Maths, algebra and making puff pastry

Me and maths aren’t usually friends. But I’ve been intrigued to find that there’s a lot of maths that can explain the fluffy lightness of rough puff and puff pastry.

The folding method and total number of folds for puff pastry is crucial to creating the many layers. Mille feuille means thousands leaves in French, and it’s literally possible to create more than a thousand (2187 to be exact) in just 7 ‘turns’. Although making 6 turns, or 729 layers, is usually the norm for recipes.

The process of building puff pastry is to roll out into a rectangle and fold the bottom third of the middle third, then the top third over the other two, and then turning 90˚ (or -90˚ – it doesn’t matter as long as you’re consistent throughout) as in the image below. This process is one ‘turn’.

The first turn makes three layers from the initial rolled out sheet of pastry.

Turn two or more is where the maths comes in as every turn creates three layers out of the pastry block you already have.

For the first turn: it’s 3×1 making 3 layers.

For turn two: you’ve already got three layers so when you do the folds the layers are mutilplied 3×3 or 3 $x²$ which results in 9 layers.

I’ve drawn a sketch to show what’s happening a little more clearly…

Illustration by Ink Sugar Spice on the number of layers of puff pastry created at each turn when you make it yourself

For turn three: its 3 x 3 x 3 or 3 x³ giving 27 layers

For turn four: it’s 3 x 3 x 3 x 3 or 3 x⁴ giving 81 layers

Four turns is good for rough puff pastry. Most pies can be made with rough puff, such as apple pie or tart tatin. Eccles cakes and apple turnovers are also made with rough puff.

For turn five: it’s 3 x 3 x 3 x 3 x 3 or 3 x⁵ giving 243 layers

Five turns is totally fine for puff pastry, but as pastry is normally rested in the fridge after every second turn made (ie on an even number of turns) it’s normal to keep going for one more turn.

For turn six: it’s 3 x 3 x 3 x 3 x 3 x 3 or 3 x⁶ giving 729 layers

Six turns is the classic number for a very flaky yet still manageable patisserie bake.
You can see how quickly the numbers have added up!

Seven turns is a really extreme and would give 2,187 layers with 3 x 3 x 3 x 3 x 3 x 3 x 3 or 3 x⁷

You’d normally get to six turns only for puff pastry. Some very delicate patisserie recipes call for seven turns but it is so fine you do risk tearing the pastry.