Posted by
Claire
19 yrs ago
I'm not really mathematically challenged, just out of practise. Can someone double-check my (simple) calculation before I start cooking?
Recipe for a tart makes a 30cm round one and I want to make two rectangle ones instead.
I calculate I can make two rectangle ones of 20 x 17.5 cm. Do I have this right?
Cheers.
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I am assuming that you mean 30 cm diameter. That is approximately right.
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TC
19 yrs ago
Confirmed. Area of circle of 30cm diameter (15cm radius) would be ~707 sq cm compared with the total area of 2 rectangles each of 20 x 17.5cm which would be 700 sq cm. The optimum cooking time might not be the same, though, if you are cooking whether you are cooking them separately or together. Do we all get a taste?!
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Thanks to you both. And I was always one of those who said "we'll never need to use this" in maths class!
TC>I'll wave them in front of the computer monitor so you can have a smell! Or can give you the recipe - it's tarte fine aux tomates and tastes as good as it smells.
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TC
19 yrs ago
Thanks, very kind, but I was hoping more for a luscious deep apple pie with lashings of fresh cream!
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TC,
My maths may be rusty, so pls correct me if I am wrong.
Firstly, need to clarify whether Claire require conversion for the tart crust or for the fillings that is inside the tart?
If crust, my assumption is that Claire's tarts will have the bottom and sides covered with crust and filled with tomatoes/fruits. I don't think that by using squared surface area of circle(707 for the round tin) will be sufficient to cover bottom & sides of the 2 rectangular tins which will have > perimeters than original circular tin.
Squared area will be fine if only for surface area only, meaning no sides to consider.
If for fillings, then volume based formula?
In this case, there may be a small difference in the filling amount, depending on the height
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Good point samos. Assuming a 2cm rim (it's puff pastry so no need for tins) for the 30cm diameter tart and 2cm for each of the two rectangular tarts, I had calculated that the volume of filling would need to be reduced by approx. 19%. I would be happy for you to confirm this.
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Are you baking tarts which have bottom and sides with pastry and open at the top?
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The tart is flat rolled-out pastry (on a baking sheet) and the "filling" is placed on top with a 2cm rim clear of filling - this becomes the crust of tart, a bit like a pizza.
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I'm no chef so approaching this from a calculation aspect. Open to feedback from others.
Volume of fillings for the circular pie, where "pi" is the constant 3.141592
pi x radius x radius x height
Workout = 1414
Volume of fillings for a rectangular pie
length x width x height
Workout for 2 tins : 1400 ( 700 per tin)
In your case, you can use your existing filling formula easily as the diff is minimum. The variance will be higher if height is increased.
Pastry for 2 rectangular tins is increased by about 10%
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The "height" cannot be changed otherwise it would not cook right, so I have to stick with length and width.
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Claire,
which height are you refering to?
I am refering to your 2 cm and using for volume calculation purpose.
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44
19 yrs ago
For the two rectangular tins, the surface area for the pastry is greater (there is more rim). So, if you did not adjust the recipe, then you would have made two tarts with thinner pastry. To be correct, you should have made approximately 10% more pastry.
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samos> Alas I realise I haven't been terrible clear.
The mixture is spread over the pastry, leaving a 2cm band clear of mixture all the way around. This non-covered rim rises during the first stage of cooking.
44> I have already made the pastry which is in my freezer for the 30cm tart. But I want to make two smaller rectangular tarts instead using the quantity of pastry I have made. So I figured I could make two 20 x 17.5cm tarts and then reduce the mixture by 19% to allow for the additional non-covered areas.
The area of the 30cm is diameter 26cm (less the 2cm non-covered rim), so r=13. The area is then 531 sq cm. The areas of the two rectangular tarts are 20 x 17.5 cm, or 16 x 13.5cm (less the 2cm rim) which is, I think, 216 sq cm x 2 = 432.
For the difference between the areas the mixture is to cover, I work it out as less 19% of the original mixture amount.
Yikes, this should be easier!
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44
19 yrs ago
So, the 2cm is thickness of the rim, and not the height. What would be the height of the rim? And, what is the thickness of your base (the pastry)?
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44> The 2cm is the width of the rim. The height of rim depends on the cooking temperature, it is flat till then and not relevant to the equation. It is like a pizza - filling in the middle with an non-covered rim around the outside which rises during the cooking.
samos> Does my maths work out?
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44
19 yrs ago
What I mean is, how thick do you roll out the pastry?
How many layers of pastry do you use for the rim?
Do you need to bake them in a pie tin? And if so, what size pie tins do you have which are smaller than 20 x 17.5 cm. (Does the size have to be pre-defined?)
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1. Approx. 3-4mm
2. I don't understand your question. The whole thing is a single rolled out sheet of puff pastry. The "rim" appears when cooking as it is not covered.
2. No. As mentioned, the pastry is placed on a baking sheet. With puff pastry tarts, tins are not neccesary.
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44
19 yrs ago
Okay, so your tart is not designed to contain volume.
Based on the surface area, you will require only 81% of the filling of the original tart.
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Thanks for confirming my figures, 44.
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Claire, you are correct on the 19% reduction.
My apologies over the misunderstanding on the 2" depth of the rim/edges.
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Well no pictures...
From a cook not a mathematician, the tart is cooked at a higher temperature to begin with so uncovered pastry puffs up around the mixture and stops everything from running all over the place. If you haven't made one, it is perhaps not easy to understand what happens - also I wasn't terribly clear on my description.
Appreciate your help. Now I don't have to spend a couple of hours making another batch of puff pastry.
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For the record, I think that this is one of the best threads I have ever seen in my life.
It has everything. Look at some of the quotes:
"it's tarte fine aux tomates and tastes as good as it smells. "
"If for fillings, then volume based formula?"
"I had calculated that the volume of filling would need to be reduced by approx. 19%."
"I'm no chef so approaching this from a calculation aspect."
It's made my day.
Honestly.
And I think I might have learnt how to make a tart.
Claire - did they turn out all right - all this culinary mathematics not only has my mouth watering, but now i need to know how it all ends.....
:)
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I agree with Alberto eggplant -very very fun thread.
and so many helpful people as well! I showed it to some of my students (one in particular who loves to cook but hates math) and tried to get her to see the value of an education.
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Well I'm glad my thread proved enjoyable, just as I hope the tartes aux tomates will be when I make them this weekend.
hkchoi> As I mentioned I was one of those who always said "we'll never need this" and promptly forgot it all after my maths A level. Even with bachelor and master degrees, I have been humbled by a simple Pi x r squared!
Ah well, now to figure out (fortunately a lot easier) scaling a 275g weight recipe to 225g, 350g, 375g and 500g weight. But scaling a 30cm diameter cake down to a 22cm diameter cake, while maintaining the same height, will be a bit more difficult.
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'fraid I cannot offer anything other than encouragement.
Am waiting for the next installment though....
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you never know WHEN you're going to need some vital piece of your education, eh? AT least you got a lot of support from people who were willing to rack their brains on your behalf! You'll have to send everyone a piece of your tart. (sounds incredibly delicious by the way.)
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This thread does provide a good laugh. My key learning from this - "tarts" need not have depth for filling and my baking knowledge is not even at Baking 101 level.
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788
19 yrs ago
33% less diameter while maintaining a 2cm height is a whole another tart! Entirely better than 19% reduction, and which would approx. equal to volume of 1/2 a wedge of 5cm high, 45cm dia chocolate cake. Hope you scale down several 30cm ones to 22 and we'll all get some.... we are salivating just in the hope of getting this very deliciously mathematical tart! No more rectangles? So much easier to calculate.
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