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It’s a Numbers Game

I found a clue: Outside of Science World, there are rectangles all over the place — big coloured tiles. The kind of thing that would impress architects and Piet Mondrian fans. 

The bottom layer is pretty squashed, not that high.
The next layer is the same height as the first one.
The third layer is 2 times as high, the next one is 3 times higher. 
A pattern… 1,1,2,3… the next one should be 4.

It gets weird.

The next layer is 5 times as high, then 8 times as high, then 13 times…  What is going on?

1,1,2,3,5,8,13…

Someone had hidden a Fibonacci Sequence on the TELUS World of Science building. Each number is formed by adding together the two previous numbers:

1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8
8+5 = 13

A mathematician named Leonardo Bogollo first studied it. Rumour has it he was trying to calculate how many rabbit babies you get from one pair of rabbits.  Numbers in this sequence come up a lot in nature. When you count the number of spirals in each direction on a pinecone or a pineapple you end up with Fibonacci numbers (and some sticky hands).

Spies and codebreakers look for patterns like this all the time. And shortcuts, too.

In the Fibonacci sequence you add 2 numbers together to get the next number. Suppose you had to add more than 2 numbers at a time?  Add every number from 1 to 10 together and give me the total.  Go try it and come back. I’ll wait.

How long did that take you? A mathematician named Carl Gauss once had to add every number from 1 to 100. It took him two seconds and he was only 8 years old. Carl found there was a shortcut to solve the addition problem. Take a look:

Write down the numbers 1 to 10

1

2

3

4

5

6

7

8

9

10

Underneath them write the same numbers in reverse order

10

9

8

7

6

5

4

3

2

1

Carl realized that if you add the top and bottom number in each column they always add up to 11. 

11

11

11

11

11

11

11

11

11

11

You have a total of ten sets of 11

10 x 11 = 110

Because you added the numbers from 1 to 10 twice (once forward and once backwards) divide the total number in half to get the final answer

110/2 = 55


Identifying patterns and creating shortcuts is great in math class because you'll be able to take information and find ways to interpret it. It might also mean that you'd be good at the reverse, creating patterns to make information difficult to understand, or encrypting information. A lot of private information today is protected using RSA Encryption. It is used for credit card transactions, digital radio signals, even emails you don’t want other people reading. If you see an https:… address in your web browser, chances are the site is using RSA. (the R, S and A are actually the initials of the team that invented it—pretty sweet). RSA keeps information secure using some very complicated mathematics that is almost impossible to crack, even for a computer. 

Unless someone has come up with a shortcut…

Until next week, keep on counting those rectangles.  - Cluckminster

 

This week’s challenge:

Try these number sequences. What number comes next?

2,4,6,8,10….

1,4,9,16,25,36….

31,28,31,30,31,30…

3,3,5,4,4,3,5,5,4,3,6…

Share your answers with Agent Cluckminster at cluckminster@scienceworld.ca


Check out Cluckminster's previous mission briefing.