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Archimedes Crown
In reading the article about Archimedes measuring the density of the crown, I believe that the explanation given creates a much more complicated scenario than Archimedes needed to deal with.
1) To effectively perform the operation prescribed, Archimedes would have needed a sample of gold which was the same weight as the crown...presumably this is a lot of gold...likely very hard to come by.
2) To get around this...There is no need to submerge both halves of the balance. That just complicates the problem. Without doing that, you are simply measuring the difference of wight of the crown in water and out of water (i.e. the difference in tension on a string holding up the crown in and out of the water). The difference in tension of the string is equal to the buoyant force of the water acting on the crown:
(change in weight) = (buoyant force) = (density of water) x (volume of water displaced)
This is all that is necessary to solve the problem. Now, he knows the volume of water displaced, because the density of water is easy to measure (if not already known at the time). Once he knows the volume of water displaced, of course, he knows the volume of the crown, and thus he knows the density of the crown...problem solved. If he submerged both halves, the problems is more complicated...unless the other half is gold.
I am not a historian, but this solution seems to make far more sense than the diagram on the website.
Oskampj (talk) 00:22, 30 October 2009 (UTC)Jeff
- The article stresses that the crown story does not appear in the known works of Archimedes, and is due to Vitruvius writing in Roman times. The balance experiment is due to Galileo Galilei, and is based on his Bilancetta (little balance). The question of whether both sides of the balance need to be immersed in water is an interesting one. In Chris Rorres' account here, both sides are submerged, but in this version only one half of the balance is submerged. Both versions would work, although in this illustration for Galileo's 1586 treatise, only one half of the balance is submerged. The balance method is more accurate than the bath story, which would have led to a rough answer at best.--♦IanMacM♦ (talk to me) 08:30, 30 October 2009 (UTC)
- I'm no expert, but this doesn't sound right. In fact obtaining use of the same weight of gold would have been no problem as he was working for the king. Johnbod (talk) 04:33, 22 May 2010 (UTC)
- He wouldn't have needed a balance; he only would have needed to know the density of pure gold, which was probably known already. Even if it wasn't, he would have found it easy to calculate even if he only had a small amount of it (make a cube or sphere of pure gold, then divide its weight by its volume, and Archimedes knew how to calculate the volume of spheres and cubes). Knowing the density of pure gold, all you need to do is weigh the crown, submerge the crown, measure the volume of water displaced, divide the crown's weight by the displaced volume, then voila; you have the density of the crown. So there's no reason to doubt the veracity of the crown story. As an aside, a mixture of equal parts copper, silver, and gold would have a very similar color to pure gold (see [1]) but would have less than 70% the density of pure gold, so it's possible that's what the goldsmith used. Stonemason89 (talk) 15:36, 3 August 2010 (UTC)
- The "easy" method of measuring the volume of water displaced by the crown is mathematically correct, but Chris Rorres argues that it would not have been very accurate.[2] The balance method is, strictly speaking, nothing to do with Archimedes because it was suggested by Galileo in a paper published in 1586. The golden crown story, like other anecdotes about Archimedes, can be questioned for its reliability.--♦IanMacM♦ (talk to me) 15:45, 3 August 2010 (UTC)
Legacy section
Archimedes also lends his name to the Acorn range of computers by the same name, by way of the Eureka! story. Acorn's description at the time was that the creation of the machine was a Eureka moment, and that its users would experience similar moments when they realised the power of the machine and what they could do with it, hence the name choice. This information could do with adding to the article, along with a link to the relevant WP article. -Preceding unsigned comment added by WikiPhu (talk - contribs) 23:36, 24 January 2010 (UTC)
I've now added this. My post above took me over the 10-post mark, and allowed me to edit the semi-protected page. -Preceding unsigned comment added by WikiPhu (talk - contribs) 23:42, 24 January 2010 (UTC)
Archimedes and the Lever
The unsourced claim that Archimedes authored the first rigorous explanation of the principles of the lever is incorrect. A much better explanation appears in Aristotle's Mechanica, a work that predates Archimedes birth.
