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6.13: Exercise

  • Page ID
    86210
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Before you go on, you might want to work on the following exercise.

    Exercise 6.1

    There is an interesting connection between Fibonacci numbers and Pythagorean triples. If \(F\) is a Fibonacci sequence, then

    \[\big(F_i F_{i+3}, \, 2 F_{i+1} F_{i+2}, \, F_{i+1}^2 + F_{i+2}^2 \big) \notag \]

    is a Pythagorean triple, for all \(i \ge 1\).

    Write a function named fib_triple that takes n as an input variable, computes the first n Fibonacci numbers, stores them in a vector, and checks whether this formula produces Pythagorean triples for numbers in the .


    This page titled 6.13: Exercise is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Carey Smith via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.