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Square Puzzle by John Golden

Square Puzzle by John Golden
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2015-05-31 02:03
PolygonTransformationGeometric Construction
In collections Elementary Geometry
This example demonstrates how to form a square by assembling multiple shapes. Key mathematical concepts include geometric transformations and polygons. Using GeoGebra commands such as Segment, LineBisector, Intersect, etc., complex geometric figures can be constructed. Suitable for middle school and above students to learn about geometric transformations and polygon-related knowledge.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. LineBisector(a) → b
  3. Intersect(b, a) → C
  4. Circle(C, B) → c
  5. Intersect(c, b, 1) → D
  6. Point(a) → E
  7. OrthogonalLine(A, a) → d
  8. Rotate(D, 90*°, D) → D'
  9. Rotate(E, 90*°, D) → E'
  10. Ray(D', E') → e
  11. Polygon(E, D, E', A) → poly1, e_1, d_1, e', a_1
  12. Point(Circle[F, Distance[A, E]]) → F_2
  13. Rotate(Polygon[Translate[E, F - A], Translate[D, F - A], Translate[E', F - A], Translate[A, F - A]], (-Angle[F_2, F, Translate[E, F - A]]), F) → poly2
  14. Point(Circle[G, Distance[A, E']]) → G_2
  15. Rotate(Polygon[Translate[E, G - A], Translate[D, G - A], Translate[E', G - A], Translate[A, G - A]], (-Angle[G_2, G, Translate[E', G - A]]), G) → poly3
  16. Point(Circle[H, Distance[D', E']]) → H_2
  17. Rotate(Polygon[Translate[E, H - D'], Translate[D, H - D'], Translate[E', H - D'], Translate[A, H - D']], (-Angle[H_2, H, Translate[E', H - D']]), H) → poly4
  18. Point(Circle[I, Distance[D', E]]) → I_2
  19. Rotate(Polygon[Translate[E, I - D'], Translate[D, I - D'], Translate[E', I - D'], Translate[A, I - D']], (-Angle[I_2, I, Translate[E, I - D']]), I) → poly5