Why does Rudolph have a shiny nose?

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

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• 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

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Santa has 36 hours of darkness during Christmas
night to deliver all of the presents
Can he get round in time?
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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
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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
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Speed 475Gm/(363600) 3.6M metres per second
Thats 9600 Mach
Sound 375 ms-1 Light 300 M ms-1
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So why does Rudolph have a shiny nose?
Sleigh is travelling at hypersonic speeds
Hyperbolic shock wave
Air friction heats up Rudolphs nose till it
glows!
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How does Santa get down the chimney?
Large diameter Santa
Small diameter chimney
10m
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Solution one Einsteins theory of relativity
C 3 00 000 000 metres per second
Lorentz Contraction
The faster you go the smaller you get
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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 Lbefore
is not enough
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Solution two Use a fractal
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Christmas is a magical time
Maths can be part of the magic!
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Orange Kangaroo

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

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Four Aces

1. 1 9
2. 2 9
3. 3 9
4. 4 9
5. 5 9
6. 6 9
7. 7 9
8. 8 9
9. 9 9
10. 10 9

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Great Christmas Cards
Chased Chicken
Celtic Knot
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Grid
Edge
Corner Patterns
Corner
A
B
C
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Stockings and the 12 Days of Christmas
But How Many presents did my true love send?
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Day one 1 Day two 12 Day three
123 Day four 1234 Day five
12345 Day six 123456 Day seven
1234567 Day eight
12345678 Day nine
123456789 Day ten
12345678910 Day eleven
1234567891011 Day twelve
123456789101112
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1 1 12
3 123 6 1234
10 123...n n(n1)/2
Triangle numbers
Triangle numbers
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Pascals Triangle
Triangle numbers
Day of Christmas
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Need to add them up
Use a Christmas Stocking
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364
What happened to the lost
present?
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OK, so my true love forgot one day
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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

A C E
Who do you invite?
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Now have 200 friends and want 100 to come to a
party
Who do you invite?
Have a book saying who hates who
90000000000000000000000000000000000000000000000000
0000000000000000
Parties to check
Takes a high speed computer
6000000000000000000000000000000000000000
Years to check them
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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!
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Conclusion . your

• Party
• Presents
• Christmas Cards
• Magic
• Visit from Santa

Are safe in the hands of a mathematician
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