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Famous Theorems

Proof of Pythagoras' Theorem in Euclid's GreekThe Italian-American mathematican, Juan Carlos Rota (1932-1999) wrote … We often hear that mathematics consists mainly of “proving theorems.” Is a writer’s job mainly that of “writing sentences?”  Mathematics is much, much more than just dealing with theorems.

Having said that, just as a good writer knows how to craft his/her sentences, a good mathematican builds their understanding on theorems.  Theorems are the firm foundations, the principles upon which the rest of mathematics is built.  Everything that we ‘know’ and every skill that we use in mathematics has been analysed and proven by someone … from the very mundane and practical to the amazingly abstract and beautiful.

Why does 1 + 1 = 2?  Well, we know it does … but why?  Such thoughts are not trivial.  Entire books have been written about such matters.  The great British astrophysicist, Sir Arthur Eddington (1882 – 1944), wryly observed, “We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about ‘and.’”

The image to the left is of Euclid’s proof of Pythagoras’ Theorem in Greek.  In his day, all the Greek would have been written in capital letters and run together, but the text used here is easier to read.  Why did I choose this image?  Simply because Pythagoras’ Theorem is one of the most famous theorems of mathematics.  Also, the fact that you can see it in its Greek form underscores the fact that mathematics is a discipline that transcends cultures and times.  I found the image on a most marvellous site designed by J B Calvert called Reading Euclid. Let me encourage you to browse this site and learn something of the Greek (language) from which our geometry came. What J B Calvert shares about Pythagoras’ Theorem is fascinating!

Sadly, I could not find out how to contact him for permission to use this image (and his site was last revised on 16 June 2002) … but I hope he doesn’t mind.

I recently read that mathematicans today are expanding the numerous branches of mathematics at something like 250,000 published theorems per year!  Obviously, no one can keep up with such rapid development.  I certainly will not try.  All you will see here are some key historical theorems presented and discussed … as I am able to add them.

From the beginning of my schooling I had struggled with Mathematics. Highly discouraged by my results, I grew to eventually hate Maths and lost all motivation to improve. Then part way through year seven my parents decided to send me to Crystal Clear Mathematics. Graeme was able to quickly identify areas I needed to improve and explain Maths in a way that finally made sense to me. I was able to understand Maths. This in turn then affected my confidence in my own ability.

Since working with Graeme I have gone from failing to significantly improved results. I now get As & Bs both in examinations and for assignment tasks. Graeme is patient, kind and his tutoring is individualised. He was so helpful and I am grateful for his help.

Tessa M (student, 2014-2017)

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