Calculating surface area

My half sister, in her early years, only encountered cheese that was grated. When she saw ungrated cheese for the first time she described it as fastened. As far as she was then concerned this was an abnormal state for cheese, and presumably must have required some ingenuity to produce from its natural unfastened state.

Can anybody suggest a practical, ideally non-destructive, method of measuring the surface area of unfastened cheese?

Interesting problem.

In order to work towards an answer, I need to ask you some questions:

To what accuracy do you need to know the answer?

I watched a TV programme some time ago that pointed out that the measurement of the length of a coastline, for example, depends on how small a detail it’s measured to. (I dont know the correct term for this.) If you measure with a large ruler, you’ll step over some of the tiny irregularities in the edge; if you measure with a small one, you’ll follow the contours more accurately. Thus, measuring with a small ruler will end up with a larger value. You have a similar problem with surface area of cheese, as the cheese isn’t smooth – there are tiny microcracks in it, and there is a general surface roughness which, if accurately followed, will produce a higher measurement of surface area than ignoring it. (A sheet of A4 paper has an area of one sixteenth of a square metre per side when measured macroscopically, but maybe substantialy more if the roughness were taken into account.) So, how small a detail of surface contour do you need to be taken into account?

The simplest method would probably be to assume that the cheese gratings are flat.

Sprinkle it across a flat surface of uniform colour (preferably not the same colour as the cheese itself). Take a photo from above, making sure to measure the dimensions of the area you’re photographing. Run it through a simple piece of software which counts the number of non-background coloured pixels. From the dimensions of the image and the dimensions of the surface you should be able to work out the area each pixel represents; multiply that by the number of non-background pixels and then multiply by two to get a rough measure of the surface area of the cheese.

You could probably improve the accuracy quite a bit by estimating the average thickness of the cheese gratings and running a different algorithm which does edge detection on the image. Then for each edge pixel you just add thickness of cheese * length of pixel to the total area.

To save future trouble the next time someone asks you the surface area of your cheese, you could calculate the average surface area per unit mass, so that you can calculate the area of the cheese just be weighing it (n.b. I am not liable for any damages caused by incorrectly calculating the surface area of cheese).

This is silly. What’s required is to arrange for an ISO standard cheese grating to be defined. This simplifies things as any piece of cheese that doesn’t match the standard shape and size can’t be called a cheese grating any more and therefore doesn’t need to be taken into account. It’s then just a matter of counting how many cheese gratings you have and multiplying by the standard surface area.

Isn’t the coastal thing to do with fractals?

I was thinking about mould spores. They seem to spread initially over the surface of cheese rather than burrow into it. So I was wondering whether unfastened cheese would go mouldy quicker. Yes, I guess it is a fractal problem. How about using the diameter of a mould spore as the key parameter?

I like the photography trick. Just one more amazing use for a mobile phone.

I think Jeffrey has betrayed a technical aptitude and a basic grounding in practical maths.¹

To answer Fed’s question: yes. The degree of complexity of the observed edge is dependent on the accuracy of the observation.

The cheese edges will feature similar increasing complexity.
Note that the edge complexity will also vary with cheese type and mouse trap “cheddar” will be less likely to present a complex edge at a macro level than wensleydale.
The likes of brie or goats cheese are best measured by wrapping in a bin liner and measuring the lump.

¹ On no account should such things be held against him :)

Can anybody suggest a practical, ideally non-destructive, method of measuring the surface area of unfastened cheese?

Unfastened cheese. Brilliant.

then multiply by two

Cheese is not flat. So maybe 2.1 or 2.2 to get a better “rough” figure? This depends greatly upon the dimensions of the cheese gratings. Big like the way I used to grate cheddar for potatoes, or tiny like parmesan?

So I was wondering whether unfastened cheese would go mouldy quicker.

I think dampness is a necessity. Mould seems to like damp spots on the cheese. And in my experience grating the stuff is a great way to make it go dry and inedible. Plus, for extra bonus points, it changes shape so the previous surface area will no longer be correct. ;-)

Also depends on what cheese you are trying to unfasten and what device you are using.
St. Agur or Stilton may have the advantage in the mould stakes, but would be a bu99er to unfasten, and as for Brie?!
The size, shape, cutting pitch and sharpness of the unfastening device will have an effect, as too will speed and pressure applied.
Have you taken into account the odd extra bits of digit that may come from the over-enthusiastic unfastener operative?

On a more serious note?!
Weigh a 1cm cube of said dairy based produce.
Coat in a fine powder, eg plain flour or cornflour, and weigh again. That should give you a datum for 6cm2.
Then weigh out the same of the unfastened product, coat and weigh again.
Some maths may be involved at this point, which is where I start to lose it!

