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From: rwt@dcs.ed.ac.uk (Rainer Thonnes)
Subject: Re: degrees Celsius
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Date: Wed, 12 Feb 1997 11:35:51 GMT
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In article <199702112117.VAA04290@mauve.demon.co.uk>,
Ian Stirling <root@mauve.demon.co.uk> writes:
> Edward Rice (ehrice@his.com) wrote:
> : rwt@dcs.ed.ac.uk (Rainer Thonnes) wrote:
> :  > ehrice@his.com (Edward Rice) writes:
> :  > >  A cubic centimeter would be more like a small bouillon cube, right?
> :  > Right, but bouillon "cubes" do tend to come in a variety of ... sizes.
> :  > If you can't picture a cm, nor hence a cc, just think
> :  > of the cube as being two thirds of an inch across the space diagonal.
> :  > That's a little over 2% out, so it's near enough.
> 
> Bummer, now I have to do some maths.

Arithmetic, actually.

> 2/3rds of an inch = 1.6853 cm.  Ohh, what a round number :)

Not very round, admittedly, but not very correct either.
1" = 2.54cm; 2.54*2/3 = 1.6933.

> So, a cubes with sides of 1cm has a space diagonal (between opposite corners,
> the firthest points you can get on a cube) of [sqrt(3)cm =] 1.732cm
> 
> This is 2.7% bigger, so cube it, to get the volumetric increase, and it comes
> out to 8.5% small.  Not a bad ballpark.

Actally, it's less than 2.3% bigger, and there's no need to cube it since I
did mean to imply that it was the *length* rather than the volume which was
a little over 2% out.  The aim of the exercise was to be able to "picture"
the size of the cube, so the linear rather than cubic dimension was more
relevant.  I started with sqrt(3)cm and looked for the simplest fraction of
an inch that was close enough.  I would have been even simpler just to say
its sides are 2/5".  I admit that I was being shamelessly obfuscative in
going for the diagonal.

> : The problem I'm having, aside from some occasional trouble with my knee, is
> : picturing *five* such "bouillon cubes", each about 2/3" in length and width
> : and height, fitting into a single US-measure teaspoon.  The teaspoon /is/
> : supposed to be 5 ml, I know that; but there's no way it's five times the
> : size of a 2/3" cube.  So we've got some kind of confusion or mixup in this
> : discussion, and I can't seem to pinpoint it.

The confusion arises from your misreading of my message.  The cube's
*diagonal* is about 2/3", not its side.  Its side is, near as dammit, 2/5",
with only a 1.6% error.

Still, all is not lost.  Sticking with your bouillon cube of 2/3" *sides*,
you don't need to imagine five of them.  Just take one and you'll be near
enough (less than 3% out).  (2/3")^3 = 4.855ml.
