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Primary Magazine - Issue 18: 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This page has been archived. The content was correct at the time of original publication, but is no longer updated.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 30 November 2009 by ncetm_administrator
Updated on 15 December 2009 by ncetm_administrator

Primary Magazine Issue 18Pythagoras
 

A little bit of history
Famous Mathematicians - Pythagoras

Pythagoras was born on the island of Samos in Greece in 570 BC. He died in 495 BC. You might like to plot these and a few AD dates on a timeline and see if the children can work out the differences between different BC and AD times and also the age Pythagoras was when he died.

map of Greece showing Samos

He is often thought of as a great mathematician and was known as the ‘father of numbers’, however some people have questioned the scope of his contributions to mathematics. Very little is known about him because none of his writings have survived and it is thought that many of the accomplishments credited to him may actually have been down to his colleagues and successors.

Over the years, because of the lack of information about him, Pythagoras became a bit of a legend and various myths arose surrounding him, for example, that the god Apollo was his father, that he had a golden thigh and that he could be seen in different places at the same time! There were several sources of factual information, which is what people have relied on in their studies of him. These came from his followers.

From these sources, historians have deduced that he was the son of Mnesarchus, a gem engraver or merchant, and his wife Pythias. He was born in Samos, the Greek island in the eastern Aegean. He lived there for 40 years and then spent many years travelling the world, finally settling in Croton in Italy.

It seems that he had a lot teachers assigned to him from many countries around the world, for example Chaldea, Greece, Egypt and the Orient. They taught him in their languages, which must mean he was, to some degree, a linguist. It is said that the Egyptians taught him geometry, the Greeks arithmetic and the Chaldeans astronomy. They may well have also given him his desire to travel. It is believed that Pythagoras travelled extensively visiting such countries as Egypt, Arabia, Phoenicia, Babylon and India in order to collect all the knowledge he could.

Many mathematical and scientific discoveries have been attributed to Pythagoras, including his famous theorem, as well as discoveries in music, astronomy and medicine.

Let’s look at two of them now:

The famous Pythagoras’ Theorem

Pythagoras found that in a right-angled triangle, the square of the hypotenuse (side opposite the right angle) is equal to the sum of the squares of the other two sides.

He proved this by drawing squares from the sides of the triangle. He found that the two squares alongside the perpendicular sides of the triangle (a and b) had the same area as the one alongside the hypotenuse (c).

the square of the hypotenuse of a triangle is equal to the sum of the squares of the other two sides

Why not ask the children to check it out! Sides a = 3cm, b = 4cm, c = 5cm so the adjacent square areas would be 9cm2 and 16cm2 which equals 25cm2, which is 5cm.

Can they come up with the simple formula for this: a2 + b2 = c2?

Try out some more examples on the Maths is Fun website.

You could provide the children calculators, give them the lengths of the perpendicular sides of a right angled triangle and ask them to work out the hypotenuse.

Tetractys

Pythagoras devised the tetractys which is a triangular figure made of four rows of dots which add up to the perfect 10. It was a sacred pattern for the followers of Pythagoras.

Today we can use it for a triangle investigation! Try this: show the dot pattern and ask the children to make 10 triangles:

Tetractys - ten dots, ten traingles

Next, ask them how many triangles they can see. Can they see the 13 that there are?

Tetractys - thirteen triangles, three lines removed to make seven traingles

Can they remove three internal lines to leave seven?

Pythagoras is also famous for various musical theories and investigations such as this one:

According to legend, Pythagoras was passing some blacksmiths at work. He thought that the sounds they were making when they hit their anvils were beautiful and harmonious. He decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths’ to learn how this happened by looking at their tools. He discovered that it was because the anvils were simple ratios of each other, one was half the size of the first, another was two thirds the size and so on.

Why not try an experiment with water in glasses filling them to capacities that are proportions of the first and see what happens!

For more of the discoveries of Pythagoras and a lot of fun, visit the Primary Magazine Issue 14, and watch Donald in Mathemagic Land (Parts 1, 2 & 3).

You can find more information about Pythagoras on these websites:

 
 
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