2. Why does Rudolph have a shiny nose? A mathematical look at Christmas Chris Budd

3. Can maths help Santa plan Christmas??

4. Santa’s problems How can he deliver all of the presents? How does he get down the Chimney? How does he find his way round the Earth? Why does Rudolph have a shiny nose?

5. Maths can answer all of these and … Helps you make great Christmas cards Makes Christmas magical Sorts out the presents in the 12 days of Christmas Arranges your Christmas party

6. Santa has 36 hours of darkness during Christmas night to deliver all of the presents Can he get round in time?

7. Worlds population is 6, 000, 000, 000 people Estimate N = 1, 000, 000 homes with good children Assume the homes are evenly distributed an average distance of H apart H H

8. But … surface area of the continents = 226,000,000,000,000 (226trillion) m2m2 Total area A taken up by the homes Total distance that Santa has to travel = NH = 475 Gm

9. Speed = 475Gm/(36*3600) = 3.6M metres per second Sound = 375 ms -1 Light = 300 M ms -1 That’s 9600 Mach

10. Hyperbolic shock wave So … why does Rudolph have a shiny nose? Sleigh is travelling at hypersonic speeds Air friction heats up Rudolph’s nose till it glows!

11. How does Santa get down the chimney? Small diameter chimney Large diameter Santa 10m

12. Solution one: Einstein’s theory of relativity Lorentz Contraction The faster you go the smaller you get C = 3 00 000 000 metres per second

13. Quick calculation 1 000 000 000 Homes visited in 36 hours 130 micro seconds per house Allow 1 micro second to descend a 10m chimney Chimney velocity V = 10 000 000 metres per second Lorentz contraction L after = 0.999 L before is not enough

14. Solution two: Use a fractal

15. Christmas is a magical time Maths can be part of the magic!

16. 1 9 9 4 2 18 9 4 3 27 9 4 4 36 9 4 5 45 9 4 6 54 9 4 7 63 9 4 8 72 9 4 9 81 9 4 Orange Kangaroo

17. 10 1 9 11 2 9 12 3 9 13 4 9 14 5 9 15 6 9 16 7 9 17 8 9 18 9 9 19 10 9 Four Aces

18. Great Christmas Cards Chased ChickenCeltic Knot

19. ABC Grid Corner Patterns Corner Edge

20. Stockings and the 12 Days of Christmas But … How Many presents did my true love send?

22. Day one 1 Day two 1+2 Day three 1+2+3 Day four 1+2+3+4 Day five 1+2+3+4+5 Day six 1+2+3+4+5+6 Day seven 1+2+3+4+5+6+7 Day eight 1+2+3+4+5+6+7+8 Day nine 1+2+3+4+5+6+7+8+9 Day ten 1+2+3+4+5+6+7+8+9+10 Day eleven 1+2+3+4+5+6+7+8+9+10+11 Day twelve 1+2+3+4+5+6+7+8+9+10+11+12

23. 1 = 1 1+2 = 3 1+2+3 = 6 1+2+3+4 = 10 1+2+3+...+n = n(n+1)/2 Triangle numbers

24. Pascal’s Triangle Triangle numbers Day of Christmas

25. Need to add them up Use a Christmas Stocking

26. 364 What happened to the lost present?

27. OK, so my true love forgot one day

28. You have five friends, Annabel, Brian, Colin, Daphne, Edward Want to invite three to a Christmas party Annabel hates Brian and Daphne Brian hates Colin and Edward Daphne hates Edward Who do you invite? A C EA C E How to organise a Christmas parties

29. Now have 200 friends and want 100 to come to a party Have a book saying who hates who Who do you invite? Parties to check Takes a high speed computer Years to check them 9000000000000000000000000000000000000000000 00000000000000000000000 6000000000000000000000000000000000000000

30. Works for a party and many other problems Using maths we can solve it in seconds SATNAV devices … useful for Santa to find his way round the Earth! Simulated annealing

31. Conclusion …. your Party Presents Christmas Cards Magic Visit from Santa Are safe in the hands of a mathematician