90° - α, B) → I
  29. Vector(A, I) → u
  30. Rotate(Translate[Mirror[G, ch], B - A], 90° - α, B) → J
  31. Mirror(J, H) → J'
  32. Vector(A, J') → v
  33. Sequence(Sequence[Polygon[Translate[A, Vector[(k * u) + (j * v)]], Translate[C, Vector[(k * u) + (j * v)]], Translate[E, Vector[(k * u) + (j * v)]], Translate[B, Vector[(k * u) + (j * v)]], Translate[G, Vector[(k * u) + (j * v)]], Translate[C', Vector[(k * u) + (j * v)]]], k, -3, 3], j, -3, 3) → l1
  34. Sequence(Sequence[Polygon[Translate[A', Vector[(k * u) + (j * v)]], Translate[C'_1, Vector[(k * u) + (j * v)]], Translate[E', Vector[(k * u) + (j * v)]], Translate[B', Vector[(k * u) + (j * v)]], Translate[G', Vector[(k * u) + (j * v)]], Translate[C'', Vector[(k * u) + (j * v)]]], k, -3, 3], j, -3, 3) → l2
  35. Sequence(Sequence[Translate[poly2, Vector[(k * u) + (j * v)]], k, -3, 3], j, -3, 3) → l3
  36. Sequence(Sequence[Translate[poly2', Vector[(k * u) + (j * v)]], k, -3, 3], j, -3, 3) → l4

AI Drawing Prompt Reference

Draw a tessellation pattern composed of kites and degenerate hexagons. Start by plotting the intersection of the coordinate axes and a semicircle. Construct a kite using the intersection points of the semicircle with the x-axis. Apply reflections and rotations to the kite to generate multiple kites and degenerate hexagons that interlock. Use translation and further reflections to arrange the shapes into a complete tessellation pattern.
The prompt above was compiled from the original drawing commands and is for reference only.