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Construction of a Golden Rectangle

Construction of a Golden Rectangle
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2015-05-27 02:29
PolygonGeometric Construction
In collections Geometry Constructions
This example demonstrates how to construct a golden rectangle from a square. A golden rectangle has a length-to-width ratio of the golden ratio. The core mathematical concepts involved include proportion and the golden ratio. Using GeoGebra commands such as Polygon, Midpoint, and Segment, the construction process is visually illustrated. Suitable for students in middle school and above learning geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Midpoint(b) → E
  3. Segment(E, D) → e
  4. Line(B, C) → f
  5. Circle(E, e) → g
  6. Intersect(g, f) → F, G
  7. OrthogonalLine(G, f) → h
  8. Line(A, D) → i
  9. Intersect(i, h) → H
  10. Polygon(D, C, G, H) → poly2, d_1, c_1, g_1, h_1
  11. Polygon(A, B, G, H) → poly3, a_1, b_1, g_2, h_2

AI Drawing Prompt Reference

Draw a golden rectangle constructed from a square. Start with a square. Draw a line from the midpoint of one diagonal to the opposite corner. Then draw a perpendicular line from that midpoint and intersect it with a line from the other diagonal. Finally, draw a triangle using the endpoint of the other diagonal, the intersection point, and the endpoint of the perpendicular line. The result should illustrate proportion and geometric construction, suitable for educational purposes.
The prompt above was compiled from the original drawing commands and is for reference only.