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 2 – you’ve already got three layers so when you do the folds the layers are mutilplied 3×3 or 3 which results in 9 layers.

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

maths, algebra and pastry
For turn 3 –  it’s 3x3x3 or 3x³, giving 27 layers.
 
For turn 4 – it’s 3x3x3x3 or 3x⁴ giving 81 layers – this is where you’d stop if you wanted 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 5 – it’s 3x3x3x3x3 or 3x⁵ giving 243 layers – you can stop here for puff pastry but as pastry is normally rested in the fridge after every second turn made (ie after turn 2, 4 or 6) it’s normal to keep going.
For turn 6 – it’s 3x3x3x3x3x3 or 3x⁶ giving 729 layers. 
You can see how quickly the numbers have added up! This is where you’d normally get to for puff pastry although some people prefer 7 turns or you may find some very delicate recipes calling for it. 7 turns would give you 2,187 layers. 

A finished 6 turn block of puff pastry (this lot was made for the palmiers recipe)
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