The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.
Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone. They also arise in computer science, especially in sorting or organizing data.
Amazingly, the ratios of successive terms of the Fibonacci sequence get closer and closer to a specific number, often called the golden ratio. It can be calculated as $\frac(1 + \sqrt5)(2)$, or 1.6180339887…. For instance, the ratio 55/34 is 1.617647…, and the next ratio, 89/55, is 1.6181818….
Fibonacci's immortal rabbit problem. A red rectangle designates a newborn pair, which doesn't produce offspring until the second month.