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