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Fibonacci Ratios

Fibonacci Ratios
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2017-01-07 08:40
FunctionSequenceCoordinate Geometry
This example demonstrates the dynamic changes in the ratio of consecutive terms in the Fibonacci sequence. It involves core mathematical concepts such as sequences, function graphs, coordinate geometry, and probability & statistics. The construction utilizes GeoGebra commands and objects like Sequence, Text, Element, and Textfield. It is suitable for high school and above students to understand the mathematical properties of the Fibonacci sequence and its representation in function graphs.

GeoGebra Commands & Parameters

  1. Sequence(Element[matrix1, 1, i], i, 1, 91) → list1
  2. Sequence(Element[matrix3, 1, i], i, 1, 90) → list2
  3. Text(Element[list1, m + 1]) → text1
  4. Text(Element[list1, m]) → text2
  5. Element(list2, m) → a
  6. Text(Element[list2, m]) → text3
  7. Sequence(Element[list1, i], i, 1, m + 1) → list3
  8. Sequence(Text[(Element[list1, i] * ", "), (-4 + Mod[floor((10 * log(Element[list1, i]) / log(10))) + 2, 20], 5 - floor((0.3 * log(Element[list1, i]))))], i, 0, m) → list4
  9. Text(Element[list1, m - 1]) → text10
  10. Textfield(A1) → InputBox1
  11. Textfield(A2) → InputBox2