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Golden Section Euclidean Construction

Golden Section Euclidean Construction
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2015-02-16 01:00
CircleTrigonometryGeometric Construction
In collections Bling things
This example demonstrates the step-by-step Euclidean construction of the golden section of a line segment. Key math concepts include line ratios, geometric constructions, and symmetry. It uses commands like Polygon, PointIn, Segment, Midpoint, OrthogonalLine, Circle, Intersect in GeoGebra. Suitable for high school mathematics education or for enthusiasts of geometric constructions.

GeoGebra Commands & Parameters

  1. Polygon({PP1, PP2, PP3, PP4}) → peep
  2. PointIn(peep) → B
  3. PointIn(peep) → A
  4. Segment(A, B) → segmAB
  5. Polygon(A, B, 4) → poly1, i, j, k, l, C, D
  6. Midpoint(A, D) → E
  7. OrthogonalLine(A, segmAB) → b
  8. Circle(E, Segment[B, E]) → c
  9. Intersect(c, b, 2) → P_{1}
  10. Intersect(c, b, 1) → F
  11. Circle(A, Segment[A, F]) → d
  12. Segment(A, P_{1}) → e
  13. Intersect(d, e, 1) → Q
  14. Intersect(d, segmAB) → P,
  15. Segment(A, P) → g
  16. Segment(A, P) → h
  17. Segment(E, B) → segmEB