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 Archimedes' Principle

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Caro
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Caro

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PostSubject: Archimedes' Principle   Archimedes' Principle EmptyFri 19 Aug 2022, 03:22

I came across this in the book I am reading (Ann Patchett's The Dutch House) and it had a definition for it, but I could remember word for word what I knew it as: "When a body is immersed in a liquid it loses weight, and the weight it loses is equal to the" but then I have lost the last two words (sum dispersed?). And I don't know why it has stayed in my mind so long: was it something we learnt at school? Or something my grandmother (who brought me up from the age of 4) said? I feel the latter, but I don't quite understand why she would have said this. But somehow it makes more sense that I would remember something she might have repeated when we had a bath than something I would have retained from school.
Did any of you learn this or have anything like it stick in your mind?
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Green George
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Green George

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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptyFri 19 Aug 2022, 12:57

"Liquid displaced" perhaps? The classic one is "weight of liquid displaced" iirc.
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Meles meles
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Meles meles

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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptyFri 19 Aug 2022, 13:07

Caro wrote:
"When a body is immersed in a liquid it loses weight, and the weight it loses is equal to the..."

 ... weight of the liquid displaced.

That's not something I've ever really had to quote before although I've certainly used it practically, for example when determining a material's density. Neither - at least not since having first learned it in junior school - have I ever had to put Pythagoras' theorem into words: both are concepts that I just sort of know, understand and have used, but without ever usually having had to articulate them. If anything I tend to see Pythagoras' theorem (although it's no longer really a theorem as it can easily be demonstrated, graphically and with no sums involved, to be universally true) mentally as a diagram of a right-angled triangle with squares drawn on the three sides. But perhaps that is just the way my mind works and how I tend to learn things, ie not in words but as mental pictures.

Now that you've raised the point, I also think I do not generally learn the order of things by mnemonic rhymes, but rather just as the words themselves albeit perhaps to a particular mental rhythm. For example the intervals of a musical scale in a major key: tone, tone, semitone / tone, tone, tone, semitone; French 'er' regular verb endings: e, es, e / ons, ez, ent; or the Latin declension: amo, amas, amat / amamus, amatis, amant. Indeed at school (when such a fact was deemed vitally important) for a while the only way I could remember that Richard III was of the House of York, was by using the mnemonic for remembering the colours of the rainbow and then working back: red, orange, yellow ... so that's Richard of York. Similarly the only way I can quote here the well-known (at least to metallurgists) mnemonic for remembering the atomic number order of the first period transition metals: Scary Tight Virgin Crew Members Fer Cold Night Cuddles ... is simply by knowing from long use that they are: scandium (Sc), titanium (Ti), vanadium (V), chromium (Cr), manganese (Mn), iron (Fe), cobalt (Co), nickel (Ni), copper (Cu)

In terms of remembering things by association with an actual event, the only one I can think of is knowing the rivers of Yorkshire (north to south flowing into the North Sea) again to a mental rhythm: the Swale, the Ure, the Nidd, the Wharfe / the Aire, the Calder, the Don and the Trent. This my mother always recited as we crossed the river Trent on our way north to visit Granny in Northumberland. Actually however the rhyme isn't true because the Trent doesn't flow through Yorkshire, although as the Humber it does form the southern border with Lincolnshire, which is perhaps another reason why I can remember it because having quoted it my mother always explained why it wasn't quite correct.

I do however still use two metric/imperial conversion rhymes that were popular in the 1970s: two and a quarter pounds of jam / weigh about a kilogram, and, a litre of water's / a pint and three-quarters.


Last edited by Meles meles on Sat 20 Aug 2022, 04:12; edited 8 times in total (Reason for editing : the spelling of rhythm and rhyme - which I always have trouble with plus I got my pounds to kilos poem wrong)
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Green George
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptyFri 19 Aug 2022, 13:19

Yes, the Hartsprung-Russell sequence of "Oh Be A Fine Girl Kiss Me" is one I can cope with but the extension to add "Right Now Sweetheart" trips me up.

MM do you recall "The negative log to the base ten of the hydroxonium ion concentration"? How about "Facilis Difficilis Similis Dissimilis Gracilis Humilis"
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Meles meles
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptyFri 19 Aug 2022, 13:51

Well yes some things, such as the definition of pH (as a measure of acidity) you just have to learn as they are somewhat abstract from normal life, although once you understand what it really means other things in chemistry do then make a lot more sense.

"Facilis Difficilis Similis Dissimilis Gracilis Humilis" ... isn't that about comparison of adjectives? I was never any good at Latin and dropped it/was chucked out of the class, after just a couple of months.
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LadyinRetirement
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptyMon 22 Aug 2022, 07:56

Did I mention it before - in 3rd year senior school our science teacher tasked us with each making an individual small booklet about a scientist and I got Archimedes, lucky me.  I kept to the correct facts except that I drew the great man in a 1930s cast-iron enamel covered bath rather than a sunken ancient Greek one.  Fear not, I didn't show anything I shouldn't have.

