[Maths-Education] Ratio and Proportion
Dick Tahta
d.tahta@open.ac.uk
Sat, 6 Oct 2001 11:48:07 +0100
I cannot resist teasing David Pimm:
>The phrase 'the proportion of goldfish' is itself a nonsense as you cannot
>have a proportion of a >single thing: there is always (he asserted rashly)
>....
My understanding is that "logos" became "proportio" (more common than
"ratio") and "alogon" became "proportionalitas". And that it is the most
common English usage to call a ratio a proportion:
1387 Proportion of roundeness about of a circle .... of twenty two to seven.
1692 Proportion of births to burials .... fifty to forty.
2001 What is my proportion of the bill. (Heard in a local cafe yesterday!)
David did of course cover himself:
>'everyday usage' cares little for mathematical distinctions or desires to
>keep things straight (hence >the 'part to whole' observation might be
>empirically accurate with respect to common usage ...
Should we bother to fight against common usage? (Confirming common
caricature of mathematics teachers as as slightly obsessive other-wordly
people.)
of a single thing , for example, "dividing in the proportion of 2 to 3",
"your proportion of the expenses"
>>>>
>The phrase 'the proportion of goldfish' is itself a nonsense as you cannot
>have a proportion of a single thing: there is always (he asserted rashly)
>a double comparison, a comparison of comparions, if you like). But in this
>compressed usage here it is completely tacit. I agree with Geoff: 'The
>proportion of goldfish is 6 out of 24' implicitly means "the ratio of
>goldfish compared with all fish in this particular tank is as the ratio of
>6 to 24" - or am I simply saving the phenomena?. And writing 6:24 as the
>fraction 6/24 compounds things further.
>
>I think it is an instance of how a simple little word can reveal quite
>another way of thinking about the things: 'the square on the hypotenuse'
>(geometric figure related to another geometric figure versus 'the square
>of the hypotenuse' (arithmetical operation carried out on numerical
>measure of length) provides another.
>
>David Fowler's account of pre-Eudoxan ratio theory (The Mathematics of
>Plato's Academy) reconstructs an independent definition of 'the ratio of A
>to B' (based on anthyphairesis, "continued subtraction in turn"),
>independent, that is, of any definition of proportion, whereas Eudoxus'
>theory (in Euclid book 5) is really a theory of proportion.
>
>But I think another compounding problem is that- I don't have the Collins
>COBUILD English dictionary to hand, but it would be interesting to look
>there and see what usages they managed to cull from the large database of
>actual useage).
>
>David
>
>
>
David Pimm
Dept of Secondary Education,
Faculty of Education,
University of Alberta,
Edmonton, AB
Canada T6G 2G5
David.Pimm@ualberta.ca
tel: (780)-492-0150
sec: (780)-492-0148
fax: (780)-492-0162