MathPlotAI Logo MathPlotAI

Common Tessellations

Common Tessellations
Loading the math board and drawing, please wait…
2014-08-08 10:12
PolygonVectorCoordinate GeometryTransformationGeometric Construction
In collections Symmetry, Transformation and Tessellation
This example demonstrates how to construct common tessellations using GeoGebra, achieving seamless plane coverage through polygon rotation and assembly. Key math concepts include polygon construction, vector rotation, matrix application, and coordinate geometry. Construction highlights from the summary involve commands like Polygon, Midpoint, Rotate, Vector, and Sequence, along with objects such as A, B, C, poly1, etc. Suitable for high school mathematics education to understand tessellation principles, transformation applications, and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(B, C) → D
  3. Rotate(A, 180*°, D) → A'
  4. Rotate(B, 180*°, D) → B'
  5. Rotate(C, 180*°, D) → C'
  6. Polygon(A', B', C') → poly2, c', a', b'
  7. Vector(B, C) → u
  8. Vector(B, A) → v
  9. Sequence(Sequence[Polygon[Translate[A, Vector[(m * u) + (n * v)]], Translate[B, Vector[(m * u) + (n * v)]], Translate[C, Vector[(m * u) + (n * v)]]], m, -3, 3], n, -3, 3) → list1
  10. Sequence(Sequence[Polygon[Translate[A', Vector[(m * u) + (n * v)]], Translate[B', Vector[(m * u) + (n * v)]], Translate[C', Vector[(m * u) + (n * v)]]], n, -3, 3], m, -3, 3) → list2