This is the first blog from GCSE Maths Tutor about the wider world of mathematics. So look forward to blogs on what's new in math, famous mathematicians, jokes, brain teasers, weird math symbols and just about anything else mathematic.
Here is an entertaining story about the mathematician Carl Friedrich Gauss, from when he was a young boy at school, showing his genius at the tender age of eight.
It was a hot sultry summer afternoon and the teacher was sitting back in his chair trying not to fall asleep after his large lunch.
"Class!" he said in his characteristic gruff voice, standing up and getting everyone's attention immediately.
"We shall be doing arithmetic this afternoon. No, don't get your books out. It's written work. All you need is a single page in your jotter."
"What I want you to do is to add up all the numbers from 1 to 100. "
"Good luck!" he said, smiling to himself, 'well that should keep them busy for a while';
the intention being that he could shut his eyes for ten minutes or so.
"Sir!" called out a boy almost at once, "I know the answer Sir."
"Yesss, Gauss." replied the teacher, looking unhappy that his rest was denied.
"It's 5050," said the boy.
"My word Gauss. You are right," exclaimed the teacher, flustered and red faced.
"You are right. How on earth did you do that?"
"Class!" he said in his characteristic gruff voice, standing up and getting everyone's attention immediately.
"We shall be doing arithmetic this afternoon. No, don't get your books out. It's written work. All you need is a single page in your jotter."
"What I want you to do is to add up all the numbers from 1 to 100. "
"Good luck!" he said, smiling to himself, 'well that should keep them busy for a while';
the intention being that he could shut his eyes for ten minutes or so.
"Sir!" called out a boy almost at once, "I know the answer Sir."
"Yesss, Gauss." replied the teacher, looking unhappy that his rest was denied.
"It's 5050," said the boy.
"My word Gauss. You are right," exclaimed the teacher, flustered and red faced.
"You are right. How on earth did you do that?"
Gauss did the sum by using a neat trick to do with pairing numbers.
He added the first and last numbers together (1 + 100). This made 101. Then he added the second and second-last numbers together (2 + 99). This made 101 aswell. He new that there would be 50 such pairs of numbers that would add up to 101. Then all he had to do was multiply the number of pairs (50) by the sum of each pair (101).
So 50 x 101 = 5050
Try it for yourself. What is the sum of all the numbers from 1 to 1000?
(answer in the next blog)
Hope you enjoyed this snippet. Will be writing again soon.
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1 comment:
That is a neat trick! I've tried it and it works really well. You can impress a lot of people with Gauss' pairing technique. I first heard about this through my Maths tutor Nottingham. Anything to make it more exciting and easier!
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