ABSTRACT
The tenth chapter applies many theorems from chapter nine to a particular sequence—the Fibonacci numbers. Known for centuries, this sequence possesses many surprising properties and is intimately linked with the Golden Ratio, a constant that has many interesting properties of its own. For example, here is one nonintuitive fact: if the Golden Ratio, which is an irrational number, is raised to a large integer power, the result becomes arbitrarily close to an integer! In relation to the Golden Ratio, one section recalls a sequence with nested radicals and another discusses continued fractions. There are many other surprising facts, such as a particular way that any integer can be represented as a sum of Fibonacci numbers.
