# Maths problem



## Pudsey_Bear (Sep 25, 2008)

As mentioned a few times, I am crap at maths, no really, I'm terrible, but I need to make a pastry cutter for Lizs sons bakery shop, and I thought Okay how difficult can it be to do it properly, so I went to YT to find a vid I could understand and found this one:-





OK so PI = 3.14 but using that the numbers do not work IE D=22.6cm x 3.14 = 70.964cm so 71 for cash, but using the same tape around the upturned test bowl as it has a flat part at the top I get 71.9cm

The maths work, but the size is incorrect.

Am I wrong or is it the video? if it's me where am I going wrong, it's a dress makers tape and does not stretch.

Please try to reply with worms of one silly bubble or I wont get it.


----------



## tugboat (Sep 14, 2013)

What are you trying to end up with, Kev? Size-wise. Is it something custom not available off the shelf?


----------



## Pudsey_Bear (Sep 25, 2008)

tugboat said:


> What are you trying to end up with, Kev? Size-wise. Is it something custom not available off the shelf?


Custom by it's nature is not on any shelf so has to b e made Geoff:wink2::wink2:

Prices are ludicrously expensive, I've made some out of large tins etc, but I don't have any of the right size.


----------



## peribro (Sep 6, 2009)

Few thought Kev: 

Are you sure you were measuring the diameter at the widest point?

Did you try moving one end around to get the widest point? 

Did you measure outside to outside? 

Is the bowl truly circular? 

Are you sure the diameter was exactly 22.6cm and the circumference exactly 71.9cm? A few mm can make a difference.

ps pi is 3.14159265359 plus billions more!


----------



## Pudsey_Bear (Sep 25, 2008)

Yes I did as you say even with a steel tape to check and got the same no matter where I measured.

I'd need to be approx 3mm out on the OD to get that error though I think.

71.9 is from the tape measure so not to any decimal place.


----------



## Penquin (Oct 15, 2007)

You are correct that Pi is 3.142 (22/7) *the rhyme was "around the side is Pi times D

so the formula for the circumference is Pi x diameter

BUT you have measured the EXTERNAL diameter and the distance you need is the INTERNAL, do you have a internal micrometer? That will give you the most accurate measurement.....

tape measures are not that precise either so the differences are probably within £experimental error" for the measuring devices you are using......

Good luck, Pi has been calculated to more than a million decomal places (by a mathemtacian with nothing to do presumably...)

if you are bored go to;

One million places

Have fun......

I hope the pastry cutter turns out OK, I suspect the hardest thing would be securing a sheet of stainless steel at EXACTLY the correct diameter......

Dave


----------



## peribro (Sep 6, 2009)

I'm wondering if it's somehow the thickness (although thin) of the tape measure when measuring the diameter?


----------



## cabby (May 14, 2005)

I am also perplexed with this problem, can I ask, as I am a bit slow today,is it not the inner edge of the round cutter that will be the most important, so what happens if you measure the circumference on the inside. 

cabby


----------



## Pudsey_Bear (Sep 25, 2008)

Penquin said:


> You are correct that Pi is 3.142 (22/7) *the rhyme was "around the side is Pi times D
> 
> so the formula for the circumference is Pi x diameter
> 
> ...


The circumference needs to be the outside diameter so the excess can be trimmed, so the number itself in this case doesn't matter too much it's more how the sums don't add up, I'll try another bowl and tape tomorrow and see how that works out.

I'm not using Stainless as it would need to be TIG welded plus a handle, so I'm using food grade white plastic instead, much easier to work with and can be glued or welded, possibly with a wooden handle,


----------



## pippin (Nov 15, 2007)

How are you going to make it corrugated - as most pastry cutters are?

The mathematics of that would be hideously complicated for you, but a simple exercise for a mathematician.


----------



## Pudsey_Bear (Sep 25, 2008)

Doesn't need to be, it's to make discs to fit into round foil trays, so the edge will need slight trimming.


----------



## listerdiesel (Aug 3, 2012)

Circumference is (2 * pi * R) or (2 X 3.142 X 113) = 710mm or 71cm.

(pi * D) gives the same answer 

Can't make that any different I'm afraid.

Peter


----------



## Pudsey_Bear (Sep 25, 2008)

The numbers are fine Peter, it must be the tape or something, same each time though.


----------



## Penquin (Oct 15, 2007)

pippin said:


> How are you going to make it corrugated - as most pastry cutters are?
> 
> The mathematics of that would be hideously complicated for you, but a simple exercise for a mathematician.


Having checked with a higher authority, some are fluted (technical term apparently means corrugated), some are straight, it depends on what you wish to cut.....

Mary Berry is wonderful.....

