Talk:Archimedes

Talk:Archimedes

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Contents 1 Surviving Works: "On the Sphere and the Cylinder" 2 an ingenious system for expressing very large numbers 3 Development of Pi value 4 Archimedes Crown 5 Infinitesimals 6 Legacy section

Surviving Works: "On the Sphere and the Cylinder"

There seems to be a typo. "... and 4Ï€r² for the cylinder (including its two bases) ..." should read "... and 6Ï€r² for the cylinder (including its two bases) ..." This gives credence to the 2/3 statement in the next sentence. The surface area of the cylinder is "A = 2Ï€rh + Ï€r² + Ï€r² = 2Ï€r2r + 2Ï€r² = 6Ï€r²" Yalitzot (talk) 04:14, 20 July 2009 (UTC)Yalitzot

Thanks for pointing this out. There was a long argument about how to calculate the surface area of a cylinder some time back [1]. It is clear that the bases should be included for the 2/3 ratio to be valid.--♦IanMacM♦ ^{(talk to me)} 06:55, 20 July 2009 (UTC)

an ingenious system for expressing very large numbers

I'd like to see a cite on this topic. Or examples. Is it the exponential concept ? He was a physics and complex math person - I suspect - but want a verification on the topic.

Martin -Preceding unsigned comment added by 64.92.35.246 (talk) 18:38, 11 August 2009 (UTC)

This is a reference to The Sand Reckoner. It does not have a source in the lead at the moment, but is discussed and sourced in its own section.--♦IanMacM♦ ^{(talk to me)} 18:46, 11 August 2009 (UTC)

Development of Pi value

If They were so concerned about the Pi value in Archimedes' day, why didn't they just closely approximate it (as they did) and then just put a notch in their instrument of measurement and indicate that that was the Pi value, in the same way as the notch they put in it to indicate the unit value. Or they could have talked about the Pi value as part of the plane geometry curriculum. After all who knows why the volume of a cone is 1/3 the volume of a cylinder if he doesn't know what Pi is?WFPM (talk) 22:13, 23 August 2009 (UTC)

But the fact that the volume of a cone is 1/3 the volume of a cylinder is independent of the value of pi is it not? Adrionwells (talk) 08:24, 7 November 2009 (UTC)

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)

Infinitesimals

The article says that Archimedes used infinitesimals. That is misleading. He postulated that if x and y are unequal, then |x - y|n can be made indefinitely large by choosing n large enough. This implies that x = y if and only if |x -y| < 1/n for all integers n, and that rules out infinitesimals. This is the Archimedean property of the real numbers and it should be mentioned. -Preceding unsigned comment added by Adrionwells (talk - contribs) 08:52, 7 November 2009 (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)

Talk:Archimedes

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