Maths, magic and mystery Chris Budd. Who likes magic? We like magic because Its mysterious Its dramatic It has an element of surprise It has glamour and.
Post on 28-Mar-2015
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Maths, magic and mystery
Chris Budd
Who likes magic?
We like magic because
• It’s mysterious
• It’s 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!
Maths is a highly creative subject full of mystery and surprises
But an even more mysterious fact is …
Most people don’t realise this!
Maths is the study of abstract objects and the patterns that link them together
Links are called theorems
They are often deeply amazing, mysterious,beautiful and very, very useful!
Some amazing theorems
...13
1
11
1
9
1
7
1
5
1
3
11
4−+−+−+−=
π
222 cba =+
1−=πie
a
bc
Pythagoras
Gregory
Euler
Unfortunately, not everyone appreciates their mystery and beauty
But … most people like magic, art and storytelling!
Some people are even scared of maths!
By linking maths to magic, art and storytelling we can unlock some of its mysteries
Theorems can lead to some great magic tricks!!!
Some Mathematical Magic Tricks
• Clocks
• Cards
• Mind reading
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
The Clock Trick
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
Theorem: y – (y – x) = x
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
Where’s the Joker?
The Cards who Know Their Names
3 8 7 A Q 6 4 2 J K 10 9 5
K
AA C E T W O 2 T H R E E
3 A 2F O U R 4 F I V E 5
3
3
A
A
4
4
2
2
5
5
S I X 6
68 7 Q J 10 9
1 2 3
4 5 6
7 8 9
10 11 12
13 14 15
16 17 18
19 20 21
Row is given by round up (x/3)
New position by f(x) = 7 + round up (x/3)
21 Card Trick
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
11
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
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
Theorem
The difference z between two numbers with the same digital root, has a digital root which is always a multiple of 9
Maths in Celtic and African Art
Celtic
African
How to draw simple Celtic Knots
Start with a grid
(5 , 4) grid
(5,6)
(4,8)
(2,2) 2
(3,2) 1
(5,3) 1
(4,4) 4
How many pieces of string are needed?
Simple Celtic Knots are very similar to plaited mat sona drawings
Sona … African sand patterns
(3,4) (2,4)
We can also produce more advanced African sona …
Chased Chicken designLions Stomach design
J
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