A maths wizard has discovered the largest recognized prime number
and it's an amazing 17
MILLION digits long.
 |
| Maths Wizard |
You might not have to be a maths mastermind to know that a prime is
a number greater than 1, which can only be divided by itself and 1, like 2, 3,
5, 7, 11, but to find one that big, GCSE maths would be a good start.
However, in the numbers world, size doesn't matter when it comes to
the fascinating and bizarre.
Here is a magic trick behind something many of us struggle to get
our heads around...
Multiplication and Addition
Doing Fibonacci’s Lightning
Calculation
On a piece of paper, write the numbers 1 to
10 in a column. You are now all set to amaze with the speed at which you can
add ten numbers.
Ask your friend to choose any two two-digit
numbers and write the numbers down in the first two spaces of your column, one
under the other. Your friend then makes a third number by adding these first
two numbers together and writes it below the first two, in effect starting a
chain of numbers. They make
a fourth number by adding the second and
third, a fifth by adding the third and fourth, and so on, until your column of
ten numbers is full.
To show how brilliant you are, you can turn
away once your friend has understood the idea, say after the seventh number in
the list. Now you can’t even see the numbers being written.
Meanwhile, with your back turned, you are
actually multiplying that seventh number by 11 to get the final answer.
Let’s imagine your friend chose 1 and 21 to
start with. The list would look like this:
1. 16
2. 21
3. 37
4. 58
5. 95
6. 153
7. 248
8. 401
9. 649
10. 1050
You now turn round and write the sum of all
ten numbers straight away!
Lightning quick, you say it is 2728. Let
them do it slowly on a calculator to show your brilliant mind skills are 100
per cent correct.
The final answer just involves multiplying
the seventh number by 11. Why?
Well this chain of numbers where the next
term is made by adding the previous two terms is called a Fibonacci sequence. Fibonacci sequences have
special mathematical properties that most folk don’t know about…
So let’s look at the trick. We start with
the two numbers A and B. The next number is A+B, the next number is B added to A+B which is A+2B and so on. Going through
the number chain we find:
Adding up
1. A
2. B
3. A+B
4. B+(A+B) = A+2B
5. (A+B)+(A+2B) = 2A+3B
6. (A+2B)+(2A+3B) = 3A+5B
7. (2A+3B)+(3A+5B) = 5A+8B
8. (3A+5B)+(5A+8B) = 8A+13B
9. (5A+8B)+(8A=13B) = 13A+21B
10. (8A+13B)+(13A+21B) = 21A +34B
Adding up all 10 numbers in the chain gives
us a grand total of 55A+88B
– check
it yourself. But look at the seventh number in your column… this line is 5A+8B. It is exactly the total
of the chain but divided
by 11!
So working backwards, you can get the final
total by multiplying the seventh term by 11. And the maths proves this
lightning calculation will work for any two starting values A and B.
It is up to you to present this trick in
such a way that it looks like you are just very, very clever. Which of course
you are, as you now know how to use a Fibonacci sequence for magic.
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