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Number Theory

Fibonacci Sequence

Definition A Fibonacci sequence is easily constructed:  Start with 0 and 1, and for each following number, add the previous two: 0, 1, 0+1=1, 1+1=2, 1+2=3, and so on. Here is the beginning of the sequence:  0, 1, 1, 2, 3, 5,...

/ November 22, 2011

Prime Numbers

Prime numbers are the basic units of the system of numbers, since every natural number is either a prime, or can be expressed as a composite of prime numbers. Here are some excerpts from the Wikipedia article about Prime numbers:...

/ November 21, 2011

Perfect Numbers

Perfect numbers are gateways to the wonders of the mathematical world. Contemplating them, one realizes how small our human minds really are compared to the reality that surrounds us, and creates us. Definition A perfect number is a positive integer...

/ November 21, 2011

The Number Pi

From Wikipedia: “π (sometimes written pi) is a mathematical constant that is the ratio of any circle’s circumference to its diameter. π is approximately equal to 3.14 in the usual decimal notation. Many formulae in mathematics, science, and engineering involve...

/ November 21, 2011

Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic states that every positive integer can be written as a product of prime numbers in a unique way. The following description of the theorem and its proof is quoted from the Wikipedia encyclopedia: Definition “In...

/ November 20, 2011

Prime Number Theorem

The Prime Number Theorem (PNT) describes the distribution of prime numbers. Euclid could prove that there is an infinite number of primes, but their location can only be predicted by statistical means, as an approximation.  As ordinary numbers get larger...

/ November 20, 2011

Number Theory

The concept of “numbers” is itself very perplexing, and shows the evolution of mathematics from simple arithmetic,  to very complex operations.  Here is a brief overview of the types of numbers: Each type of numbers in the list includes all...

/ November 8, 2011