A note

Dear all,

It has been an extremely long time since I have posted anything on here. The reasons for this is because I have seeing some of this wonderful world!

On my little adventures I have come across quite a lot of interesting maths (as if you would believe such a thing). So I will endeavour to explain all and give you some lovely little facts from around the world of Mathematics.

Regards,

Onemanandhismaths

Mathematician of the week: Hubble

Mathematician of the week:

Edwin Hubble: 1889 -1953

Hubble was born on the 20^th November 1889 In Missouri and apart from changing our view of the universe he was actually rather good at sport! He held a state record for the high jump and he also played basketball for the University of Chicago.

He went to Oxford to study law and it was his return to America which heralded the start of his work into astronomy. He helped determine what galaxies are during the 1920’s and he also measured the distance to the Andromeda galaxy in 1924. This also helped to form the conclusion that it was a similar size to our galaxy!

Hubble then began to measure the distances to other galaxies and he realised that their apparent brightness was an indication of their distance from us. Now another smart thing that Hubble calculated was the speeds at which these galaxies were travelling at. He performed this calculation by using the Doppler shift of the light emitted by the galaxies. You can think of the Doppler shift as if you moved a sound source away from you the sound becomes lower then as a light source moves away the light becomes redder.

Hubble then found that the amount of redshift was proportional to its distance. This means that galaxies are moving away from us and each other as the universe expands! Brilliant! (this happened in 1929)

The Hubble telescope bears his name in recognition of his fantastic work.   

Maths fact!

Right everyone I know that we haven't had a fact in a while so...........

The sum of the reciprocals of all prime numbers diverges:

This was proved by Leonhard Euler in 1737!

This also links to the another fact that there is an infinite number of primes (two facts for the price of one!) which was proved by Euclid (300 B.C) way before Euler was even a twinkle in his mothers eye.

Problem 4

 

Here is an nice gentle problem to kick off a new season of problems. I found this one from a British Mathematical Olympiad (1993)

 

Find the first integer n > 1 such that the average of

 

12 , 22 , 32 , . . . , n2

is itself a perfect square.

Have a go you might surprise yourself!

Wolfram Mathworld

Wolfram Mathworld a fantastic resource for all you mathematicians out there! I have spent a many hours just searching for some of my favourite topics!

It is extremely easy to use and it offers the user clear definitions. It has a very simple interface where you can search for topics or just look around at your own pace. You really must try it! (I sound like some tedious advert!)

Try it out at:

http://mathworld.wolfram.com/

Maths Fact!

The set of numbers {1,2,...,n} has the property that the sum of its cubes is the square of its sum!

1³ + 2³ + ... + n³ = (1 + 2 + ... + n)²

 

 

Tell your friends and family. They will like you for it!

Hardy: A Mathematician’s Apology

Hardy: A Mathematician’s Apology

You rarely get an insight into the workings of a mathematician mind. However in, A Mathematician’s Apology G.H Hardy gives an excellent account of what mathematics is. Its usefulness (or lack of) and how it is more than just a science it is a creative art!

The apology was written as his powers as a mathematician were on the decline. This detail offers the reader an insight into how Hardy viewed his career as a mathematician and how he viewed some of his contemporaries. He mentions his work with Littlewood, his discovery of Ramanujam and his time at Oxford and Cambridge.

Hardy gives a brilliantly composed account of ‘real’ mathematics and this comes from his background in pure mathematics. He was known as ‘a real mathematician’ and this style of thinking comes across in the well-constructed, eloquent argument he proposes for his subject. His dislike of war and the lack of involvement that mathematics has had upon it is displayed in the book. He acknowledges the use of applied mathematics on ballistics however he hardly ranks them as ‘real’. He further states that the mathematics involved are “indeed repulsively ugly and intolerably dull.” You can’t help but like the language he uses.

This book is a must for anyone (not just mathematicians) as it is not only fantastically written but it offers an insight into one of the finest mathematical minds of the twentieth century.