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Golden Rectangles

Golden Rectangles
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2015-02-19 09:16
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the construction of golden rectangles, which are special rectangles with a length-to-width ratio of the golden ratio. Key construction steps include using the Polygon command to draw the rectangle, the Midpoint and Line commands to find the midpoints and perpendicular bisectors of the sides, and the Distance command to measure the lengths of the sides. Suitable for middle school and above students to learn geometric construction and ratio concepts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Line(A, B) → e
  3. Line(C, D) → f
  4. Line(A, D) → g
  5. Line(B, C) → h
  6. Midpoint(D, C) → E
  7. Circle(E, B) → k
  8. Intersect(k, f, 1) → F
  9. OrthogonalLine(F, f) → i
  10. Intersect(e, i) → G
  11. Polygon(A, G, F, D) → poly2, a_1, g_1, f_1, d_1
  12. Distance(G, A) → distanceGA
  13. Distance(A, D) → distanceAD
  14. Circle(B, G) → p
  15. Intersect(p, h, 2) → H
  16. OrthogonalLine(H, b) → j
  17. Intersect(i, j) → I
  18. Distance(B, G) → distanceBG
  19. Distance(B, C) → distanceBC
  20. Midpoint(G, I) → J
  21. Circle(F, I) → q
  22. Intersect(q, f, 2) → K
  23. OrthogonalLine(K, f) → l
  24. Intersect(j, l) → L
  25. Distance(F, C) → distanceFC
  26. Distance(H, C) → distanceHC
  27. Distance(H, C) → HC
  28. Polygon(B, G, F, C) → poly3, b_1, g_2, f_2, c_1
  29. Polygon(H, I, F, C) → poly4, h_1, i_1, f_3, c_2
  30. Circle(K, C) → r
  31. Intersect(r, l, 2) → M
  32. OrthogonalLine(M, l) → m
  33. Intersect(h, m) → N
  34. Distance(K, C) → distanceKC

AI Drawing Prompt Reference

Draw a figure consisting of two nested golden rectangles. Start by constructing a rectangle, find the midpoints of its sides and draw perpendicular bisectors. Use circles and intersections to locate new vertices, forming an inner golden rectangle. Measure and label the lengths of the sides to demonstrate the ratio of length to width is the golden ratio.
The prompt above was compiled from the original drawing commands and is for reference only.