Double sided cutters 

Dave


----------



## delawaredandy (Oct 12, 2012)

Kev, sorry mate but FFS get a life, it's a pastry cutter, time to take to the bottle me thinks. :drinking::drinking:


----------



## erneboy (Feb 8, 2007)

Using a tape to measure the circumference will produce sufficient error to make the sums wrong.

For the OD mark a place on the edge and roll the bowl along the edge of a table top (near the edge to keep the line straight) give it one revolution and measure how far it's gone.


----------



## rayrecrok (Nov 21, 2008)

Maybe a dress makers tape might get stretched as it attempts to go round some woman's arses.... Just a theory.:grin2:...

ray.


----------



## Pudsey_Bear (Sep 25, 2008)

erneboy said:


> Using a tape to measure the circumference will produce sufficient error to make the sums wrong.
> 
> For the OD mark a place on the edge and roll the bowl along the edge of a table top (near the edge to keep the line straight) give it one revolution and measure how far it's gone.


I don't see how that would change anything Alan as it is strong dress makers tape, and does not stretch, I tried to when I got the anomaly.

I will try yours in the morning though:wink2:


----------



## Pudsey_Bear (Sep 25, 2008)

rayrecrok said:


> Maybe a dress makers tape might get stretched as it attempts to go round some woman's arses.... Just a theory.:grin2:...
> 
> ray.


You'll go straight to hell for that one Ray>>>


----------



## erneboy (Feb 8, 2007)

Well it's a small circle and you're adding the thickness of the tape for one thing, that might give you an extra mm or two for a start.


----------



## Penquin (Oct 15, 2007)

The diameter that you gave is 22.6 so 22.6 x 3.142 = 71.0092 mm

the tape measure with which you measured the circumference has a thickness of say 1mm if it is a cloth tape measure

so the diameter measured may be inaccurate, and the circumference WILL be

if the tape measure was 1mm out then the figures would be 22.5 x 3.142 = 70.695 

the tape measure must also have a very small amount of stretch in it - otherwise it could not bend at all as the inside of the curve must be slightly shorter than the outside - so either the inside is compressing or the outside is stretching - or most likely both are happening around a mid point.

A difference of 0.9mm which is what you have reported, can be partially accounted for by the fact that Pi does not equal 3.14 or even 3.142 but is an approximation 

But the important thing is to relax and just go ahead and make the cutters - they might be useful for Pi(es) and I am sure there will be enough to go round...... (sorry pun intended)

Certainly the maths does work in everyday life, and I suspect that when engineers need to calculate the strength pf a circular beam they will use the formula Pi x r x r , although there will always be a safety margin built in - but of course, they do not use a tape measure to ever check the circumference of e.g. the pilings for supporting bridges, or the circumference of the cables for suspension bridges or lift wires.....

Dave


----------



## Pudsey_Bear (Sep 25, 2008)

Penquin said:


> The diameter that you gave is 22.6 so 22.6 x 3.142 = 71.0092 mm
> 
> the tape measure with which you measured the circumference has a thickness of say 1mm if it is a cloth tape measure
> 
> ...


Seems near enough to me Dave, makes sense, accounts for the discrepancy, and it's not going to affect the spin of the planet, and 0.9cm isn't going to affect the diameter greatly (not even going to attempt what it would be at this ungodly hour) too be honest I'm just glad that at this time in my life I found a use for some crap a bloke who liked to cane me for fun actually finally became useful.

Thanks to everyone who participated in my hour of need, MHF to the rescue again, and nowt to do with a MoHo too > >

Btw Dave, why do you use 3.142, surely the additional 2 makes the error larger?


----------



## H1-GBV (Feb 28, 2006)

Kev_n_Liz said:


> ... and 0.9cm isn't going to affect the diameter greatly ...


An OLD question used to get students thinking:

Imagine you took a long, (non-stretching) rope and pulled it taut round the equator of the Earth (ignore mountains, marine tranches etc!).

Then you ADD 6" to the length.

What would be the average distance from the surface of the Earth to the rope if it stands out all the way round?

ONE of these answers is approx correct: - 0.000 000 1", 0.000 1", 0.01", 1", 6".

Gordon


----------



## Pudsey_Bear (Sep 25, 2008)

H1-GBV said:


> An OLD question used to get students thinking:
> 
> Imagine you took a long, (non-stretching) rope and pulled it taut round the equator of the Earth (ignore mountains, marine tranches etc!).
> 
> ...


