id: 05668521
dt: j
an: 2010b.00389
au: Turner, Paul
ti: A family of sequences.
so: Aust. Sr. Math. J. 23, No. 1, 58-62 (2009).
py: 2009
pu: Australian Association of Mathematics Teachers (AAMT), Adelaide, SA
la: EN
cc: F65
ut: number theory; number concepts; Fibonacci sequence
ci:
li:
ab: Summary: Perhaps a business colleague threw out a challenge. The year:
around 1200. The place: Pisa. The challenge: Calculate how many pairs
of rabbits will be produced in a year, beginning with a single pair, if
in every month each pair bears a new pair which becomes productive from
the second month on. The question and its solution found its way into
the book "Liber abaci" by Leonardo of Pisa (known as Fibonacci),
completed in 1202. It gives rise to the Fibonacci sequence. A colleague
of the author issued the challenge: Prove that the sum of the squares
of any two consecutive terms of the Fibonacci sequence is a term of the
sequence. In this article, the author gives a more general context in
which the sum of consecutive squares property is true, and a surprising
connection with Pythagorean triples. (ERIC)
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