A Family of Sequences

Autor/in	Turner, Paul
Titel	A Family of Sequences
Quelle	In: Australian Senior Mathematics Journal, 23 (2009) 1, S.58-62 (5 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0819-4564
Schlagwörter	Number Concepts; Mathematics Instruction; Secondary School Mathematics; Validity; Mathematical Logic; Problem Solving; Equations (Mathematics); Geometric Concepts + Suchen Sie Ihr Suchwort? Number concept; Zahlbegriff; Mathematics lessons; Mathematikunterricht; Gültigkeit; Mathematical logics; Mathematische Logik; Problemlösen; Equations; Mathematics; Gleichungslehre; Elementare Geometrie
Abstract	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).
Anmerkungen	Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2021/2/06