Tuesday 20 November 2012

Mathematician of the week: Hubble


Mathematician of the week:

Edwin Hubble: 1889 -1953

Hubble was born on the 20th 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.   

Friday 16 November 2012

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:
\sum_{p}\frac1p = \frac12 + \frac13 + \frac15 + \frac17 + \frac1{11} + \frac1{13} + \cdots = \infty
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.

Wednesday 14 November 2012

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!