What comes next in the sequence: 1, 1, 2, 3, 5, 8, ...?

The next number in the sequence, 1, 1, 2, 3, 5, 8, is 13. This pattern is known as the Fibonacci sequence, a series where each number is the sum of the two preceding numbers. For example, to get 2, you add 1 and 1. To get 3, you add 1 and 2. Following this rule, to find the number after 8, you simply add the two numbers before it: 5 + 8, which equals 13.

This famous mathematical sequence was introduced to Western European mathematics by Leonardo of Pisa, known as Fibonacci, in his 1202 book "Liber Abaci". He described it using a problem about the growth of a hypothetical rabbit population. However, the sequence was known in Indian mathematics centuries earlier.

Beyond its mathematical origins, the Fibonacci sequence is remarkable for its frequent appearance in nature. You can observe Fibonacci numbers in the spirals of a pinecone or a sunflower's seed head, the branching patterns of trees, and the arrangement of leaves on a stem. This natural phenomenon highlights an underlying mathematical order in the world around us, making the Fibonacci sequence a fascinating example of how math and nature intertwine.