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Primary Magazine - Issue 24: A little bit of history

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 10 May 2010 by ncetm_administrator
Updated on 01 June 2010 by ncetm_administrator


Primary Magazine Issue 24statue of Euclid at the Oxford University Museum of Natural History - photograph by Wilson44691

A little bit of history
Famous Mathematicians - Euclid

statue of Euclid at the Oxford University Museum of Natural History - photograph by Wilson44691Euclid of Alexandria lived around 300BC. He is, by all accounts, the most prominent of the earliest mathematicians. He is best known for his essay on mathematics, The Elements. This work shows the logical development of geometry and other branches of mathematics and it has influenced all branches of science since, particularly mathematics and the exact sciences. It has been studied for over 2000 years and has been translated into many old and modern languages. It was clearly an extremely long essay because it was divided into 13 books!

More than one thousand editions of The Elements have been published since it was first printed in 1482. The long-lasting nature of The Elements must surely make Euclid the leading mathematics teacher of all time.

Little is known of Euclid's life – the date and place of Euclid’s birth and the date of his death are unknown. We don’t know how he died and we have little knowledge of what he did during his life. We don’t know what he looked like and therefore any pictures of him are products of the artist’s imagination!

There are a couple of references to him, written centuries after he lived, by the Greek philosopher Proclus and the Greek mathematician Pappus of Alexandria. From these we know that he taught in Alexandria in Egypt and that he may have studied at Plato’s Academy in Greece.

There is other information written about him that is considered to be entirely fictitious, for example, that he was the son of Naucrates and that he was born in Tyre – or, according to another source, Megara, but this could be confusion with the philosopher, Euclid of Megara.

Over the years, three possible suggestions have been proposed as to who he actually was:

  • he was a historical character who wrote The Elements and the other works attributed to him
  • he was the leader of a team of mathematicians working at Alexandria. They all contributed to writing the ‘complete works of Euclid’, even continuing to write books under Euclid's name after his death
  • he was a fictional character - the ‘complete works of Euclid’ were written by a team of mathematicians at Alexandria who took the name Euclid from the historical character Euclid of Megara who had lived about 100 years earlier.

Despite this lack of actual knowledge, whoever he might have been, Euclid has had a significant influence in the world of mathematics due to his writings.

 Back to top

Back to the famous The Elements
Oxyrhynchus papyrus showing fragment of Euclid's ElementsApparently, the results of this work originated earlier than when Euclid wrote about them, but he was able to present them in a single, logical and coherent framework making it easy to use and reference. They remain the basis of mathematics today.

The first eight of the 13 books consider geometry, now known as Euclidean geometry to distinguish it from the other non-Euclidean geometries that were discovered in the 19th century. Among other things, he claimed that it is possible to draw a straight line between any two points, all right angles are equal and only one line can be drawn through a point parallel to a given line.

You could ask the children to explore these – are these statements always/sometimes/never true?

Books seven to nine look at number theory, and consider such things as the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid's lemma on factorisation and the Euclidean algorithm for finding the greatest common divisor of two numbers.

Why not try some investigations?
For example:

Explore the four perfect numbers – how are they made up using the clues below:
6 = 1 + 2 + 3
28 = 1 + 2 + 4 + 7 + 14
496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
8 128 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1 016 + 2 032 + 4 064

What is a prime number? What do you notice about the prime numbers to 100?

What does it mean to factorise? What are the prime factors of 24 140 etc?

Book 10 deals with irrational numbers and books 11 to 13 deal with three-dimensional geometry.

In addition to The Elements, at least five works of Euclid have survived to the present day. They follow the same logical structure, with definitions and proved hypotheses.

Dutch mathematician B L van der Waerden made this comment in his assessment of the importance of The Elements:
“Almost from the time of its writing and lasting almost to the present, the Elements has exerted a continuous and major influence on human affairs. It was the primary source of geometric reasoning, theorems, and methods at least until the advent of non-Euclidean geometry in the 19th century. It is sometimes said that, next to the Bible, the "Elements" may be the most translated, published, and studied of all the books produced in the Western world.”

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