# Math help, please
**URL:** https://boards.straightdope.com/t/math-help-please/804391
**Category:** Factual Questions
**Created:** [December 13, 2017, 1:55pm UTC](https://boards.straightdope.com/t/math-help-please/804391 "2017-12-13T13:55:19Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@Chefguy](https://boards.straightdope.com/u/Chefguy)
#### Post date: [December 13, 2017, 1:55pm UTC](https://boards.straightdope.com/t/math-help-please/804391/1 "2017-12-13T13:55:19Z")
I’m 70, so no, this isn’t homework. I’m usually pretty good at this stuff, but this has me stumped. I’m planning to make mince tarts this week, which requires pie dough cut into small circles, say about 3" in diameter. Rather than guess how many pie crusts I need to buy, I’d like to be able to come up with an estimate.
So the question is, how many 3" circles can I get from a 9" pie crust? If someone can provide a formula for figuring this out, I’d appreciate it.
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### Author:  [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)
#### Post date: [December 13, 2017, 1:56pm UTC](https://boards.straightdope.com/t/math-help-please/804391/2 "2017-12-13T13:56:25Z")
> [@Chefguy](#):
>
> I’m 70, so no, this isn’t homework. I’m usually pretty good at this stuff, but this has me stumped. I’m planning to make mince tarts this week, which requires pie dough cut into small circles, say about 3" in diameter. Rather than guess how many pie crusts I need to buy, I’d like to be able to come up with an estimate.
>
> So the question is, how many 3" circles can I get from a 9" pie crust? If someone can provide a formula for figuring this out, I’d appreciate it.
I would guess nine, three rows of three.
Wait the pie crust is round.
NM
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### Author:  [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)
#### Post date: [December 13, 2017, 2:00pm UTC](https://boards.straightdope.com/t/math-help-please/804391/3 "2017-12-13T14:00:35Z")
> [@carnivorousplant](#):
>
> I would guess nine, three rows of three.
>
> Wait the pie crust is round.
> NM
.-O-
OOO
.-O-
You’ll be able to get three across at the center. You’ll be able to get three down at the center. That makes five, and I’m not thinking there’s any more efficient use of the space, since any way you rotate it will lead to a similar pattern.
You could instead get two across as soon as there’s an arc with a length of 6 inches, but I think that’d lead to a total of four, not five.
My apologies if I’m missing something obvious :).
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### Author:  [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)
#### Post date: [December 13, 2017, 2:04pm UTC](https://boards.straightdope.com/t/math-help-please/804391/4 "2017-12-13T14:04:29Z")
> [@Left\_Hand\_of\_Dorkness](#):
>
> My apologies if I’m missing something obvious :).
That’s what I came up with more slowly than you using geometry rather than algebra. 🙂
Can the remaining dough be remixed and used?
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### Author:  [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)
#### Post date: [December 13, 2017, 2:06pm UTC](https://boards.straightdope.com/t/math-help-please/804391/5 "2017-12-13T14:06:50Z")
(Radius of larger)[sup]2[/sup] ÷ (radius of smaller)[sup]2[/sup] = number of smaller that can be made from larger … both factors have a π term but I’ve taken the liberty to cancel those out for you …
The answer to the example is 9[sup]2[/sup] ÷ 3[sup]2[/sup] = 9 …
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### Author:  [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)
#### Post date: [December 13, 2017, 2:08pm UTC](https://boards.straightdope.com/t/math-help-please/804391/6 "2017-12-13T14:08:21Z")
> [@carnivorousplant](#):
>
> Can the remaining dough be remixed and used?
That’s what I wondered.
The amount of dough in a 9" diameter (4.5" radius) circular pie crust (pi \* 4.5²) is 9 times as much as the amount of dough in a 3" pie crust (pi \* 1.5²).
On preview, I see that **watchwolf49** has already calculated this. He used diameters instead of radii in his calculation, but it doesn’t matter if all you care about is the ratio.
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### Author:  [@Colophon](https://boards.straightdope.com/u/Colophon)
#### Post date: [December 13, 2017, 2:08pm UTC](https://boards.straightdope.com/t/math-help-please/804391/7 "2017-12-13T14:08:31Z")
If you roll out the remaining scraps then you can make 9[sup]2[/sup] / 3[sup]2[/sup] = 9, of course. (The pis cancel out; hopefully the pies won’t.)
Edit: beaten to it.
> [@watchwolf49](#):
>
> The answer to the example is 9[sup]2[/sup] ÷ 3[sup]2[/sup] = 9 …
Nine, not nine recurring 😉
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### Author:  [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)
#### Post date: [December 13, 2017, 2:10pm UTC](https://boards.straightdope.com/t/math-help-please/804391/8 "2017-12-13T14:10:29Z")
> [@Thudlow\_Boink](#):
>
> That’s what I wondered.
>
> The amount of dough in a 9" diameter (4.5" radius) circular pie crust (pi \* 4.5²) is 9 times as much as the amount of dough in a 3" pie crust (pi \* 1.5²).
>
> On preview, I see that **watchwolf49** has already calculated this. He used diameters instead of radii in his calculation, but it doesn’t matter if all you care about is the ratio.
[hangs head in shame] … my only excuse is that I _always_ use diameter when filling out tax forms …
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### Author:  [@Chefguy](https://boards.straightdope.com/u/Chefguy)
#### Post date: [December 13, 2017, 2:10pm UTC](https://boards.straightdope.com/t/math-help-please/804391/9 "2017-12-13T14:10:45Z")
This is really embarrassing, but then it’s only just 6 a.m. and I’ve been up for two hours without coffee. The above seems logical. But what if I started at the top and then worked around the perimeter with the small circles touching each other? Do I gain anything, or do I end up the same?
