Archive for the ‘Uncategorized’ Category
How fast do the Fibonacci numbers grow?
Posted by: Gary Ernest Davis on: December 1, 2010
Fibonacci numbers The sequence of Fibonacci numbers begins . The defining feature of these numbers is that each is the sum of the preceding two: . We can write this defining property as a recurrence relation by naming the Fibonacci number , starting from . So, . The recurrence for the is then: x […]
When is an integer a square?
Posted by: Gary Ernest Davis on: November 30, 2010
This post came out of a conversation with James Tanton (@jamestanton) about squares of integers being exactly the integers not represented by rounding for an integer (see here for background). To say that rounding yields an integer is to say that: ……………………………. (*) Subtracting from the inequalities in (*) and squaring – as we can […]
