Mathematics is widespread in nature, and mathematical concepts are essential to understanding the biosphere, the rocks and oceans, and the atmosphere. This article explores a few examples.

The Fibonacci Series

In 1202 a monk in Italy, by the name of Leonardo Pisano Fibonacci, wanted to know how fast rabbits could breed in ideal circumstances. Suppose a newly born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of 1 month. So at the end of its second month, a female can produce another pair of rabbits. Suppose that these rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was: How many pairs would there be after 1 year?

1. At the end of the first month, they mate, but there is still...