50 Mathematical Ideas You Really Need to Know

42 Magic squares ‘A Mathematician’, wrote G.H. Hardy, ‘like a painter or a poet, is a maker of patterns.’ Magic squares have ver ...

If we add up all the numbers in the grid we have 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 and this total would have to be the same ...

Dürer and Franklin’s squares The Lo Shu magic square is well known for its age and uniqueness but one 4×4 magic square has becom ...

In this normal magic square there are all kinds of symmetries. All the rows, columns and diagonals add up to 260, as do the ‘ben ...

fourth powers. The search for squared squares has, however, been successful for larger squares. Magic 4×4 and 5×5 squared square ...

Remarkably, this is a magic square consisting of the consecutive numbers 3, 4, 5, up to 11. We also find that the number of lett ...

43 Latin squares For a few years the world has been Sudoku mad. Across the land, pens and pencils are chewed waiting for the rig ...

compelling. Addicts of both forms of self-torture have much in common. 3×3 Latin squares A square array containing exactly one s ...

For example, Mary from Team One, has a meeting with Tom from Team Two on Monday (the intersection of the M row with the T column ...

in each row and column. In 1782 Euler posed the same problem for ‘36 officers’. In essence he was looking for two orthogonal squ ...

If we mark out a square field into 16 plots we can envisage the Latin square as a description of the field where the soil qualit ...

44 Money mathematics Norman is a super salesperson when it comes to bikes. He also sees it as his duty to get everyone on a bike ...

Compound interest formula When talking about mathematics, it is always good to have Albert Einstein on side – but the widespread ...

£1,000? Each year he gets £70 interest so all he has to do is divide 1000 by 70. This gives 14.29 so that he can be sure in 15 y ...

Now that Charlie’s father has promised to give £100,000 to his son in ten years time, he has to save the money up. This he plans ...

the condensed idea Compound interest works best ...

45 The diet problem Tanya Smith takes her athletics very seriously. She goes to the gym every day and monitors her diet closely. ...

cartons. Surely this will be OK? She recalculates and finds she has 2 × 40 + 3 × 15 = 125 mg vitamins and 10 × 40 + 50 × 15 = 11 ...

she would like to do is to go home and analyse the problem with a pencil and paper. Linear programming problemsTanya’s always be ...

was before, that is, she should purchase no Solido at all and 40 cartons of Liquex at a total cost of £200, even though she will ...