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Golden Rectangle by James Bilbe

Golden Rectangle by James Bilbe
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2015-04-12 14:39
CirclePolygonGeometric Construction
This example demonstrates how to construct a golden rectangle using geometric shapes, involving concepts like rectangles, fractions, parallelograms, polygons, division, and cylinders. Key GeoGebra commands used include Polygon, Midpoint, Circle, Ray, Intersect, OrthogonalLine, Distance, Segment, and Point. Suitable for middle school and above students learning geometric constructions and exploring the golden ratio.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Midpoint(b) → E
  3. Circle(E, D) → e
  4. Ray(A, D) → f
  5. Ray(B, C) → g
  6. Intersect(e, g, 1) → F
  7. OrthogonalLine(F, g) → h
  8. Intersect(h, f) → G
  9. Polygon(A, G, F, B) → poly2, a_1, g_1, f_1, b_1
  10. Distance(A, B) → distanceAB
  11. Distance(B, F) → distanceBF
  12. Segment(D, G) → i
  13. Point(Circle[B, a + f_1]) → H
  14. Segment(B, H) → j