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Graphing Golden Rectangles

Graphing Golden Rectangles
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2018-08-16 02:11
Geometric ConstructionGraphing
This example demonstrates how to draw golden rectangles using GeoGebra, highlighting the concept of golden ratio and geometric construction. Key mathematical concepts include proportion, golden division, and geometric drawing. The construction involves commands like Point, Polygon, and CircleArc, allowing users to adjust parameters. Suitable for students from middle school onwards to understand geometric proportions and drawing techniques.

GeoGebra Commands & Parameters

  1. Point(Circle[A, f]) → B
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Polygon(Corner[1], (x(Corner[1]) + (0.3 * Distance[Corner[1], Corner[2]]), y(Corner[1])), (x(Corner[4]) + (0.3 * Distance[Corner[1], Corner[2]]), y(Corner[4])), Corner[4]) → poly10, i_2, j_2, k_2, l_2
  4. First(Fibonacci, n + 1) → list1
  5. Element(list1, n - 1) → last
  6. Element(list1, n) → beforeLast
  7. Polygon((-22, 3), (-22, 4), (-21, 4), (-21, 3)) → poly2, g, h, i, j
  8. CircleArc((-21, 3), (-21, 4), (-22, 3)) → e
  9. Polygon((-21, 3), (-20, 3), (-20, 4), (-21, 4)) → poly3, l, m, p, q
  10. CircleArc((-21, 3), (-20, 3), (-21, 4)) → k
  11. Polygon((-22, 3), (-22, 1), (-20, 1), (-20, 3)) → poly4, s, t, a_1, b_1
  12. CircleArc((-22, 3), (-22, 1), (-20, 3)) → r
  13. Polygon((-22, 4), (-25, 4), (-25, 1), (-22, 1)) → poly5, d_1, e_1, f_1, g_1
  14. CircleArc((-22, 4), (-25, 4), (-22, 1)) → c_1
  15. Polygon((-20, 4), (-20, 9), (-25, 9), (-25, 4)) → poly6, i_1, j_1, k_1, l_1
  16. CircleArc((-20, 4), (-20, 9), (-25, 4)) → h_1
  17. Polygon((-20, 1), (-12, 1), (-12, 9), (-20, 9)) → poly7, m_1, n_1, q_1, r_1
  18. CircleArc((-20, 1), (-12, 1), (-20, 9)) → p_1
  19. Polygon((-25, 1), (-25, -12), (-12, -12), (-12, 1)) → poly8, t_1, a_2, b_2, c_2
  20. CircleArc((-25, 1), (-25, -12), (-12, 1)) → s_1