The science teacher from the year before gave out 'discipline marks' to any pupil who had the temerity to confuse relative density with specific gravity because she had explained the difference.  You'll probably remember covering these topics in senior school science but the measurements are similar but RD uses SI units whereas SG just mentions the ratio.  Of course some people put in the SI units when describing SG which was incorrect but 'deliberate disobedience'?  No, it was a silly mistake.

If anyone feels they can describe the difference between RD and SG more clearly than myself, please do so.
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Caro
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptyTue 23 Aug 2022, 05:49

Ugh, just wiped what I had written. I remember things in order better than using a mnemonic: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto (has it been reinstated as a planet?). I remember my very (something) mother but then I get lost and have to go back to the planets as I remember them, probably because I remember things from the far past better than later, and it is only reasonably recently (as in the last half of my life) that I heard that mnemonic.
I don't think I got as far in science to get to relative density and specific gravity. Or if we did it I have totally forgotten, as I have most things we did in Science (though I did a pass mark for it in School Certificate, just, as I recall. SC is what kids sit in their third year at Secondary School, ie when they are turning 16 or thereabouts). When I write these long sentences with brackets I do lose my way with punctuation!
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Green George
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptyTue 23 Aug 2022, 16:08

LadyinRetirement wrote:
Did I mention it before - in 3rd year senior school our science teacher tasked us with each making an individual small booklet about a scientist and I got Archimedes, lucky me.  I kept to the correct facts except that I drew the great man in a 1930s cast-iron enamel covered bath rather than a sunken ancient Greek one.  Fear not, I didn't show anything I shouldn't have.
Did you explain him running down the street shouting "Fetch me a towel"? Maybe that was Didactylos, or even Ibid, though?
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptyWed 24 Aug 2022, 17:52

I know you are joking GG - it was a small booklet (the nearest modern size I can think of is A5 but we still used the old-fashioned sizes then).  I may have put some handwriting across the great man's middle as he was running down the street.
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Caro
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptySat 27 Aug 2022, 06:54

The daily quiz in our Otago Daily Times newspaper has a question (fortunately in the Expert section, though there are only 10 questions in all) which says: "Which mathematical term beginning with L is defined as the exponent to which a base figure is raised to produce a required value?" Not only did I not know the word but I didn't understand the definition. I will leave it unanswered for a while to let you knowledgeable people tell me what it is.
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Meles meles
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptySat 27 Aug 2022, 08:48

That's as easy as falling off a log, although perhaps one needs a bit of rithm too.
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Green George
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptySat 27 Aug 2022, 16:54

Get to the point, man! 'tiss a simple enough query!
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Caro
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptySun 28 Aug 2022, 23:43

I should have said I did know the word when I saw the answer, but didn't when I saw the question. Everyone these days has heard of logarithms. I just think of them as those awkward things used to confuse!
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Meles meles
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptyMon 29 Aug 2022, 10:04

Like Caro's stating of Archimedes' Principal in words (in the opening post), I don't think I've ever learned a verbal definition for logarithm and so to understand your quiz question I had to write it out in mathematical notation:

ie,       y = logb x         where        x = by

Hence if using common decimal logs to base 10 (ie, b = 10) the log of 1000 (x = 1000) is 3, because 1000 = 10 x 10 x 10 = 10, while the log of 100,000 is 5 because 100,000 = 10 x 10 x 10 x 10 x 10 = 105. Similarly the decimal log of 150 ie log10 150, must lie somewhere between 2 and 3, because 150 lies between 100 (102) and 1000 (103), although intuitively it's likely closer to 2 than 3 as 150 is only a bit more than 100 and quite a long way off 1000. In fact log 150 is approximately 2.176.

Oh yes I well remember the joys of using log tables. By university we were allowed electronic calculators for the number crunching but at school, if you weren't to do all multiplication manually, it could only be done using log tables or slide rules (a slide rule is basically an analogue version of a digital log table). Using logs reduces multiplication to a operation of addition, which is generally much easier, and follows from the addition of indicies, such that,

na x nb = n (a + b)

and so to multiply a by b all you need do is look up there logs, add these two numbers together, and then convert this sum back to the required answer using anti-log tables.

But enough of all that. Although the maths itself is not particularly hard, when posting mathematical equations here it's the typing of all the coding, which is necessary to get the indices and suffices correct, that's the really tricky bit.


Last edited by Meles meles on Mon 29 Aug 2022, 17:53; edited 6 times in total (Reason for editing : as anticipated I made several coding errors in the text)
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Green George
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PostSubject: Re: Archimedes' Principle   Archimedes' Principle EmptyMon 29 Aug 2022, 13:25

At my school, only those doing "A" level Double maths (i.e. Pure Maths and Applied Maths as seperate subjects) were allowed to use the jolly old slipstick. We plebs taking the single "Pure and Applied Mathematics" had to struggle on with log tables. Worse, if we needed more sig. figs. we had a set which has 6-figure mantissas. However, no anti-log tables for those, so you had to find, by inspection and interpolation, the correct answering mantissa, and then read off the question, so to speak.
(the mantissa is the part after the decimal point, which really isn't a decimal point. The number in front is the characteristic, and is powers of 10 [powers of e for natural logs])
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