Unbelievable only 6'' I think, it was on TV a while back in one of those maths shows, but they phrased it the other way around IE if you took a rope and raised it 6" how long would it be, 40,000 (ish)km +150(ish)mm


----------



## HarleyDave (Jul 1, 2007)

Also interesting and sort of related

The World Pool-Billiard Association Tournament Table and Equipment Specifications (November 2001) state:

"All balls must be composed of cast phenolic resin plastic and measure 2 ¼ (+.005) inches [5.715 cm (+ .127 mm)] in diameter and weigh 5 ½ to 6 oz [156 to 170 gms]." (Specification 16.

This means that balls with a diameter of 2.25 inches cannot have any imperfections (bumps or dents) greater than 0.005 inches.

In other words, the bump or dent to diameter ratio cannot exceed 0.005/2.25 = 0.0022222

The Earth's diameter is approximately 12,756.2 kilometres or 12,756,200 metres.
12,756,200 x 0.0022222 = 28,347.111

So, if a billiard ball were enlarged to the size of Earth, the maximum allowable bump (mountain) or dent (trench) would be 28,347 metres.

Earth's highest mountain, Mount Everest, is only 8,848 metres above sea level. Earth's deepest trench, the Mariana Trench, is only about 11 kilometres below sea level.

So if the Earth were scaled down to the size of a billiard ball, all its mountains and trenches would fall well within the WPA's specifications for smoothness.

However, it should be also be noted that if the Earth is not a perfect sphere. It is an oblate spheroid and should therefore also be tested for conformity to WPA specifications due to its shape.

The distance between Earth's poles is shorter than its diameter at the equator by approximately 43km. The maximum deviation with the respect to the Earth's average diameter is half that distance, or 21.5km, which is within the scaled up WPA tolerance of 28.3km.

It can therefore be seen that the Earth would conform to WPA specifications for billiard balls if it was scaled down to the appropriate size, and it could said to be smoother than at least some billiard balls that would be permitted by the WPA.

Cheers

Dave


----------



## nicholsong (May 26, 2009)

Dave

You would have been better off spending your Sunday morning in Church, because that post will never get you to Heaven:laugh:

Geoff


----------



## nicholsong (May 26, 2009)

Kev

What you worried about - pastry is elastic it will expand or contract to take up any minor variation. You are not fitting a turbine blade into a shroud.:smile2:

Geoff


----------



## Pudsey_Bear (Sep 25, 2008)

nicholsong said:


> Kev
> 
> What you worried about - pastry is elastic it will expand or contract to take up any minor variation. You are not fitting a turbine blade into a shroud.:smile2:
> 
> Geoff


You should not overwork pastry Geoff, the post was about maths anyway (if you kept up  ) not the pastry as obviously any minimal excess could be cut off, and possibly re-used if it's only been rolled once, the size will be fine at 71 if I was actually going to use a cutter that size, but that was just a handy bowl in the kitchen I used to work out the maths, as once I do something like that I can usually come back to it years later and not forget, unlike just reading it and hoping I remember which usually fails.


----------



## nicholsong (May 26, 2009)

Kev_n_Liz said:


> You should not overwork pastry Geoff, the post was about maths anyway (if you kept up  ) not the pastry as obviously any minimal excess could be cut off, and possibly re-used if it's only been rolled once, the size will be fine at 71 if I was actually going to use a cutter that size, but that was just a handy bowl in the kitchen I used to work out the maths, as once I do something like that I can usually come back to it years later and not forget, unlike just reading it and hoping I remember which usually fails.


Kev

You should have said it was an intellectual excercise - I thought it was a practical problem:wink2::laugh:


----------



## HermanHymer (Dec 5, 2008)

No wonder you can't get the right answer! Ask any baker - pi are not square, they are round!


----------



## Penquin (Oct 15, 2007)

except steak and kidney, chicken, steak and onion and so on......

but they are neither square or round....... they are rectangles......

us pendants will always swing together...... (but not in that way.......)

Dave


----------



## Penquin (Oct 15, 2007)

Kev_n_Liz said:


> Btw Dave, why do you use 3.142, surely the additional 2 makes the error larger?


Force of habit, 3.142 is what was always used in the school I taught in, and so it has sort of stuck....

and yes you are correct but the accurate figure (from memory) 3.14159 etc....

is rounded up to 2 significant decimal places to 3.142.....

We used to have to use statistics etc heavily at A level and we were always teaching that any error LESS than 5% was not significant and that if it was OVER 5% it had to be considered significant and a possible reason identified.

It makes me smile when I see Government (and Opposition) and the BBC particularly really concentrating on differences of 0.5% - statisticians would not be concerned..... just think how many Governmental things have been justified by saying that there is a 1, 2 3 or even 4% change...... when a true statistician would not be concerned by such an occurrence.....

the truth of the statisticians position can perhaps be illustrated by the dependence that the BBC and others placed on the pre-election opinion polls - based on VERY small population samples and showing an error way more than + or - 5%.......

