Wikipedia:Featured article candidates/Euclidean algorithm/archive1
- Nominator(s): Proteins (talk) 16:22, 27 April 2009 (UTC)
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I am nominating this mathematical article because I believe it meets the Featured Article criteria. In its simplest form, the Euclidean algorithm is often taught to 10-year-old children; for many, it is the only algorithm they encounter in school. It has several important applications, such as the RSA algorithm (often used in electronic commerce) and solving Diophantine equations. Although the oldest known algorithm (23 centuries), it continues to play a role in developing new mathematics. It would be helpful for Wikipedia to have an excellent article on this topic, both for itself and for the introduction it provides to advanced mathematics such as abstract algebra. Proteins (talk) 16:22, 27 April 2009 (UTC)
- I'm a bit concerned about the inclusion of the "Game of Euclid" in the historical development section. It doesn't seem to be very important as a research topic or achievement, and it certainly doesn't even come close to the other developments in that section. What was the reason for including this? --C S (talk) 17:19, 27 April 2009 (UTC)
- The FA criteria require that the article be "comprehensive" (criterion 1b). I admit that the game of Euclid is relatively unimportant, but it has been discussed in mathematical journals and textbooks, as referenced in the article. There didn't seem to be a better place to put that material besides "Historical development". Proteins (talk) 17:43, 27 April 2009 (UTC)
- Well, I spy less than half a dozen "mathematical journals and textbooks" that mention the game. Surely there are many topics with more coverage that have not been included in this article. So I can't see how omitting this game would violate criterion 1b. Not to mention, these math journals you talk of are mainly math education related ones, except the journal INTEGERS, which seems like an ok journal but not particularly well-known. Of course, I don't mean to disparage journals whose primary audience may be math educators, but in terms of using such journals as a justification for including a mathematical topic in this article, I don't think it is sufficient. One has to separate a topic which is primarily used as an educational device from a topic which is considered an important development in understanding of the Euclidean algorithm. --C S (talk) 19:23, 27 April 2009 (UTC)
I think that the sentence "The Euclidean algorithm is the oldest algorithm in the historical record" is wrong because of Old Babylonian algorithms used to solve problems. --El Caro (talk) 18:04, 27 April 2009 (UTC)
- This is a good point. The passage stated is uncited, but there is further down a box with a quote by Knuth which makes the nuanced observation that it is the "oldest nontrivial algorithm" that has survived to the present day. Since Knuth actually wrote an article in 1972 on ancient Babylonian algorithms [1] where he examined written records of their algorithms, presumably he was aware that the "nontrivial" is an important and necessary modifier. "Oldest nontrivial...", of course, is his opinion. --C S (talk) 19:21, 27 April 2009 (UTC)
- I've read the quote in the box. Is this "only" Knuth's opinion or a statement on whom most specialists agree ? --El Caro (talk) 19:39, 27 April 2009 (UTC)
- This is a good point. The passage stated is uncited, but there is further down a box with a quote by Knuth which makes the nuanced observation that it is the "oldest nontrivial algorithm" that has survived to the present day. Since Knuth actually wrote an article in 1972 on ancient Babylonian algorithms [1] where he examined written records of their algorithms, presumably he was aware that the "nontrivial" is an important and necessary modifier. "Oldest nontrivial...", of course, is his opinion. --C S (talk) 19:21, 27 April 2009 (UTC)
- "Euclid's algorithm can be applied to real numbers, as described by Euclid in Book 10 of his Elements" looks like an anachronism. Did Euclid know real numbers ? --El Caro (talk) 18:17, 27 April 2009 (UTC)
- Well, now we're getting into metaphysical matters that I think are tangential. For example, when Euclid considered arithmetical operations on whole numbers, it's not the same in a sense as what we consider such arithmetic, nor is probably what the ancient Greeks considered whole numbers the same as what we do now. So strictly speaking Euclid did not know real numbers, but he didn't know whole numbers, addition, or subtraction either. So that makes your point kind of moot. --C S (talk) 19:21, 27 April 2009 (UTC)