MathPlotAI Logo MathPlotAI

Happy Cats in Paving

Happy Cats in Paving
Loading the math board and drawing, please wait…
2020-11-15 23:46
PolygonVectorCalculusTransformationGeometric Construction
This example demonstrates creating happy cat patterns in paving through similarity transformations and geometric constructions. It involves core math concepts like similarity, geometric transformations, orthocenter, angles, trapezium, integral calculus. Construction highlights the use of GeoGebra commands such as Polygon, PointIn, Spline, Vector, Sequence, and Rotate. Suitable for high school students learning geometric transformations and calculus.

GeoGebra Commands & Parameters

  1. Polygon(A, J, 4) → poly1, f, g, h, i, I, K
  2. PointIn(poly1) → C
  3. PointIn(poly1) → D
  4. PointIn(poly1) → E
  5. PointIn(poly1) → F
  6. PointIn(poly1) → G
  7. PointIn(poly1) → H
  8. PointIn(poly1) → B
  9. Spline(l1, 3) → a
  10. Vector(A, J) → u
  11. Vector(A, K) → v
  12. Sequence(Sequence[Translate[a, Vector[(i * u) + (j * v)]], i, 0, p], j, 0, q) → l2
  13. Rotate(Z, (-2 * c), W) → V
  14. Spline(l3, 3) → b
  15. Sequence(Sequence[Translate[b, Vector[(i * u) + (j * v)]], i, 0, p], j, 0, q) → l5

AI Drawing Prompt Reference

Draw a paving pattern composed of multiple similar cat-shaped patterns. First, draw a quadrilateral, then place several points randomly inside it to use as control points for a smooth curve. Next, draw vectors along the sides of the quadrilateral and translate the curve along these vectors to generate multiple translated curves, forming cat-shaped patterns. Finally, rotate one of the patterns and translate it again to generate more patterns, ultimately creating a paving pattern composed of multiple similar cat-shaped patterns.
The prompt above was compiled from the original drawing commands and is for reference only.