recurrence relations - Fibonacci, tribonacci and other similar . . . Whoever invented "tribonacci" must have deliberately ignored the etymology of Fibonacci's name - which was bestowed on him quite a bit after his death Leonardo da Pisa's grandfather had the name Bonaccio (the benevolent), which was also used by his father The name "filius bonacii" or "figlio di Bonaccio" (son of Bonaccio) was contracted to give Fibonacci By the way: the Fibonacci sequence
Square Fibonacci numbers - Mathematics Stack Exchange Here is a paper of Bugeaud, Mignotte, and Siksek proving that the only perfect powers in the Fibonacci sequence are 0, 1, 8, 144 Therefore the only squares are 0, 1, and 144
What is the meaning of limit of Fibonacci sequence? The existence of the limit reflects the fact that the Fibonacci sequence is essentially a geometric sequence (it is actually a linear combination of two geometric sequences but one of them dominates the other)
geometry - Where is the pentagon in the Fibonacci sequence . . . The Fibonacci sequence is related to, but not equal to the golden ratio There is no reason to expect that the sequence mimics the geometric series $\varphi^n$ than there is to expect that the Fibonacci spiral is the same as the golden spiral
Fibonacci sequence starting with any pair of numbers Their closed form is differs by to the Fibonacci sequence by a factor of $\sqrt5$ (according to Wolfram MathWorld) Some Lucas numbers actually converge faster to the golden ratio than the Fibonacci sequence!