SERVICE ABOVE SELF
JULY 2017: ISSUE 100
Carl Friedrich Gauss (1777-1855) is recognised as being one of the greatest mathematicians of all time. During his l i f e t ime h e ma d e s i g n i f i c a n t contributions to almost every area of mathematics, as well as physics, astronomy and statistics. Like many of the great mathematicians, Gauss showed amazing mathematical skill from an early age, and there are many stories which show how clever he could be. The most well-known story is a tale from when Gauss was still at primary school. One day Gauss' teacher asked his class to add together all the numbers from 1 to 100, assuming that this task would occupy them for quite a while. He was shocked when young Gauss, after a few seconds thought, wrote down the answer 5050. The teacher couldn't understand how his pupil had calculated the sum so quickly in his head, but the eight year old Gauss pointed out that the problem was actually quite simple. He had added the numbers in pairs - the first and the last, the second and
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the second to last and so on, observing t h a t 1+1 0 0=1 0 1 , 2+9 9=1 0 1 , 3+98=101,
...so the total would be 50 lots of 101, which is 5050. It is remarkable that a child still in elementary school had discovered this method for summing sequences of numbers, but of course Gauss was a remarkable child. Fortunately his talents were discovered, and he was given the chance to study at university. By his early twenties, Gauss had made discoveries that would shape the future of mathematics. Whilst the story may not be entirely true, it is a popular tale for maths teachers to tell because it shows that Gauss had a natural insight into mathematics. Rather than performing a great feat of mental arithmetic, Gauss had seen the structure of the problem and used it to find a short cut to a solution. Gauss could have used his method to add all the numbers from 1 to any number - by pairing off the first number with the last, the second number with the second to last, and so on, he only had to multiply this total by half the last number, just one swift calculation. Can you see how Gauss's method works? Try using it to work out the total of all the numbers from 1 to 10. What about 1 to 50 and 1 to 500? The answers are at the bottom of the back page.
The human brain is a busy pla ce. We each hav e about 100 billion neurons. Each of the 100 billion n e u r o n s
a c t i v e l y
communicates with 1000 - 10,000 others. Each of the 100 billion neurons can be 'on' or 'off', and can generate 2100,000,000,000 (or roughly 1030,000,000,000) unique brain states. The number of the possible brain states is greater than the number of particles in the universe!
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