# The Formula For The Perfect Mince Pie

19th December 2016

It’s one of our favourite times of year for us, and for the team at ConquerMaths HQ Christmas has come early in more ways than one. Firstly the London Science museum has just opened a gorgeous new gallery completely devoted to mathematics, which you can read about in more detail here. We are seriously considering an office day trip to visit it at some point, and if we do, we shall review the experience for you.

Winton Gallery

This was exciting enough but then we found out that the people at Samsung have shown a keen interest and have been working closely with the museum. To commemorate their partnership Samsung challenged our favourite amazing baking mathematician Dr Eugenia Cheng who has graced our pages more than once with her brilliant mathematical culinary creations to demonstrate just how far the influence of maths reaches.

To demonstrate this Dr Cheng decided to go the Christmassy route and set to work on creating the perfect mince pie. She explained that “ I know that people of all ages and abilities often think that 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.”

We all know that just following a recipe involves mathematical thinking and Dr Cheng helpfully reminds us of the basic recipe for pastry but she also considers two important factors.

“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.”

She deconstructs her mince pie to produce two circles of pastry, one large (R) and one small ®, with the larger being the case and the smaller being the lid. To produce the largest volume she then applies calculus. Next she uses her results to consequently work out the correct proportions between R and r to get the most possible juicy mince-y filling crammed in the pie. More is better when it comes to Christmas food after all!

Next Dr Cheng needs to work out how much pastry will be in her pie, i.e the volume of the pastry and she does this by multiplying the two R circles by the thickness of the pastry, applying Pi

P = π (R² + r² ) t

and finally dividing the volume of the pie by the volume of the pastry itself. She then looks at her pastry cases.

The overall radius of the pastry in Dr Cheng’s particular pastry cases are 5cm, with a 30 degree angle.

She explains: “My formula comes to 0.54 x R but my cases comes to 0.4 x R, which means for that amount of pastry I’m not going to get the most possible filling in my pie.”

The answer to this is simply to make the big circle of pastry smaller so the proportions and ratios stay static.

The next task was to work out the thickness of the pastry.

Dr Cheng said: “If we look at the formula for the ratio, when the thickness is bigger, the answer is going to be smaller. And I would want my ratio of mince to be big, so I make my pastry thin.”

Confused? Since it’s Christmas you’re lucky that BarcroftTV and Samsung have released a helpful tutorial in which Dr Cheng explains everything in detail so you can actually have a go at working out the maths yourself.

In the past Dr Cheng and other maths enthusiasts have produced some incredible demonstrations of practical maths, such as the perfect doughnut, the perfect pancake, the perfect cream tea and so on, but some of the formulae have been a little too complicated for the average person to follow.

However with Dr Cheng’s helpful and enthusiastic video (a very enthusiastic video – this is a maths professor who really loves her food!)

Using Dr Eugenia’s formula, you can modify your own mince pie to your own preference of pastry thickness, how much filling you would like, and create hopefully the best mince pie you’ve ever had!