A Touch of Mathematical Magic

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A Touch of Mathematical Magic Chris Budd
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From a recent first year example sheet
B E E R B E
E R _________ D R U N K
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Who likes magic?

• We like magic because
• Its mysterious
• Its dramatic
• It has an element of surprise
• It has glamour and excitement!

This seems a bit different from a logical and
rational subject like maths!
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But an even more mysterious fact is
Maths is a highly creative subject full of
mystery and surprises
Most people dont realise this!
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Maths is the study of abstract objects and the
patterns that link them together
Links are called theorems They are often
magical, mysterious, beautiful and very, very
useful!
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Some amazing theorems
c
b
Pythagoras
a
Gregory
Euler
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By linking maths to magic we can unlock some of
its mysteries
Theorems can lead to some great magic
tricks!!!
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Wheres the Joker?

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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21 Card Trick

• 2 3
• 5 6
• 8 9
• 11 12
• 14 15
• 17 18
• 19 20 21

Row is given by round up (x/3) New position by
f(x) 7 round up (x/3)
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21
8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 13 13 13 14
14 14
10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 12 12
12 12 12 12
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Contraction Mapping Theorem
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The Cards who Know Their Names
3 8 7 A Q 6 4 2 J K 10 9 5
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A
A
C
E
T
W
O
2
T
H
R
E
E
3
A
2
F
O
U
R
4
F
I
V
E
5
3
A
4
2
5
S
I
X
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K
3
A
4
2
5
6
8
7
Q
J
10
9
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Erik Demaines Fold-and-cut problem
If you fold a piece of paper and make one cut,
what shapes can you make?
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eg. Angel Fish
Also a five pointed star
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Some mind reading
Take a 4 digit number x
eg. 7563 Scramble the digits to give y
eg. 3567 Subtract y from x (or
vice versa) 3996 Cross out
a non-zero digits and tell me the others eg. 396
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Digital root of a number sum of digits
x and y have the same digital root
Theorem The difference z between two numbers with
the same digital root, has a digital root which
is always a multiple of 9
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Maths in Celtic and African Art
Celtic
African
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(No Transcript)
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How to draw simple Celtic Knots
Start with a grid




(5 , 4) grid
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(5,6)
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(4,8)
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How many pieces of string are needed?
(2,2) 2
(3,2) 1
(5,3) 1
(4,4) 4
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Simple Celtic Knots are very similar to plaited
mat sona drawings
Sona African sand patterns
(3,4)
(2,4)
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We can also produce more advanced African sona
Chased Chicken design
Lions Stomach design
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Chase that Chicken
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J
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A bit of mind reading

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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The Clock Trick
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Unfortunately, not everyone appreciates their
mystery and beauty
Some people are even scared of maths!
But most people like magic, art and
storytelling!
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Theorem y (y x) x
Mystery number is x Total number of taps is
21 x After 8 random taps we have 13
x Number we get to from the top is
13 (13 x) Rearrange 13 (13 x) x
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Some Mathematical Magic Tricks

• Clocks 9 2 2 8 1 8 4 5 6
• Cards
• Mind reading