MathPlotAI Logo MathPlotAI

Parametric Surfaces: Tile Tiling

Parametric Surfaces: Tile Tiling
Loading the math board and drawing, please wait…
2013-10-25 19:01
VectorSolid GeometryComplex NumberParametric EquationGeometric Construction
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates how to draw a tile tiling surface using parametric equations. It involves core mathematical concepts such as parametric equations, surfaces, ellipses, diagrams, complex numbers, vectors, and linear equations. Key GeoGebra commands used include Corner (corner points), If (conditional statements), Segment (line segments), Point (points), Sequence (sequences), Join (joining points), and Element (element selection). Suitable for high school and above mathematics education to understand parametric surfaces and geometric constructions.

GeoGebra Commands & Parameters

  1. Corner(4) → W04
  2. Corner(1) → W01
  3. If(e, y(B), y(W01) + (Bild - 1) * sy) → y0
  4. Corner(2) → W02
  5. Segment(W01, W02) → d
  6. Point(d) → E
  7. If(e, x(B), x(E)) → x0
  8. If(e, Ny, 40) → Ny1
  9. If(e, Nx, 1) → Nx1
  10. If(e, c, sy) → yW
  11. Sequence(y(C0 - yW * (j - 1)), j, 1, Ny1) → my
  12. Sequence(x(C0 + xW * i), i, 0, Nx1) → mx
  13. Join(Sequence[Sequence[{(Element[mx, i], Element[my, j]), (Element[mx, i + 1], Element[my, j])}, i, 1, Nx1], j, 1, Ny1]) → l1
  14. Element(l1, b) → z0
  15. Sequence(Text[i], i, 1, (Nx1 + 1) * Ny1) → l2
  16. Element(l2, b) → z1
  17. Corner(3) → W03

AI Drawing Prompt Reference

Draw a tile tiling surface generated by parametric equations, showcasing core mathematical concepts like parametric equations, surfaces, ellipses, complex numbers, and vectors. Start by defining four corner points, use conditional statements to create a series of points, connect these points to form line segments and ellipses, then generate a grid using sequences and conditions, and finally connect the grid points to form the surface, demonstrating geometric construction and linear equations.
The prompt above was compiled from the original drawing commands and is for reference only.