*The following information comes from a wonderfully readable math history book by Julia E. Diggins called, STRING, STRAIGHT-EDGE, & SHADOW, THE STORY OF GEOMETRY Copyright 1965, Published by Viking Press and by The Macmillan Company of Canada Limited.

A book well worth the time. If you would like to go back in time and learn what the birth of mathematics must have been like, this book is for you. This link may help you locate a copy if your library does not have one.



The early history of Greek geometry is a mixture of myth, magic, shapes and rules, and most of it revolves around  the fabulous figure of Pythagoras.  In fact without this man, school may never have been invented nor much of what we know of mathematics!

The latter part of the 6th century B.C. was still a time of superstition.   Most men continued to believe that gods and spirits moved in the trees and the wind and the lightning.  Cults were popular all over the Greek world - "mysteries," they were called.  These cults promised to bring their members closer to  the gods in secret rites.

Pythagoras was the head of one of these cults.  His cult, known as the secret brotherhood, was one that worshiped numbers and numerical relationships.  His reputation for wisdom and magic grew so strong that, even while he was still alive, some people referred to him as the son of the god Apollo.

Now let's see how this all started........

Pythagoras was born in the late 6th century B.C. on the island of Samos.  His mother was most likely a Phoenician, his father a Greek stonecutter.   He was one of those rare, truly genius types.  He was very smart and thirsted for all the knowledge he could find. 

At a young age he left home to travel the known world and learn everything he could find. He studied under the Greek named Thales who was just beginning to discover the concepts of geometry.  Thales encouraged the young Pythagoras to travel for himself in the ancient lands and study the development of learning at its source.

So Pythagoras went to Babylon and studied with the Chaldean stargazers.He studied where knowlege was at it's peak.  He went to Egypt and studied the lore of the priests at Memphis and Diospolis.The Egyptians taught him much. 

In Egypt he studied with the people known as the "rope-stretchers".  These were the engineers who built the pyramids. The "rope stretcher" were comparable to civil engineers.

They held a very special secret in the form of a rope tied in a circle with 12 evenly spaced knots.  It turns out that if the rope was pegged to the ground in the dimensions of 3-4-5,  a right triangle would emerge instantly. The amazing power in this rope is still used by carpenters today.

This enabled them to lay the foundations for their buildings accurately.

He traveled to all the known parts of the Mediterranean world. During his travels he came to the conclusion that the earth must be round.  In history, he is given credit as the first person to spread this idea.

Pythagoras spent many years learning by travelling.  Some say he made it the whole way to India and was deeply influenced, for he took up Oriental dress, including a turban.  Many of his mystical ideas like number magic and reincarnation, were typical of the East.

Finally he returned home.  He was probably the single most educated man on the face of the earth at that point.  He wanted to share what he knew, but the people of  his home town Samos were less than enthusiastic.

Tired of finding no one who would listen to his learning, he decided to "buy" a student.  He found a homeless child and offered him a bribe.  Pythagoras would pay him three obli for every lesson the boy mastered.

Now the boy thought this was great.  He could sit all day in the shade of a large tree and listen to this old man and could make better wages than in a whole day's work in the hot sun. Naturally, he concentrated hard while Pythagoras introduced him to mathematical disciplines.

From the simple calculations of the Egyptian rope-stretchers, to the methods of the Phoenician navigators, to abstract rules and reasoning, Pythagoras led his pupil on.  Soon the subject became so interesting that the boy begged for more and more lessons. 

At this point, Pythagoras explained that he could not afford to pay someone to just listen to him anymore.  So they reached a bargain.  The boy had saved enough to pay Pythagoras for his lessons.  This was probably the start of organized education.

Eventually Pythagoras left the island of Samos and settled on the Isle of Croton.  This is where he formed his Secret Brotherhood. 

The Secret Brotherhood was a religious order with initiation rites  and purifications and Pythagoras was its supreme unquestioned leader.  He taught them that KWOWLEDGE WAS THE GREATEST PURIFICATION, and for them knowledge meant mathematics.

The most famous discovery that Pythagoras made came from his fascination with the Egyptian 3-4-5 rope-stretchers triangle.

He had spent years thinking about it and what magic it might hold.  Lo and behold, DID hold a great deal of mathematics and for Pythagoras that was the same thing as magical power.

One day while drawing in the sand he found that if a square is drawn from each side of the 3-4-5 triangle, the area of the two small squares added together equals the area of the large square.


9 + 16 = 25

He examined other right traingles and found it was true with them also:
6^2 + 8^2 = 10^2
36 + 64 = 100

9^2 + 12^2 = 15^2
81 + 144 = 225

So he decided to announce it as a revelation from the god Apollo, who many claimed to be his father.

When he revealed this finding to his followers, he used the general terms of  a & b for the shorter legs and c for the longer side which he gave the name "hypotenuse". Thus we have the famous PYTHAGOREAN THEOREM!

a^2 + b^2 = c^2

A book well worth the time.