Friday, December 18th, 2009
Explanation of the Pigeon-Hole Principle
Description
A detailed tutorial on the pigeon-hole principle. Step by step tutorial including several examples of the pigeon-hole principle for reference.
Overview
The pigeon-hole principle is an important principle in math that states that if n items are to be put into m pigeon-holes, and n > m, then at least one pigeon-hole must contain more than one item. It is thought of as an extension of the counting principle. The pigeon-hole principle was first referred to as the drawer principle, or the shelf principle. Because of this, it is commonly called Dirichlet’s box principle or Dirichlet’s drawer principle. It is most commonly used with finite sets of elements; however, this principle can also be used with infinite sets.
Tags: algebra, box, counting, Dirichlet, drawer, elements, extension, finite, infinite, leftover, more, pigeon-hole, principle, remainder, sets, shelf, theory
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Friday, October 30th, 2009
Introduction to the Euclidean Algorithm
Description
A detailed tutorial on the Euclidean algorithm. Step by step tutorial including several examples of the Euclidean algorithm for reference.
Overview
The Euclidean algorithm, sometimes referred to as Euclid’s algorithm, is the most efficient way of determining the greatest common factor of two numbers. The greatest common factor of two numbers is the largest number that divides them both evenly. The Euclidean algorithm is used in a series of steps – it follows a pattern that helps to find numbers and their factors with accuracy.
Tags: algebra, algorithm, common, divides, divisor, Euclid, Euclidean, evenly, factor, greatest, highest, negative, pattern, positive, remainder, steps
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