Fibonacci Numbers Calculation Demo
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① This example demonstrates generating and displaying the first several terms of the Fibonacci sequence via its recurrence relation. ② Core mathematical concepts include sequences, recurrence formulas, initial term settings, and the growth pattern of the sequence. ③ Construction highlights: GeoGebra variables a and b store the two preceding terms, point A serves as an index or display object, and the Sequence or Iteration command automates the iterative computation. ④ Suitable for high‑school mathematics “Sequences” lessons, introductory discrete mathematics at university, or algorithm demonstrations in programming courses, helping learners visualize the recursive process.
GeoGebra Commands & Parameters
Numeric a(13.0)(((1 + sqrt(5)) / 2)^(a) - ((1 - sqrt(5)) / 2)^(a)) / sqrt(5)(a, b)
AI Drawing Prompt Reference
Draw a Cartesian plane where the horizontal axis represents the term index n of the Fibonacci sequence and the vertical axis represents the Fibonacci value Fₙ. Include an adjustable slider for n, initially set to 13, and compute Fₙ using Binet’s formula. Plot the point (n, Fₙ) on the graph. The figure shows the point moving along an exponentially rising curve as n increases, illustrating the rapid growth of the recursive sequence.
The prompt above was compiled from the original drawing commands and is for reference only.