Patterns in Numbers

Introduction	A brief description of why mathematics is often called the science of pattern.
Magic Squares	Examples of a variety of magic squares of various types.
Magic Stars	Examples of orders 5 to 12d with information.
Other Patterns	Selections from my collection of over 400 number patterns.

Introduction

The history of mathematics is a history of people fascinated by numbers. A driving force in mathematical development has always been the need to solve practical problems. However, man's innate curiosity and love of pattern has probably had an equal part in its development. Most written records of early mathematics that have survived to modern times were actually lists of mathematical problems i.e. recreational mathematics. Examples: the Rhind Papyrus, (circa 1700 BC), a series of 87 problems, was the key to deciphering Egyptian hieroglyphs; Diophantus' Arithmetica (circa 250 BC), a collection of 130 mathematical problems with numerical solutions of determinate equations. (Fermat's Last Theorem was found written in the margin of a copy of this book.)

The Pythagoreans (circa 6th century BC) were a secret society who considered numbers sacred and tried to find relations between numbers and nature. For example, they developed the musical scales as number ratios.
2s13.gif (4508 bytes) They discovered that 6 and 28 are the first two 'perfect' numbers (a number equal to the sum of it's proper divisors. They also knew that squared numbers are the sums of sequences of consecutive odd numbers.

A recent example of mathematics being advanced with no apparent practical purpose was the proving of Fermat's Last Theorem. This 350 year old theorem is simple to state but has occupied countless mathematicians untold hours of work. It was finally proved by Professor Andrew Wiles in 1994, after nearly 8 years of work. There are no integers that will make this equation true if n is greater then 2. (If n = 2, we have the Pythagorean triples).

See more on ...

	Magic Squares: examples of a variety of magic squares of various types.
	Magic Stars: some examples of different orders between 5 to 12d, with information.
	Other Patterns: a few selections from my collection of over 300 number patterns.

See my original Geocities, now Magic-squares.net pages for more patterns
As of November 2007 it contains about 75 pages.

See my Shaw Magic Cubes pages
As of November 2007 it contains about 45 pages.

New ! See my Shaw Magic Tesseract (4-D) pages
On November 22, 2007 I posted 11 pages to this new site.

This page was last updated Monday November 02, 2009

Your comments are appreciated. Please e-mail me at harveyheinz@shaw.ca

Patterns in Numbers

Contents

Introduction

Magic Squares

Magic Stars

Other Patterns

Introduction

See more on ...