Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians. The post The Astonishing Behavior of Recursive Sequences first appeared on Quanta Magazine
In mathematics, simple rules can unlock universes of complexity and beauty. Take the famous Fibonacci sequence, which is defined as follows: It begins with 1 and 1, and each subsequent number is the sum of the previous two. The first few numbers are: 1, 1, 2, 3, 5, 8, 13, 21, 34 … Simple, yes, but this unassuming recipe gives rise to a pattern of far-reaching significance, one that appears to be…