Phone giant Samsung has been working with the Science Museum in London as part of an upcoming exhibition, Mathematics: The Winton Gallery at the Science Museum.
To celebrate the partnership, Samsung challenged keen cook and Professor of Pure Mathematics Dr Eugenia Cheng to investigate how far the influence of mathematics can be felt.
Author of How To Bake Pi: An Edible Exploration of the Mathematics of Mathematics, Dr Cheng believes the best way to explain maths is through our stomachs.
Dr Cheng said: “I know that people of all ages and abilities often think maths just happens in the classroom. That’s why I love to show that maths is everywhere - especially in food! I can use maths to make the perfect mince pie.”
The starting point was to investigate the mathematical balance between the mincemeat and the pastry.
Cheng said: “There are two considerations – first, how to calculate the size of the pie to maximise your filling, and second, how to calculate the perfect ratio of filling to pastry.”
The professor broke down the construction of a classic mince pie to work out the volume, using two circles of pastry – one bigger than the other. The bigger circle – represented as ‘R’ – is squashed down into the cake case to create the base of the pie and the smaller circle – denoted as ‘r’ – will be the pie lid. Mathematically, it looks like this (diagram 1).
Secondly, using calculus, Dr Cheng calculated how to maximise the volume of the pie, working out the correct proportions between R and r to get the most possible filling. Mathematically, it looks like this (diagram 2).
The third equation tackled the volume of the pastry, by multiplying the area of the two circles by the thickness of the pastry or ‘t’ (diagram 3).
Finally, to calculate the ratio of filling to pastry she divided the total volume of the pie by the volume of the pastry – mathematically, it looks like this (diagram 4).
The complete formula (diagram 5) can be applied to mince pies no matter the size of the pastry cases, to ensure the maximum amount of filling in each pie. By first measuring the pie cases, the pie base circle of pastry can then be made a little smaller or larger than the circular ‘pie lid’ so the proportions and ratios stay the same.