MathHistory1a: Pythagoras' theorem

Pythagoras' theorem is both the oldest and the most important non-trivial theorem in mathematics.

This is the first part of the first lecture of a short course on the History of Mathematics, by N J Wildberger at UNSW (MATH3560 and GENS2005). We will follow John Stillwell's text Mathematics and its History (Springer, 3rd ed). Generally the emphasis will be on mathematical ideas and results, but largely without proofs, with a main eye on the historical flow of ideas. A few historical tidbits will be thrown in too...

In this first lecture (with two parts) we first give a very rough outline of world history from a mathematical point of view, position the work of the ancient Greeks as following from Egyptian and Babylonian influences, and introduce the most important theorem in all of mathematics: Pythagoras' theorem.

Two interesting related issues are the irrationality of the 'square root of two' (the Greeks saw this as a length, but not as a number), and Pythagorean triples, which go back to the Babylonians. These are closely related to the important rational parametrization of a circle, essentially discovered by Euclid and Diophantus.

The Greeks thought of mathematics differently than we do today, and all students can benefit from a closer appreciation of the difficulties which they saw, but which we today largely ignore.

Category:

Education

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• MathHistory1a
• History
• of
• mathematics
• Wildberger
• Stillwell
• Greek
• Pythagoras
• theorem
• geometry
• UNSW
• square
• roots
• circle
• rational
• parametrization
• Euclid
• Diophantus
• Babylonians
• Pythagorean
• triples
• ancient
• Egyptians

[gregg4]

Great lecture but it has a mistake though.

He writes the year zero on the blackboard. There was no year zero.

European mathematicians using roman numerals started counting at one.

There is no zero in roman numerals. So there was 1 AD (or CE) and the year before that was 1 BC (or BCE).

[njwildberger]

Hi gregg4, Thanks for the comment. I do not think it is a major point, but I feel I must disagree with you. There might not have been a year zero in Roman times (in fact clearly the system only started some time after Jesus' death) but this is now 2011 and these days there is a year zero by convention; or at least there ought to be. A question: how many years between 20 B.C and 30 A.D? If someones dates are these, how long did they live? Surely any reasonable system has the answer as 50 years.

[MarleyNicholeTravis]

This should be taught as a requirement for any mathematically centric degree.Im a Mechanical Engineering student and my brain is well suited for math,& I feel its very important to understand the principles & reasoning behind the math, rather than just being able to follow predefined rules and systems.If you understand the context, reasoning, and principles involved I feel it exponentially expands your critical thinking ability.Math is the base for so many fields & the context is never pushed?

[cama708]

you videos are great! keep up the good work..

[pppppvideo]

Nice lecture. Sir kindly make a playlist of Lectures about Group Theory. I hope you will elaborate it very nicely as you did previously. Kindly oblige the matter!!!

Fiaz (Pakistan)

[hariveerakumar150590]

@gregg4 no worries mate.

[gregg4]

@hariveerakumar150590

Thanks for your very thoughtful answer.

[MrTelaviv123]

But the greeks didnot use the Hindu number system. Their symbols for number was quiet different eg, aplha, phi , epsilon etc.

[hariveerakumar150590]

@gregg4 fuck you

[dannyll15]

your lecture just inspired me to learn im going to go get ahead in my math class and my physics class.

[Nooreazy]

i like this lecture thx.

[Nooreazy]

Y U NO MENTION al khwarizmi?