https://studentprojects.in/software-development/c-tutorials/c/number/to-find-the-fibonacci-numbers-below-a-given-number/ Microcontroller projects, Circuit Diagrams, Project Ideas Mon, 24 Sep 2012 15:34:34 +0000 hourly 1 https://wordpress.org/?v=6.1.7 https://studentprojects.in/software-development/c-tutorials/c/number/to-find-the-fibonacci-numbers-below-a-given-number/comment-page-1/#comment-8954 Mon, 24 Sep 2012 15:34:34 +0000 http://studentprojects.in/?p=313#comment-8954 The algebraic proof does porvide certain insights as well. For example, it tells you that the property,F(n+1)^2 – F(n)*F(n+2) = –[F(n)^2 – F(n–1)*F(n+1)] for all n,is independent of the initial values F(1) = 1, F(2) = 1, and therefore that something like Cassini’s identity will hold for any choice of initial conditions.This property can be rewritten F(n+1)^2 + F(n)^2 = F(n)*F(n+2) + F(n–1)*F(n+1), which has a simple geometric interpretation:The area of the two squares* * * * * * * ** * * * * * * ** * * * * * * ** * * * ** * * * *is the same as that of the two rectangles* * * * * * * ** * * * * * * ** * * * * * * ** * * * ** * * * *

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