By Charley Sutton @CharlSutton

A MATHEMATICAL formula reveals how to make the perfect mince pie

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Videographer / director: Alexander Ayer, Ruaridh Connellan
Producer: Jack Fletcher, Nick Johnson
Editor: Jack Stevens

Dr Eugenia Cheng has created a mathematical formula for the perfect mince pie

Keen cook and Professor of Pure Mathematics Dr Eugenia Cheng has created a mathematical equation to bake one of Britain’s most loved festive treats.

Eager to prove to people that maths can be fun, Dr Cheng explains maths using everyday cooking. 

Previously Senior Lecturer at the University of Sheffield, the doctor now teaches at the School of Art Institute of Chicago and is known for her math skills in the kitchen.

The formula works out the perfect ratio of pastry to filling - to maximise the volume and get the most possible filling

Author of How To Bake Pi: An Edible Exploration of the Mathematics of Mathematics, the professor believes the best way to explain maths is through our stomachs - from comparing béchamel sauce to the number 5, to how custard proves that maths is easy but life is hard.

To celebrate its partnership with the new Mathematics: The Winton Gallery at the Science Museum, Samsung challenged Dr Cheng to create a mathematically perfect mince pie, just in time for Christmas.

The Professor of Pure Mathematics is known for teaching maths using food

She said: “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.”

Dr Cheng's complete maths for the perfect mince pie

Cake-lover Dr Cheng investigates the mathematical balance between the mince and the pastry.

She said: “There are two equations – 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.”

First, the professor 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 and the smaller circle - denoted as ‘r’ - will be the pie lid.  

Dr Cheng has written a book called How To Bake Pi: An Edible Exploration of the Mathematics of Mathematics

Using calculus, Dr Cheng is able to calculate how to maximise the volume of the pie to in turn work out the correct proportions between R and r to get the most possible filling. 

The second 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: P = π (R² + r² ) t

Samsung challenged her to create the mince pie formula to celebrate the opening of the Mathematics: The Winton Gallery at the Science Museum

To calculate the ratio of filling to pastry she divides the total volume of the pie by the volume of the pastry.

And now for the baking. Mix 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. 

While it’s chilling, Dr Cheng measures her pie moulds to incorporate her formula. 

Dr Cheng uses calculus to work out how to maximise the volume of her mince pies, which shows the proportion between r and R to to get the most possible filling

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

She explained: “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.”

So the mathematician advises to make the big circle of pastry a little smaller so the proportions and ratios stay the same. 

This equation shows how much pastry needs to be used within the formula. 'P' stands for pastry and 't' stands for the thickness of the pastry

Using Dr Eugenia’s formula, you can perfect your pie to your own preference of pastry thickness, more filling or the equal of both. 

The next task 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.”

Fill with your preferred flavour of filling and bake for 15-20 mins at 190 degree heat. 

Dr Eugenia Cheng's formula for the volume of her mince pies

The result? Your very own perfect mince pie. 

Dr Cheng added: “Maths is everywhere and in everything - even in mince pies.”

Russell Taylor, Chief Marketing Officer at Samsung UK & Ireland, said, “Maths is intrinsic to everyday life – from the technology we use on a day to day basis, to the trips we take and the mince pies we bake. As Principal Sponsor of the Science Museum’s mathematics gallery, we’re committed to inspiring young people to delve more deeply into this fascinating subject.”

Dr Eugenia Cheng's final formula, showing the ratio of the mince to the pastry

Samsung is the principal sponsor of the soon to be launched Mathematics: The Winton Gallery at the Science Museum. Designed by the world-renowned Zaha Hadid Architects, this outstanding new gallery tells the story of how mathematics has shaped our world.  To celebrate this partnership, Samsung challenged Dr Cheng to create a mathematically perfect mince pie, just in time for Christmas.