LMC2008

Lancashire Lancashire Mathematics ChallengeMathematics Challenge

20082008

County finalCounty final

LMC2008

Doctor Who and Doctor Who and famous famous

mathematiciansmathematicians

Part 2Part 2

““The Doctor must go The Doctor must go away…….”away…….”

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Fibonacci sequences

Fibonacci sequences are often used by the Doctor when coding messages. You will have to recognise them and work

out other terms.

Leonardo of Pisa was simply known as Fibonacci. Born in Pisa around 1170 he became a mathematician, considered by some as “the most talented mathematician of the middle ages,”

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Fibonacci sequencesFibonacci sequencesThe original Fibonacci sequence is:The original Fibonacci sequence is: 1, 1, 2, 3, 5, 8, 13, 21……………1, 1, 2, 3, 5, 8, 13, 21……………Each term is found by adding the twoEach term is found by adding the twoprevious terms:previous terms:1 + 1 = 2 1 + 2 = 31 + 1 = 2 1 + 2 = 32 + 3 = 5 3 + 5 = 82 + 3 = 5 3 + 5 = 85 + 8 = 13 and so on.5 + 8 = 13 and so on.

The next term of this Fibonacci styleThe next term of this Fibonacci styleSequence: 1,3,4,7,11,18,29…………Sequence: 1,3,4,7,11,18,29…………can be found by adding the last twocan be found by adding the last twoterms.terms.

18 + 29 = 47, the next term is 4718 + 29 = 47, the next term is 47

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Audience QuizWhat are the missing terms in

these Fibonacci sequences:

1. 3 , 5 , __ , __ , __ , __ .

2. 4 , __ , 9 , __ , __ , __ .

3. __ , __ , 6 , __ , 16 , __ .

4. a , b , __ , __ , __ , __ .

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Ada Lovelace

Augusta Ada Byron King, Countess of Lovelace was born on December 10th 1815, the first child of poet Lord Byron and his wife Annabella.

Today she is appreciated as the first computer programmer, since she was writing programs for a machine that Charles Babbage had designed but not yet built!

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The Doctor has started to sort outthe distinctive properties ofaliens and he isusing a binarycode.

I must be sure that you can continue this anduse the information in the Doctor’s absence.

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The Doctor has a list of questions which can only be answered by a YES or a NO.1. Are the adult aliens over 2m tall?2. Are the adult aliens biped?3. Do the aliens possess some kind of

psychic communication?4. Can the aliens fly?5. Can the aliens assimilate all

languages?

An answer of YES registers the digit 1An answer of NO registers the digit 0

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Audience Quiz

You have the completed answer forms for two aliens. Put this data into binary code.

Draw an alien who fits the data

0 0 1 1 0

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Pascal’s triangle and the Dalek’s path

Blaise Pascal was born in 1623 in France. Despite the fact that his father decided not to let him study mathematics as a young boy, Blaise started to study the work of Euclid by himself when he was 12, and soon became known as a child prodigy.

The Doctor has discovered that the Daleks base their movements on cells from my triangle. You will need to study my triangle and recognise the patterns formed.

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1

1 1

1 2 1

1 3 3 1

1 4 6 1

1 10 1

Row 1

Row 2

Row 3

The number in each cell is found by adding the two

numbers in the cells directly above

In row 3

2 + 1 = 3

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Audience QuizAudience QuizFill in the emptyCells in the Pascal’sTriangle on yourquiz sheet.

The bottom row inyour diagram is row 8.

What is the total ofThe numbers in row 9?

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René Descartes(1596 – 1650) was aFrench philosopherwhose work, Lagéométrie, includeshis application ofalgebra to geometryfrom which we nowhave Cartesiangeometry.

René Descartes

The Doctor uses my co-ordinates to plot journeys. I must be sure that you can use them and apply some transformations.

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There are four instruction sheetsdetailing the co-ordinates whichdescribe the object on the journey.

When you have sorted these out, gettogether to solve the problem of thejourney.

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Audience QuizAudience Quiz

On your quiz sheet you have a grid and a set of axes.

You also have a set of co-ordinates to plot, join them in the order you plot them. Remember “across first then up.”

Can you see the outline of an alien?

Do you recognise it?

WARN THE DOCTOR!

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Henry Ernest Dudeney

Henry Dudeney was born on the 10th April 1857 in Sussex. He came from a family which had a mathematical tradition and by the age of nine he was composing problems and puzzles.

Captain Jack at Torchwood asked for my help with security. You will need to solve the problem of the keys if you need to use their services.

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The keys to Torchwood are square which slot into a pre-formed keypad. The problem you will have is that each key is cut into pieces, you will have to fit the pieces together, into a square, before you can access Torchwood.

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Audience quiz

One of Dudeney’s famous puzzles is:

S E N D

M O R E

M O N E Y

In this addition sum each letter represents a digit, different letters being different digits. Find the sum.

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Marcus du Sautoy

I need your help! I have the opportunity of going with the Doctor on his new adventure.

I have already arranged for colleagues at Oxford University to continue my research but I need you to take care of my football team.

I need someone who understands PRIMES!

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As you saw in the film Marcus’ football team only have PRIME numbers on their shirts. There are eleven players and two reserves, so Marcus will need shirts with the first thirteen primes on the back.

Captain Jack is setting up a rival team. His team will wear ODD NUMBERS WHICH ARE NOT PRIME on their shirts. What are the first thirteen numbers which are needed for this team?

You have been sent four extra shirts. Which team will want these?

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Audience quiz

Marcus wants to set up a reserve team. These will also be numbered in PRIMES.

He is using the first thirteen primes for his first team, can you work out the next thirteen for him?