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Fibonacci Numbers and Fibonacci Spiral

Fibonacci Numbers and Fibonacci Spiral
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2014-09-28 05:54
SequenceTransformationGeometric Construction
In collections Logarithmic Spiral and Fibonacci Numbers
This dynamic worksheet demonstrates constructing squares with sides equal to the first several Fibonacci numbers and building a Fibonacci spiral from these squares. Key mathematical concepts include sequences and geometric construction. GeoGebra commands used include Point, Polygon, First, Element, etc. Suitable for middle school and above students learning sequences and geometry.

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