This is a geomagic square. If you take the shapes in any row, column or main diagonal, you can rearrange them to make a rectangle that is 3 squares tall and five squares wide.

Over 2500 years ago, Chinese mathematicians discovered a grid of numbers with special properties that we now call a magic square. If you add the numbers in any row across, or column down, or either of the two diagonals of the grid, you get the same total. Magic squares have been studied for centuries by mathematicians from around the world. Now, a recreational mathematician named Lee Sallows has come up with an entirely different type of magic square that adds shapes together, not numbers.

Lee was studying magic squares when he realised that the numbers could represent lengths. He took the magic square he had been using, and replaced each of the numbers with a line of a certain length. If you took all the lines in a column or a row and put the lines end to end then the total distance was the same, no matter which row or column you chose.

He then wondered if he could make a more interesting magic square out of shapes, not just lines. After some thinking, he managed to come up with a set of nine different shapes that he organised into a square. If he took all the pieces in the top row, he could fit them together to make a shape. If he took the pieces from any other row or column, or either of the two diagonals, he could make exactly the same shape. Lee called his new invention the ‘geomagic square’.

He soon discovered that there were lots of things that you can do with his geomagic squares. For example, it is impossible to make a 2×2 magic square with numbers unless all the numbers are exactly the same. Lee couldn’t find a 2×2 geomagic square either, although he did get quite close. After hearing about the problem, another recreational mathematician named Frank Tinkelenberg did his own investigation and managed to find a 2×2 geomagic square.

Lee is not a trained mathematician, but he continues to make new discoveries with his geomagic squares. Sometimes new and interesting maths is discovered simply by having fun.