Maths can be fun......

Oh, I checked again today, the *smooth edged pastry cutters are generally used for SAVOURY pastries*, *the crinkled edge ones for SWEET* so that if you have a plate of scones, for instance, you know rapidly which are sweet (e.g. fruit) and which are savoury (e.g. cheese)....

There, now you know.....

isn't MHF wonderful ?

Dave:nerd: > :grin2:


----------



## HermanHymer (Dec 5, 2008)

Penquin said:


> except steak and kidney, chicken, steak and onion and so on......
> 
> but they are neither square or round....... they are rectangles......
> 
> ...


awww... spoilsport!:surprise:


----------



## vicdicdoc (May 14, 2005)

Umm . . .I'm bored now. . . .so where does the answer '42' come ?


----------



## Penquin (Oct 15, 2007)

vicdicdoc said:


> Umm . . .I'm bored now. . . .so where does the answer '42' come ?


different question unless of course you are referring to the 3.142 mentioned in Pi........

Dave>


----------



## H1-GBV (Feb 28, 2006)

vicdicdoc said:


> Umm . . .I'm bored now. . . .so where does the answer '42' come ?


And it wasn't an option in my question, where the answer is that the rope will stand proud by approx 1".

Let R be the radius of the Earth, and h be the height of the rope above the surface.

2*pi*R = first length of rope

2*pi* (R+h) = second length of rope

2*pi* (R+h) = 2*pi* R+2*pi* h

Since 2*pi* R is the original length

then 2*pi* h must be the extra length = 6"

2*pi* = 2 * 3 (approx)

so h = 1" (approx) :nerd:

I was surprised when first shown this - Gordon

PS a similar calculation can be done on "how much further is it to drive round the M25 clockwise rather than anticlockwise?" [approx] :wink2:


----------



## nicholsong (May 26, 2009)

H1-GBV said:


> PS a similar calculation can be done on "how much further is it to drive round the M25 clockwise rather than anticlockwise?" [approx] :wink2:


Inside or outside lane?:wink2::laugh:


----------



## Pudsey_Bear (Sep 25, 2008)

nicholsong said:


> Inside or outside lane?:wink2::laugh:


It'd have to be lane 1 or 2 as you can't in lane 3 etc, So I'd go for lane one, as it would be a big sick bird to do it all in lane 2 etc anyway.


----------



## Easyriders (May 16, 2011)

I often found it easier to use Pi as a fraction - 22/7. So the circumference is 2 X radius X 22/7.

Do you know roughly what diameter the pastry needs to be? If so, halve this amount to find the radius. Then try out some circles using paper, a long ruler, a sharp pencil and a compass. Find the radius you want on the ruler, put the pint of the compass at one end of the measure and the point of the pencil at the other. Without moving the legs of the compass, now draw a circle using it and see if it is what you want. Adjust the compass until you have a circle the size you want, then again without moving the legs of the compass, measure the radius you now have against the ruler.

Now you can draw an exact paper template the size you want. You can then make a round metal or plastic circle that size. Or you can multiply your found radius by 22/7 to give you an exact circumference, so with a pliable material you can make a strip you can join together to make a circle of the exact circumference you want as a cutter.


----------



## Pudsey_Bear (Sep 25, 2008)

Easyriders said:


> I often found it easier to use Pi as a fraction - 22/7. So the circumference is 2 X radius X 22/7.
> 
> Do you know roughly what diameter the pastry needs to be? If so, halve this amount to find the radius. Then try out some circles using paper, a long ruler, a sharp pencil and a compass. Find the radius you want on the ruler, put the pint of the compass at one end of the measure and the point of the pencil at the other. Without moving the legs of the compass, now draw a circle using it and see if it is what you want. Adjust the compass until you have a circle the size you want, then again without moving the legs of the compass, measure the radius you now have against the ruler.
> 
> Now you can draw an exact paper template the size you want. You can then make a round metal or plastic circle that size. Or you can multiply your found radius by 22/7 to give you an exact circumference, so with a pliable material you can make a strip you can join together to make a circle of the exact circumference you want as a cutter.


My calculator doesn't do fractions so I googled it, first thing to pop was :-

"22:7 as a common fraction is 22/7 and to convert to a decimal fraction divide 7 into 22. I got 22/7 = 3.142857... Rounded to the nearest hundredth this is 3.14. If you perform the same operations with 22:5 then 22/5 = 4.4 and you don't need to round" so to sure why you'd go down that route, bearing in mind my already mentioned inability to do maths  

There are other problems in doing a cutter for this job as the foil containers are dished, but I just cut them in half, flatten them and use a ruler, shamelessly lazy but bang on accurate to get the exact diameters.


----------

