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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! 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 Links are called theorems 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 • 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 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 Some mind reading 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 Start with a grid (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 advanced African sona … Chased Chicken design Lions Stomach design J