Posted on 2004-05-22 11:53:25, modified on 2006-01-09 16:29:21
Today somebody tried to convince me that the Imperial system for measuring sizes was much better "because you could easily divide distances by 3". His example was cutting a wooden plank in three equal size pieces. Read on to see where his ideas are flawed.
Dividing objects in equal parts only works if the objects are properly pre-measured. For example I can split 100 marbles into 10 groups, because 100 divided by 10 doesn't have any leftovers.
For the same reason I can split 2 wooden planks into 2 groups, each of one plank.
But then... splitting one object is more difficult. For example, cutting an apple (pretty solid material) in half leaves you with two more-or-less half-apple pieces. And some leftover apple-juice on your knife. So you actually splitted it in three pieces: two nearly-half-apple-pieces and an some-juice-piece.
Now back to the plank. You measure it up, it's one yard. Since one yard is 36 inches, dividing it into three pieces would make every piece 12 inches. Take a measure tape, mark the plank at 12 inch and at 24 inch. And start sawing, trying to stick to the marks you've set as good as possible.
At the end, you end up with: one piece a little bit smaller than 12 inch, one piece two little bits smaller than 12 inch, another piece a little bit smaller than 12 inch and some saw dust.
In the metric system, it's the same idea. You get a plank of one meter, mark it somewhere between 32.25 and 33.5 centimeters and somewhere between 66.5 and 66.75 centimeters and start sawing, also here trying to stick to the marks you've set as good as possible.
At the end, you end up with: one piece about 33.3 centimeters, one piece just not yet 33.3 centimeters, another piece about 33.3 centimeters and some saw dust.
Moral of the story: either with the Imperial or the Metric system, you don't end up with three equal pieces because a. the mark you've set is always too wide to be exactly on 1/3rd of the size and b. you're losing material due to the sawing.
In areas where you do need to be as precise as you can be, people don't use normal rulers anymore but use the more precise caliper (dutch: schuifmaat) and they don't use a plank of one meter or yard to start with but one which is just a little bit bigger so they take the loss of sawing into account.
And remember, if a plank is sawn and is just a little bit too big, you can easily shave it a little bit off with a plane (dutch: houtschaaf).| Share on Facebook | Share on Twitter
|Posted on:||2004-08-23 16:36:41|
|Comment||When is it exactly that you find yourself in the situation where you want to cut a plank in three?
The only times I find myself in a situation where I need an object split three ways is when I need to mail a sheet of A4 size paper in a C6 size envelope. For that I use measurement by eye, which is precice enough for this application.
I surely hope that carpenters build houses by measurement and not by division-by-three...
PS. For a nice walk-through of the ISO 216 paper standard, which you know from the Nederlands (and possibly also Australia - what do I know?), see http://www.cl.cam.ac.uk/~mgk25/iso-paper.html.