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Constructing a Golden Rectangle: Geometry and Golden Ratio

Constructing a Golden Rectangle: Geometry and Golden Ratio
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2019-03-13 17:23
CirclePolygonAngleGeometric Construction
This example demonstrates the geometric construction of a Golden Rectangle. Key concepts include the Golden Ratio, rectangle properties, and proportional segments. The construction utilizes GeoGebra commands such as Circle, Point, Segment, OrthogonalLine, Intersect, and Angle to define points A, B, C, D and angles α, β. It is suitable for high school geometry classes, exploring the relationship between the Golden Ratio and Fibonacci sequences, or for visualizing mathematical aesthetics in design.

GeoGebra Commands & Parameters

  1. Circle(A, (1 + sqrt(5)) / 2) → c
  2. Point(c) → B
  3. Segment(A, B) → f
  4. Circle(B, 1) → d
  5. OrthogonalLine(B, f) → g
  6. Intersect(d, g) → C, D
  7. OrthogonalLine(D, g) → h
  8. OrthogonalLine(A, f) → i
  9. Intersect(h, i) → E
  10. Segment(A, D) → j
  11. Angle(B, A, D) → α
  12. Segment(B, D) → k
  13. Angle(j, i) → β