This is only non destructive if you then go on to make a sauce for cauliflower cheese. :)

Unfastened cheese. Brilliant.

I am glad you like the terminology. It has become standard use in our family. I suppose most families have their own vocabularies. When my mother was small she used to get bread and butter with sugar sprinkled on, which was always known as arpsley . Large juicy blackberries I used to call clarabelles ; I had a Mickey Mouse Annual in which appeared a character called Clarabelle Cow, who was depicted with large juicy lips. A family word which has entered into my programming is snerp . When we moved to my grandmother’s house in the Lake District, we found a plethora of Victorian bric-a-brac and gadgets, mostly for gardening. With these I liked to construct Heath Robinson devices. Not that they did anything. The important aspect was the Naming of Parts. One such was the snerping tube . This gave rise to the verb, a synonym of hack , bodge or contrapt .
I have come to use !Snerp as a standard name for an application that is intended for no serious purpose other than to demonstrate the use of certain libraries or expressions.

I see that stephen has hit on the way to turn unfastened cheese into fastened cheese you have to melt it then let it go hard an bob your uncle result.

Ah Hah ! You have just discovered that old Roman dish “CheeseLava”

If one assumes that Worcester Sauce can form a monolayer, is there any mileage in taking the fastened cheese of a known surface area and coating it from a known volume of Worcester Sauce and seeing how much remains.

Then do the same with the unfastened cheese. Actually, I see now it doesn’t even have to form a monolayer, just to coat uniformly.

The ratios of the Worcester sauce used in each case, calculated from the amount remaining after coating, should be proportional to the surface areas presented, and the area of the fastened cheese presented should be easily calculated.

Thus the surface area of the unfastened chese should be easily calculated in any specific case of unfastening, and the cheese itself will be delicious toasted!

So, a solution to the problem and a tasty meal as a by-product.

I would use Welsh Cheddar myself.

The ratios of the Worcester sauce used in each case

Zero. Don’t have it the house. Much better product, which I have to fetch from Sheffield at intervals.

John – I had thought about the “chuck it in water, measure the displacement”, but didn’t post it for two reasons. The first, that it is a somewhat destructive method so doesn’t fit in the design parameters, and the second, that the displacement tells you the volume, not the surface area.
As such, I would expect a piece of cheese measured in its fastened state and then measured again in its unfastened state, to have equal displacement of water (or sauce). The volume of cheese does not change, you don’t get more cheese as you grate it (else we’d all be grating our cheese).
With that in mind, I’m not sure that displacement is a viable way to measure surface area.

This leads on to the monolayer coating. While it is a good idea (although arguably equally destructive), I think there may be a question mark over exactly how much the cheese is coated in order to make any sort of useful measurement. As somebody who has put ample amounts of Yakitori Sauce on cheddar, the cheese can be slightly porous and with pretty rough edges (at least, if we’re talking a decently aged cheese) so can hold quite a lot of sauce. The texture of a piece of grated cheese is different to the fastened state of the cheese (which is often fairly smooth due to industrial cutting and shrink-wrap packaging.
That roughness – it’s the same reason you should match a bolognese sauce with fusilli and not spaghetti – the shape of fusilli lends itself to holding a sauce with bits of stuff within.
So, how does one define a “monolayer”? How much is enough? How much is too much?

Scottish or Canadian cheddar myself.
The most miserable piece of cheddar I ever bought¹ was actually bought…in Cheddar. The big ol’ ‘ole in the ground² was considerably more interesting; though not a match for Wookey Hole (that said, the linked website is enough to put anybody off ever going…at least when I went it was long enough ago that the caves pretty much sold themselves and didn’t need witches and dinosaurs and barely-dressed-gymnasts and…wow that site is taxing on the eyeballs).

¹ Actually, the worst cheddar ever was that Tesco blue-stripe stuff, but I don’t tend to consider that to be representative of cheddar. Or cheese. Or food.

² The website for Cheddar Gorge. The intro photo. You see the rockface? The BIG one on the left? I climbed it. A friend and I went there and we saw a sign on top. So we thought we’d go see what it said. A long long trek by path, or a simple straight up. So utterly recklessly with no ropes and wearing ordinary clothes, we just took the up route. Back when I was a late teenager and did dumb stuff like that. We made it, intact, unhurt, without slippage. To find a sign that said “DANGER! DO NOT CLIMB THIS ROCKFACE.” Yeah, and why didn’t they put one at the bottom too?!? We looked over the edge and decided not to tempt fate twice on the same day, and walked down the path… Oh, excellent view from the top, if it’s a nice day. You can sort of get an idea of this from the photo.

John – I had thought about the “chuck it in water, measure the displacement”, but didn’t post it for two reasons. The first, that it is a somewhat destructive method so doesn’t fit in the design parameters, and the second, that the displacement tells you the volume, not the surface area.

