Yes, we have no zeros!

Well surprisingly we didn't always have a zero. Up until the 12th century AD you could say "Yes, we have no parsnips". But you couldn't write down 'parsnips = 0'. The number zero hadn't yet come to Europe. At that time it was alive and well and living in the Arab world. Infact it had been doing so for a number of centuries.

The first record of it being used was in India in the 9th century AD. Zero only arrived here in the 12th century along with a whole batch of its friends: 1 2 3 4 5 6 7 8 9 - these being the first 10 Cardinal or Natural numbers.

All these numbers were introduced by an Italian merchant whose name might be familiar to you - Fibonacci (pronounced fee-boh-nach-ee). Fibonacci traded between Italy and North Africa so was well acquainted with Arab culture.

Fibonacci is famous for his series(0 1 1 2 3 5 8 13 21 34 etc.) which has recently come to public attention with the book and film The Da Vinci Code. However, few would doubt his most important contribution to mathematics was the introduction of the Arab number system. The new numerals along with many mathematical methods(e.g.long multiplication & division) are described in his book "Liber Abacci" (pronounced lee-ber ab-ah-chee).

The word "zero" appears to have come (surprise surprise!) from the Arab world too, but evolved through through various languages from an almost unrecognizable root.

sifr(Arab) zephyrus(Greek) zephirum(Latin) zefiro(Venetian) zero(Italian)

Zero is such an important number; perhaps the most important. It is especially useful for describing very large and very small numbers. Here are some examples of its use. You may have heard some of these names before. Now you can appreciate where the words come from.

a googol - 10 to the power of 100 (10¹⁰⁰)

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

...a really big number you will agree!

But here's an even bigger one:

a googolplex - 10 to the power of a googol (10^googol)

As a way of imagining how big even a googol is: it is estimated that there are between 10⁷⁹- 10⁸¹ elementary particles in the known universe.

At the other end of the scale, small numbers, look at the zeros in this number:

0.000 000 001 metre - called a nanometre (10^-9 m)

nanotechnology deals with scales of this magnitude

So ends our little excursion into the world of zero. I'll have more to interest and enthrall you next time.

bye for now,

GCSE Maths Tutor

GCSE Maths Tutor - Gauss's number pairing

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?"

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.

GCSE Maths Tutor