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multiplying rabbits

A newly born rabbit is capable of reproducing at one month old (when it matures). Suppose the rabbit never dies, and it continues reproducing one new rabbit every month. So, when the rabbit is born, it has one member in its own family. After a month, it matures, and by the second month it adds a new born member to its family. In the third month, the rabbit produces another offspring; its first child also matures and will be ready to have an offspring in the next month.

The sequence named by Fibonacci (1,1,2,3,5,8,13,21,...) can describe the number of members in the rabbit's family at each month. Explain how.

 Extensions
 Compare the ratio of consecutive numbers in this sequence. For example 1/ 1, 1/ 2, 2/ 3, 3/ 5, 5/ 8, .... What do you notice after a while?

 Related External Resources
 Fibonacci Numbers and the Golden Section This page discuss applications, real world phenomena, puzzles, patterns, and geometry associated with the Fibonacci numbers and golden section. Fibonacci Online Assessment Take a multiple choice quiz that tests your knowledge about Fibonacci, the Fibonacci sequence, and the golden ratio. Golden Exploration Worksheet This worksheet from Mathematics Teaching in the Middle School leads students to discover the golden ratio by making various measurements and calculations. The Fibonacci Numbers, Pineapples, Sunflowers and The Golden Mean Learn how you can find the Fibonacci's sequence on a pineapple. Math Course on the Fibonacci Numbers - View the series of lecture notes used for a class exclusively about the Fibonacci numbers. A Day at the Arcade Determine how many ways a coin machine can receive money in exchange for a specific number of game tokens.

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