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We did maths to it.

M is making croissants and I am so pleased. I have been overworking the macro setting on the camera and trying to get some closeups of the various stages, but the best part was when we did Maths to it!

Okay, so the croissant-making has a few stages — at least, M’s method does. First, the sponge.  Essentially yeast, flour and water, allowed to proof for several hours, get it good and bubbly.

Spongey goodness

Spongey goodness

Then you work in some flour, salt, butter, milk and sugar, and get it nice and doughy, and let the dough rise for a while.

Shhhh, don't wake the dough!

Shhhh, don't wake the dough!

Then, the magical croissant-specific stage: the enigmatic “folds”.  (I’m getting to the Maths: be patient.) This is how you get those lovely flaky layers.  You take your dough, lay a rolled-out sheet of butter on it, and then fold it over to make a parcel, so you end up with two layers of dough sandwiching a thin layer of butter.  After y’all let that rest for a bit in the freezer, you begin folding it up in thirds, so that you end up with multiple layers of butter/flour/butter/flour/butter/flour.  Got it?

Here, I’ve drawn a diagram, which may need an embiggening click.

croissant-1

Does that help at all? Good. Cos I’m not redrawing it.  Anyway, we sat down and wrestled out how many layers the traditional third-folds ends you up with.  That is, traditionally, you fold it into thirds on top of itself, as you would a letter to go in an envelope.  We only counted the layers of flour: the butter (if I’ve understood this correctly) melts and seals the layers of flour into hydrophobic tiers, and then the steam released as the butter boils is trapped between those tiers and you end up with individually-baked layers of very thin dough.  Goddit? So, before you start folding, you have two layers of flour.  After your first fold this way, you get four layers.  After the second, you get 10 layers of flour. After the third, you get 28.  So, each fold increases the number of folds by a particular amount: each fold results in (3n-2) layers of flour, where n is the number of layers you start with.

You usually stop there, if you’re a home baker. It’s a time-consuming process and 28 layers seems more than enough.  Or is it?  We worked out that if you fold into quarters rather than thirds (so, you would fold the two outer edges to the centre, and then do that again), each fold results in (4n-3) layers of flour, where, again, n is the number of layers of flour you start with.  So, at the beginning of the process, you’ve got 2 layers of flour — plug that 2 in as n, and after your first fold you’ve got five layers.  Do that a second time, and you end up with 17 layers; after the third, you end up with 65 layers of flour!  See! Maths makes things exponentially more exciting! Not to mention exponentially more buttery!

Showing working: the blue texta didn’t come out so clearly.

image001

Impressive, no?

Why is this exciting? Because tomorrow morning I’m going to have a super-deluxe extra-buttery, extra-flakey, raised-to-heaven-on-crispy-gossamer-mezzanines breakfast, backed up by MATHS, that’s why. (With coffee.) And you, cher lecteur de la plume de ma tante, are not. Well, you might be — but unless you are M, they shan’t be M-made and for that, I pity you.

Oh, you’re still here?  Want to see how the Maths went, eh?

March-10-Batch-10

Yeah, we all love Maths.

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