I recognize that there is controversy over who actually authored Mechanica, but that is irrelevant to the point at hand. It definitely contains a rigorous explanation of the lever, and it definitely was not authored by Archimedes.
I am therefore removing the incorrect claim, and adding a (sourced) statement re: the above. FellGleaming (talk) 03:59, 20 March 2010 (UTC)
- The wording on this issue has stood for a long time, partly because it avoids the use of black/white terms like correct/incorrect, which implies that there is a single "correct" view on the issue, and that others are "incorrect". Archimedes' role in the development of the lever is noted in the WP:LEAD as it is an important part of his work, and should not be removed in favour of stressing a much more poorly sourced claim attributed to Archytas. Marshall Clagett's view on this issue has been taken into account, as he is regarded as one of the key authorities on this subject. The article stresses that Archimedes did not invent the lever (neither did Archytas), and the wording points out that Archimedes gave a rigorous mathematical proof of the principle of the lever, rather than simply a mechanical description. The claims about the lever involving Archytas may have been made by later authors, whereas Archimedes' proof in On the Equilibrium of Planes is known to be part of his canonical work. The article should not give undue weight to the poorly sourced claims involving Archytas, although it is worth mentioning his role somewhere. This article is about the work of Archimedes, and his work should take precedence. There is a parallel with the steam engine, because it is sometimes said that Heron of Alexandria invented the steam engine, although his version is nothing like a modern steam engine. Claims that Person A was the first person to do something are always hard to source reliably, which is why the article should steer clear of doing this with the lever, particularly when there is a debate about when and how Mechanica was written.--♦IanMacM♦ (talk to me) 06:38, 20 March 2010 (UTC)
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- None of the above has any bearing on my original complaints, or the original edit. The "wording which stood for a long time" incorrectly stated-- in black and white terms, without source or attribution -- that Archimedes was the first to rigorously describe the lever. Drawing a parallel between earlier incarnations of the steam engine are far off base; a lever is a lever. The lever described in Mechanica certainly was not "substantially different" from the ones conceived by Archimedes. Further, your focus on Archytas is irrelevant. It doesn't matter who authored Mechanica; what matters is that the text predates Archimedes, and thus giving him credit for the first definition of the lever is false.
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- The new version of the text merely points out that Archimedes gave "a" description of the lever. That is both correct, and in context. FellGleaming (talk) 20:13, 20 March 2010 (UTC)
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- The new wording looks at both sides of the argument, and it should mention the earlier works including the possible link with Archytas. What is interesting is that Chris Rorres and Marshall Clagett have taken different views on the importance of the earlier works. Clagett argues that Archimedes' work was more rigorous, while Rorres does not. With both sources, people can make up their own minds.--♦IanMacM♦ (talk to me) 20:39, 20 March 2010 (UTC)
Archimedes' Stomachion
Several unstated presumptions to obtain the number 17,152, the most troubling being that we reach for a Stomachion board proposed in a questionable translation of another text which does not match the Archimedes Codex. It is unclear where Dr. Netz ever comes to grips with this problem. -Preceding unsigned comment added by 150.217.37.24 (talk) 14:23, 17 June 2010 (UTC)
- The article is based on research that has been published in reliable sources. The research by modern scholars has indicated 17,152 solutions[3] and this is the figure given by the article. Wikipedia articles should avoid original research and stick to what is available from reliable sources.--♦IanMacM♦ (talk to me) 15:06, 17 June 2010 (UTC)
Mirrors
The lead introduces the invention of the mirror array as fact but this is, at best, a popular story that has marginal acceptance among historians. There is an article in MSNBC today (see [4]) that claims this story has been debunked. This should be changed.
--Mcorazao (talk) 14:55, 29 June 2010 (UTC)
- The article has gone to great lengths not to present the Heat Ray story as a fact. Regardless of its truth, it has been discussed by sources since ancient times, so it is dealt with per WP:NPOV in the article.--♦IanMacM♦ (talk to me) 15:02, 29 June 2010 (UTC)
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