Radially Symmetric Closed Knight's Tour

Radially Symmetric Closed Knight's Tour
Loading the math board and drawing, please wait…
2023-02-17 17:23
This example demonstrates a radially symmetric closed knight's tour, where a knight moves on a chessboard following L-shaped steps, forming a closed circuit that is symmetric about the center. The core mathematical concepts involve Hamiltonian cycles in graph theory, symmetry, sequence construction, and geometric representation of polygonal paths. The construction uses GeoGebra commands such as Sequence, PolyLine, Min, First, and Append, with a series of labeled points (A to Z and subscripted variants) to trace the knight's moves and finally render them as a closed polyline. It is suitable for middle school and above to explore the intersection of symmetry and graph theory, and can be used for mathematical modeling or recreational mathematics demonstrations.

GeoGebra Commands & Parameters

  1. Append(l1, A) → l3
  2. Min(n, 65) → n2
  3. First(l3, n2) → l2
  4. PolyLine(l2) → f
  5. Min(n, 64) → m
  6. Sequence({Polygon[Element[l2, i] + (0.5, -0.5), Element[l2, i] + (0.5, 0.5), 4]}, i, 1, m) → m1
  7. Sequence(Sequence[{Polygon[(0.5 + i, 0.5 + j), (1.5 + i, 0.5 + j), 4]}, i, 1, 8, 2], j, 1, 8, 2) → l5, {{{1}, {1}, {1}, {1}}, {{1}, {1}, {1}, {1}}, {{1}, {1}, {1}, {1}}, {{1}, {1}, {1}, {1}}}
  8. Sequence(Sequence[{Polygon[(0.5 + i, 0.5 + j), (1.5 + i, 0.5 + j), 4]}, i, 0, 7, 2], j, 0, 7, 2) → l6, {{{1}, {1}, {1}, {1}}, {{1}, {1}, {1}, {1}}, {{1}, {1}, {1}, {1}}, {{1}, {1}, {1}, {1}}}

AI Drawing Prompt Reference

Draw a radially symmetric closed knight's tour path starting from the center, where the knight moves in L-shaped steps to form a closed loop symmetric about the center. First, create a series of points from A to Z and their variants, then use these points to construct polygonal paths, and finally connect these paths into a closed polyline.
The prompt above was compiled from the original drawing commands and is for reference only.