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Maths, magic and mystery Chris Budd

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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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Maths is a highly creative subject full of mystery and surprises But an even more mysterious fact is … 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 deeply amazing, mysterious,beautiful and very, very useful!

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Some amazing theorems a b c Pythagoras Gregory Euler

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Unfortunately, not everyone appreciates their mystery and beauty But … most people like magic, art and storytelling! Some people are even scared of maths!

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By linking maths to magic, art and storytelling we can unlock some of its mysteries Theorems can lead to some great magic tricks!!!

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Some Mathematical Magic Tricks Clocks Cards Mind reading

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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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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

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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 Wheres the Joker?

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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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K AACETWO 2THREE 3A2FOUR4FIVE5 3 3 A A 4 4 2 2 5 5 SIX6 687QJ10 9

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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 Row is given by round up (x/3) New position by f(x) = 7 + round up (x/3) 21 Card Trick

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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 9 10 11 12 13 14 10 11 12 11

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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 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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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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(2,2) 2 (3,2) 1 (5,3) 1 (4,4) 4 How many pieces of string are needed?

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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 designLions Stomach design

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20 19181716151413121110987654321 © S Haughton 2010 1 more than 3?

20 19181716151413121110987654321 © S Haughton 2010 1 more than 3?

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