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Fibonacci Numbers and the Fibonacci Spiral

Fibonacci Numbers and the Fibonacci Spiral
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2019-05-27 11:26
SequenceGeometric ConstructionGraphing
This example demonstrates how to draw the Fibonacci spiral by constructing squares and quarter-circles. It involves core math concepts like the Fibonacci sequence, golden ratio, and geometric construction. GeoGebra commands and objects such as Point, Polygon, First, Element are used to create geometric elements. Suitable for high school mathematics teaching to visually illustrate the connection between sequences and geometric shapes.

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