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### Author:  [@bibliophage](https://boards.straightdope.com/u/bibliophage)
#### Post date: [December 13, 2017, 2:11pm UTC](https://boards.straightdope.com/t/math-help-please/804391/10 "2017-12-13T14:11:38Z")
If you can salvage the scraps and roll them out again to the original thickness, you can get exactly 9 tarts from one pie crust (nine squared divided by three squared). If the scraps are waste and can’t be reused, you can get 7 three-inch circles from one nine-inch crust. ([cite](http://mathworld.wolfram.com/CirclePacking.html))
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### Author:  [@zoid](https://boards.straightdope.com/u/zoid)
#### Post date: [December 13, 2017, 2:17pm UTC](https://boards.straightdope.com/t/math-help-please/804391/11 "2017-12-13T14:17:15Z")
If you don’t want to use the scraps - 7
Get 7 coins of the same denomination and circle 6 of them around the seventh for a good visual.
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### Author:  [@Inner\_Stickler](https://boards.straightdope.com/u/Inner_Stickler)
#### Post date: [December 13, 2017, 2:24pm UTC](https://boards.straightdope.com/t/math-help-please/804391/12 "2017-12-13T14:24:25Z")
> [@Chefguy](#):
>
> This is really embarrassing, but then it’s only just 6 a.m. and I’ve been up for two hours without coffee. The above seems logical. But what if I started at the top and then worked around the perimeter with the small circles touching each other? Do I gain anything, or do I end up the same?
I think you end up the same. That way you can fit 5 circles around the perimeter but there’s not enough dough in the center for another pie.
According to [this website](https://www.engineeringtoolbox.com/smaller-circles-in-larger-circle-d_1849.html) for a nine inch pie crust, you can get 14 with a 2" diameter, 8 with a 2.5", 5 with a 3", 4 with a 3.5" and 3 with a 4".
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### Author:  [@DPRK](https://boards.straightdope.com/u/DPRK)
#### Post date: [December 13, 2017, 2:34pm UTC](https://boards.straightdope.com/t/math-help-please/804391/13 "2017-12-13T14:34:59Z")
You can pack 7 circles of radius 3 into a circle of radius 9, but no more.
[Here’s a picture.](http://hydra.nat.uni-magdeburg.de/packing/cci/d1.html)
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### Author:  [@Colophon](https://boards.straightdope.com/u/Colophon)
#### Post date: [December 13, 2017, 2:35pm UTC](https://boards.straightdope.com/t/math-help-please/804391/14 "2017-12-13T14:35:08Z")
> [@Inner\_Stickler](#):
>
> I think you end up the same. That way you can fit 5 circles around the perimeter but there’s not enough dough in the center for another pie.
No, you can fit one 3" circle exactly in the centre and another six all the way round, touching each other.
Like so: [Imgur: The magic of the Internet](https://i.imgur.com/g1Rivif.png)
Then if you take the leftover pieces and re-roll to the same thickness you should have exactly enough for two more.
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### Author:  [@Chefguy](https://boards.straightdope.com/u/Chefguy)
#### Post date: [December 13, 2017, 2:57pm UTC](https://boards.straightdope.com/t/math-help-please/804391/15 "2017-12-13T14:57:44Z")
Great! And yes, I can re-roll the scraps.
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### Author:  [@bibliophage](https://boards.straightdope.com/u/bibliophage)
#### Post date: [December 13, 2017, 3:14pm UTC](https://boards.straightdope.com/t/math-help-please/804391/16 "2017-12-13T15:14:01Z")
It just occurred to me that we should have asked what you meant when you said a nine-inch crust. Is it a crust with a known diameter of nine inches or a crust designed to fit in a 9-inch pie pan? If the latter, it will have to be bigger than 9 inches in diameter, in order to fit up the sides with some left over for edges. The ones I’ve bought in the past were probably at least 12 inches in diameter, maybe 13 or a little more. Assuming 12 inches you should be able to get 16 three-inch circles if you reuse the scraps.
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### Author:  [@brainstall](https://boards.straightdope.com/u/brainstall)
#### Post date: [December 13, 2017, 3:21pm UTC](https://boards.straightdope.com/t/math-help-please/804391/17 "2017-12-13T15:21:19Z")
Wouldn’t it be easier to just buy the little tart shells?
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### Author:  [@The\_Librarian](https://boards.straightdope.com/u/The_Librarian)
#### Post date: [December 13, 2017, 3:28pm UTC](https://boards.straightdope.com/t/math-help-please/804391/18 "2017-12-13T15:28:10Z")
> [@brainstall](#):
>
> Wouldn’t it be easier to just buy the little tart shells?
Hey!
That’s cheating!
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### Author:  [@Chefguy](https://boards.straightdope.com/u/Chefguy)
#### Post date: [December 13, 2017, 3:40pm UTC](https://boards.straightdope.com/t/math-help-please/804391/19 "2017-12-13T15:40:53Z")
> [@brainstall](#):
>
> Wouldn’t it be easier to just buy the little tart shells?
:smack:
> [@](#):
>
> It just occurred to me that we should have asked what you meant when you said a nine-inch crust. Is it a crust with a known diameter of nine inches or a crust designed to fit in a 9-inch pie pan? If the latter, it will have to be bigger than 9 inches in diameter, in order to fit up the sides with some left over for edges. The ones I’ve bought in the past were probably at least 12 inches in diameter, maybe 13 or a little more. Assuming 12 inches you should be able to get 16 three-inch circles if you reuse the scraps.
Double :smack:
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### Author:  [@Elendil\_s\_Heir](https://boards.straightdope.com/u/Elendil_s_Heir)
#### Post date: [December 13, 2017, 4:07pm UTC](https://boards.straightdope.com/t/math-help-please/804391/20 "2017-12-13T16:07:54Z")
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