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The Mathematically Tested Formula for the Perfect Mince Pie

Maths always makes our lives easier. Samsung, the principal sponsor of the new Science Museum’s ‘Mathematics: The Winton Gallery’, has added some light to produce the perfect Christmas mince pie, thus celebrating this fruitful partnership. Professor of Pure Mathematics Dr Eugenia Cheng was asked for help to create a mathematical equation to help us bake Britain’s most loved festive treat.

Explaining maths using everyday cooking is the fun way that Dr Cheng (also known for her maths skills in the kitchen, and author of How To Bake Pi: An Edible Exploration of the Mathematics of Mathematics), chose to prove to people how maths affects our lives, shaping the world around us. And she thought the best way to learn is through our stomachs.

This is a great way to revert the depressing results of research commissioned by Samsung into children’s attitudes to mathematics. The numbers indicated a real desire amongst children to be better at maths, with an encouraging 57% believing maths is useful to them, while just 34% found it fun. The findings also showed that as a life-skill for adulthood, children were most likely to value the ability to cook as an important skill (78%) with mathematics closely behind (76%), leading to Samsung’s challenge to see if Dr Cheng’s could combine the two topics.

The two considerations Dr Cheng had when starting to investigate the mathematical balance between the mince and the pastry was first, how to calculate the size of the pie to maximise the filling; and second, how to calculate the perfect ratio of filling to pastry. She then breaks 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:

1

Secondly, using calculus, Dr Cheng was able to calculate how to maximise the volume of the pie, in turn working out the correct proportions between R and r to get the most possible filling. Mathematically, it looks like this:

2

The third equation tackles the volume of the pastry, which is done by multiplying the area of the two circles by the thickness of the pastry or ‘T.’ Mathematically, it looks like this:

3

Finally, to calculate the ratio of filling to pastry, she divides the total volume of the pie by the volume of the pastry. Mathematically, it looks like this:

4

The complete formulae can be applied to mince pies large and small, 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.

For the pastry, Dr Cheng recommends mixing 110g of butter and 225g of flour with a pinch of salt and a splash of cold water. Knead the mixture together and leave in the fridge to chill.  Fill with your preferred mincemeat and bake for 15-20 minutes at 190-degree heat.

Now, is that clear? Just in case, watch this video where Dr Cheng clearly explains these encrypted formulae in plain cooking terms.

What a fun way to scientifically prove that mathematics can help you bake the perfect mince pie! Surprised? Using Dr Eugenia’s formula, you can have your pie (and eat it, too) to your own preference of pastry thickness, more filling or even both, thus proving that mathematics can make our day-to-day life easier, and even tastier!

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