Which is, of course, why I never even considered it as a potential method!

As somebody who has put ample amounts of Yakitori Sauce on cheddar, the cheese can be slightly porous and with pretty rough edges (at least, if we’re talking a decently aged cheese) so can hold quite a lot of sauce.

If the cheese is an invariable, I don’t see what your point is. The adherence properties should be the same for the same cheese in both forms.

I used Worcester sauce as I am familiar with its wetting and coating properties. I am unfamiliar with the sauce you are promoting and am therefore unable to comment on its suitability. However, I’m surprised that Tesco have outlets in your region remembering that it’s many years since M&S backed out of Northern France!

So, how does one define a “monolayer”? How much is enough? How much is too much?

I did correct myself over the monolayer: It is not a prerequisite. However, “enough” is what the cheese can be immersed in, and “too much” is what then drains off, leaving the coating layer on both the fastened and unfastened cheese. It is this drained residue, compared with the volume we started with, which gives us our result in each case. I would use a conical stainless steel drainer such as I use for the fusilli:

Fusilli is what I base the dog’s diet on, so we seldom use it ourselves because it’s all in a big plastic sweetie jar for convenience, but personally I would not consider serving bolognaise with anything but spaghetti.

Don’t get me wrong, I am not a purist – I even break it in half for ease of getting it in the pan – but I despair the habit of using tagliatelle as is common in Italian restaurants in (our parts of) France.

It may or may not be an authentic regional variation, but to me it’s just plain wrong!

As to the cheddar, you do not have, AFAIK, the opportunity to shop at Aldi where the Welsh cheddar is excellent!

Lidl at CB may, however, have a similar product, as the lines are often parallel between the two filial traders.

The adherence properties should be the same for the same cheese in both forms.

Something smooth ought to hold less of a gloopy liquid than something rough. Again, the “surface area” depends upon how finely you measure, but you’ll find a rough flattish bit of cheese would have a much greater surface area than a smooth piece.

However, I’m surprised that Tesco have outlets in your region

Given your sometimes-proximity, you ought to know Tesco has no presence around here. The picture is the first thing Google offered me. I buy mine from the Super U.

I would not consider serving bolognaise with anything but spaghetti.

http://www.bbcgoodfood.com/howto/guide/perfect-pairings-how-match-pasta-shapes-sauces

but I despair the habit of using tagliatelle as is common in Italian restaurants in (our parts of) France.

That’s because it is dirt cheap (350g for a euro at consumer rates, imagine the price to buy it in bulk) and the so-called Italian restaurants are braindead and useless and don’t understand that different sauces fit different types of pasta.
I bet they chuck a handful of friggin’ emmental on top to. Ewww, that rubbish is not fit to be called cheese. And for some reason the French, a country famed for its billion cheeses, put ’orrible emmental in everything. :-/

Tagliatelle is cheap because it is extremely simple to make. Roll out a big sheet of dough, then cut just pass it through a gang-cutter, basically a lot of cutting discs on a long spindle. You can get this stuff for domestic pasta machines – so there’s absolutely no finesse in it.

Lidl at CB may, however, have a similar product,

Sometimes the U has “Seriously Strong Cheddar”. That’s good. All I need is something that resembles edible bread – you know, a good solid Hovis loaf.

All I need is something that resembles edible bread – you know, a good solid Hovis loaf.

It is possible to buy the flour, in decent quantities. Hand making and baking your own is quite relaxing and the taste when it’s still warm with butter melting in…

^ I think I just decided what I’m doing tomorrow :)

personally I would not consider serving bolognaise with anything but spaghetti.

I despair the habit of using tagliatelle as is common in Italian restaurants in (our parts of) France.

It may or may not be an authentic regional variation, but to me it’s just plain wrong!

In Bologna, they absolutely refute the existence of such a thing as “spaghetti bolognaise”. The meat sauce should be served with tagliatelli, I believe, to be authentic. (My reference is one of Michael Portillo’s journeys that I watched not too long ago, and I’m certain that spaghetti is absolutely wrong to the residents of Bologna, but I’m less certain that tagliatelli is correct.)

Hand making and baking your own is quite relaxing and the taste when it’s still warm with butter melting in…

I’ve always chickened out of hand making bread. I’m on my second bread baking machine. I’ve been consistently delighted with the results (when I put the correct ingredients in, of course…)

I’ve developed my own recipe for a loaf with 30% spelt flour. It’s light, soft, and very tasty. Interestingly, it tastes best about 3 days after being baked.

I also bake loaves with enriched dough and a very high content of mixed fruit, which is a recipe straight out of Panasonic’s book. Wonderful when lightly toasted, buttered, and thinly spread with a light marmalade, such as Bonne Maman mandarin marmalade.