Lancashire Mathematics Challenge 2008 County final LMC 2008

Lancashire Mathematics Challenge 2008 County final LMC 2008

LMC 2008 Doctor Who and famous mathematicians Part 2 “The Doctor must go away……. ”

LMC 2008

Fibonacci sequences 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, ” LMC 2008 Fibonacci sequences are often used by the Doctor when coding messages. You will have to recognise them and work out other terms.

Fibonacci sequences The original Fibonacci sequence is: 1, 1, 2, 3, 5, 8, 13, 21…………… Each term is found by adding the two previous terms: 1+1=2 1+2=3 2+3=5 3 +5=8 5 + 8 = 13 and so on. LMC 2008 The next term of this Fibonacci style Sequence: 1, 3, 4, 7, 11, 18, 29………… can be found by adding the last two terms. 18 + 29 = 47, the next term is 47

Audience Quiz What are the missing terms in these Fibonacci sequences: LMC 2008 1. 3 , 5 , __ , __. 2. 4 , __ , 9 , __. 3. __ , 6 , __ , 16 , __. 4. a , b , __.

LMC 2008

Ada Lovelace Augusta Ada Byron King, Countess of Lovelace was born on December 10 th 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 LMC yet built! 2008

The Doctor has started to sort out the distinctive properties of aliens and he is using a binary code. LMC 2008 I must be sure that you can continue this and use the information in the Doctor’s absence.

The Doctor has a list of questions which can only be answered by a YES or a NO. 1. Are the adult aliens over 2 m 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 1 An answer of NO registers the digit 0 LMC 2008

Audience Quiz You have the completed answer forms for two aliens. Put this data into binary code. Draw an alien who fits the data 00110 LMC 2008

LMC 2008

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. LMC 2008 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.

The number in each cell is found by adding the two numbers in the cells directly above 1 1 In row 3 2+1=3 LMC 2008 1 1 2 3 4 10 Row 1 1 3 6 Row 2 1 1 Row 3 1 1

Audience Quiz Fill in the empty Cells in the Pascal’s Triangle on your quiz sheet. The bottom row in your diagram is row 8. LMC 2008 What is the total of The numbers in row 9?

LMC 2008

René Descartes LMC 2008 René Descartes (1596 – 1650) was a French philosopher whose work, La géométrie, includes his application of algebra to geometry from which we now have Cartesian geometry. The Doctor uses my co-ordinates to plot journeys. I must be sure that you can use them and apply some transformations.

There are four instruction sheets detailing the co-ordinates which describe the object on the journey. When you have sorted these out, get together to solve the problem of the journey. LMC 2008

Audience 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? LMC 2008 WARN THE DOCTOR!

LMC 2008

Henry Ernest Dudeney Henry Dudeney was born on the 10 th 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. LMC 2008 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.

LMC 2008 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.

Audience quiz One of Dudeney’s famous puzzles is: SEND MORE MONEY In this addition sum each letter represents a digit, different letters being different digits. Find the sum. LMC 2008

LMC 2008

LMC 2008

Marcus du Sautoy I need your help! I have the opportunity of going with the Doctor on his new adventure. LMC 2008 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!

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? LMC 2008 You have been sent four extra shirts. Which team will want these?

Audience quiz Marcus wants to set up a reserve team. These will also be numbered in PRIMES. LMC 2008 He is using the first thirteen primes for his first team, can you work out the next thirteen for him?