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Pythagorean Tiling by John Golden

Pythagorean Tiling by John Golden
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2013-10-29 21:44
TrianglePolygonCoordinate GeometryGeometric Construction
In collections Pythagorean Theorem
This example demonstrates the application of the Pythagorean theorem in plane geometry through dynamic tilings, showing the relationship between right triangles and integer side lengths. Key math concepts include right triangles, Pythagorean theorem, integer side lengths, and tiling construction. GeoGebra commands used in construction are Polygon, Point, Vector, Circle, Intersect, Sequence, and Translate. Suitable for high school mathematics teaching, helping students understand geometric construction and sequence applications.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C_1, D
  2. Point(a) → C
  3. Polygon(C, A, 4) → poly2, e, f, g, h, F, G
  4. Vector(D, C) → u
  5. Circle(B, e) → k
  6. Intersect(k, b, 1) → H
  7. Vector(A, H) → v
  8. Sequence(Translate[poly1, Vector[i * u]], i, -4, 4) → list1
  9. Sequence(Translate[list1, Vector[i * v]], i, -4, 4) → list2
  10. Sequence(Translate[poly2, Vector[i * v]], i, -4, 4) → list3
  11. Sequence(Translate[list3, Vector[i * u]], i, -4, 4) → list4
  12. Translate(A, u) → A'
  13. Polygon(A, A', 4) → poly3, i, j, l, m, I, J
  14. Sequence(Translate[poly3, Vector[i * u]], i, -4, 4) → list5
  15. Sequence(Translate[list5, Vector[i * v]], i, -4, 4) → list6

AI Drawing Prompt Reference

Draw a Pythagorean tiling pattern composed of multiple congruent right triangles. Start by creating a right triangle with integer side lengths, then use vector and translation commands to generate a series of the same triangles. Arrange them through translation and rotation to form a complex tiling pattern, ensuring each triangle adheres to the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.