### multiple of 9

```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!
But an even more mysterious fact is …
Maths is a highly creative subject full of
mystery and surprises
Most people don’t realise this!
Maths is the study of abstract objects
and the patterns that link them together
They are often deeply amazing,
mysterious,beautiful and very, very
useful!
Some amazing theorems
Pythagoras
c
b
a b  c
2
2
2
a
Gregory
Euler

1 1 1 1 1 1
 1        ...
4
3 5 7 9 11 13
i
e  1
Unfortunately, not everyone
appreciates their mystery and beauty
Some people are even scared of maths!
But … most people like magic, art and storytelling!
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
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
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
Where’s the Joker?
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
The Cards who Know Their Names
3 8 7 A Q 6 4 2 J K 10 9 5
A
C
E
A
T
W O
2
T
H
R
E
E
3
F
O
A
U
R
2
F
I
V
E
5
3
S
I
A
X
6
4
2
3
8
7
A
Q
6
4
2
4
5
J
K
10
9
5
21 Card Trick
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)
1
8
10
2
8
10
3
8
10
4
9
10
5
9
10
6
9
10
7
10
11
8
10
11
9
10
11
10
11
11
11
11
11
12
11
11
13
12
11
14
12
11
15
12
11
16
13
12
17
13
12
18
13
12
19
14
12
20
14
12
21
14
12
11
Take a 4 digit number
x
Scramble the digits to give y
Subtract y from x (or vice versa)
eg.
7563
eg.
3567
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
Maths in Celtic and African Art
Celtic
African
How to draw simple Celtic Knots
(5 , 4)
grid
(5,6)
(4,8)
How many pieces of string are needed?
(2,2)
2
(3,2)
1
(5,3)
1
(4,4)
4
Simple Celtic Knots are very similar to
plaited mat sona drawings
Sona … African sand patterns
(3,4)
(2,4)
We can also produce more