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Pentagram and Various Appearances of the Golden Ratio

Pentagram and Various Appearances of the Golden Ratio
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2019-03-13 17:34
PolygonFunctionGeometric Construction
In collections Golden Ratio and STEAM education
This example demonstrates various appearances of the golden ratio in a pentagram. The golden ratio is a special mathematical proportion commonly found in nature and art. By constructing a pentagram, we can observe how the golden ratio manifests in geometric figures. This example uses commands such as Intersect, Point, Segment, Polygon, and Line in GeoGebra, suitable for middle school and above students to learn about geometric construction and the golden ratio.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Segment(A, B) → f
  4. Polygon(A, B, 5) → poly1, g, h, i, j, k, C, D, E
  5. Segment(A, D) → l
  6. Segment(D, B) → m
  7. Segment(B, E) → n
  8. Segment(E, C) → p
  9. Segment(C, A) → q
  10. Intersect(q, n) → F
  11. Segment(A, F) → r
  12. Line(F, f) → s
  13. Intersect(s, m) → G
  14. Segment(F, G) → t