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

Why does Rudolph have a shiny nose? A mathematical look at Christmas Chris Budd. Can maths help Santa plan Christmas??. 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?

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

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

  2. Can maths help Santa planChristmas??

  3. 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?

  4. 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

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

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

  7. Total area A taken up by the homes But … surface area of the continents = 226,000,000,000,000 (226trillion) m2 Total distance that Santa has to travel = NH=475 Gm

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

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

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

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

  12. 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 Lafter = 0.999 Lbeforeis not enough

  13. Solution two: Use a fractal

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

  15. Orange Kangaroo • 9 9 4 • 18 9 4 • 27 9 4 • 36 9 4 • 45 9 4 • 54 9 4 • 63 9 4 • 72 9 4 • 81 9 4

  16. Four Aces • 1 9 • 2 9 • 3 9 • 4 9 • 5 9 • 6 9 • 7 9 • 8 9 • 9 9 • 10 9

  17. Great Christmas Cards Chased Chicken Celtic Knot

  18. Grid Edge Corner Patterns Corner A B C

  19. Stockings and the 12 Days of Christmas But … How Many presentsdid mytrue lovesend?

  20. 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

  21. 1 = 1 1+2 = 3 1+2+3 = 6 1+2+3+4 = 10 1+2+3+...+n = n(n+1)/2 Triangle numbers Triangle numbers

  22. Pascal’s Triangle Triangle numbers Day of Christmas

  23. Need to add them up Use a Christmas Stocking

  24. 364 What happened to the lost present?

  25. OK, so my true love forgot one day

  26. How to organise a Christmas parties 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 ACE Who do you invite?

  27. Now have 200 friends and want 100 to come to a party Who do you invite? Have a book saying who hates who 900000000000000000000000000000000000000000000000000000000000000000 Parties tocheck Takes a high speed computer 6000000000000000000000000000000000000000 Years to check them

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

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

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