Talk:Rhind Mathematical Papyrus 2/n table

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This pages seems to be about the history of mathematics, but doesn't say so. Also it uses jargon in the lede that I as an ordinary mathematician cannot grok. I suggest the page provide more context to the reader. Marc van Leeuwen (talk) 17:59, 19 April 2008 (UTC)

A copy of the (translated) 2/n Table should be included in the body of article. —Preceding unsigned comment added by 66.67.96.142 (talk) 20:21, 7 September 2008 (UTC)

The RMP 2/n table offered scribal conversions of rational numbers to concise unit fraction series. Ahmes generally converted n/p, any rational number to a concise unit fraction series by consulting the 2/n table. In RMP 36 30/53 was converted by solving for 28/53 + 2/53. In RMP 31 Ahmes converted 28/97 by solving 26/97 + 2/97. Best Regards, Milogardner (talk) 13:46, 2 October 2010 (UTC)


 * Are you suggesting a short paragraph stating that the table was used to facilitate computations? Maybe in the introduction? I think that is what the general consensus is regarding the meaning of the tables. There are several tables (Lahun, EMLR etc) Not to mention RMP 47 and RMP 61. In comparison to modern texts this is not so much different form finding logarithmic tables in some older math books I think. Or am I misunderstanding your post?--AnnekeBart (talk) 14:57, 2 October 2010 (UTC)

The 2/n table did facilitate computations by outlining a method that generally converted rational numbers to concise unit fraction series. Modern number theory scholars, Paul Erdos, David Eppstein and others have argued over algorithmic methods, most often in a modern context. Our goal here should be to focus on scribal data and scribal methods, reported by scholars, placing modern number theory scholars into an interested footnote category.Milogardner (talk) 15:28, 2 October 2010 (UTC)
 * There is no mention of modern number theory here. Everything here is based on what is in the literature.--AnnekeBart (talk) 16:14, 2 October 2010 (UTC)

Griffith's Book I (RMP 1-23) II (RMP 24-59) and III (RPM 60 - 87) structured meta considerations of Egyptian fraction math that need to be mentioned at some point. Book I began with worker performances recorded in quotient and remainders (in RMP 1-6), a scribal method that was recorded in a Reisner Papyrus building construction project. Gillings stumbled through the data not accurately reporting the quotient and remainder details. The data speaks for itself, yet, scholarly discussions are important. Book I included scribal arithmetic recorded in red auxiliary numbers and scaling factors of rational numbers. Book II covered algebra and geometry problems recorded in 2/n table rational numbers, hekat, cubit, and setat units. RMP 35-39 discussed one hekat equal to 320 ro. In RMP 38 320 ro was multiplied by 7/22, with the vulgar fraction rational number answer multiplied by 22/7 to return 320 ro. RMP 38, and other RMP problems showed that the scribal division was inverse to scribal multiplication, by inverting divisors and multiplying. Book III, and problems in Book II, offered economic valuations of products, bread, beer, water fowl, and cattle recorded in hekat, malt and meal (feeding rates). Hekat, hin and ro hekat sub-units tables were also presented and discussed by many scholars. Milogardner (talk) 15:33, 2 October 2010 (UTC)
 * The Book I, II, III division of the RPM is mentioned in the Rhind Mathematical Papyrus article. It does not belong in this article. Considering that the Egyptians had no notation for fractions of the for p/q, one should be careful using that notation. The scribes were NOT computing with fractions like that. There is something a little bit more subtle going on. They would multiply by a multiple of the divisor(s) and thereby converted the problem to a computation over the integers. Then they would convert back to fractions at the end.
 * This is an article about 2/n tables and the hekat computations are just one example where the tables were used (and why they were of interest to the Ancient Egyptians). I'm not sure the focus on hekats is appropriate within the context of this article. --AnnekeBart (talk) 16:14, 2 October 2010 (UTC)

Please provide examples that support your position. We can discuss these issues case by case if you desire, or in Book II. The RMP algebra problems (RMP 24-34) go beyond 2/n table info and converted n/p rational numbers working easy problems. The Berlin Papyrus offers two second degree algebra problems that are also fun. Pick a couple of problems and we can discuss the scribal math line by line, if you wish. Best Regards, Milogardner (talk) 19:54, 2 October 2010 (UTC)
 * This is standard knowledge and part of any reliable text about Egyptian mathematics. I find myself surprised that you are not familiar with these very basic facts about Egyptian mathematics. Reinterpreting texts would be original research again. Please stick to the standard interpretations as documented in the reliable literature. --AnnekeBart (talk) 21:11, 2 October 2010 (UTC)

It is true that many scholars have "considered that the Egyptians had no notation for fractions of the for p/q". But there have been major exceptions. Riding a minimalist low road and spending little time reading the complete scholarly record (that includes Hultsch, Griffith, and Schack-Schackenberg) offers few opportunities to discuss or resolve this intellectual class of controversy. Milogardner (talk) 00:12, 3 October 2010 (UTC)
 * You clearly do not understand the topic very well. I'm done discussing this with people who do not have the basic background to understand the relevant points. Continuous misuse of terminology and misrepresentation of results by others shows there is no real understanding of the salient points. The condescending comments and thereby insults are a source of incivility on your part. And yes I am responding in kind as I am wholeheartedly sick and tired of dealing with such a profound arrogance and condescension on your part where that is clearly not based on any real knowledge. You are obviously in way over your head and do not understand this topic in any significant manner whatsoever. After being accused several times now of ridiculous "conspiracies", "belonging to groups with alternative motives" and other such drivel, I am really fed up with dealing with such an ill mannered, uninformed Randy in Boise type as yourself. Your dishonesty in accusing other of name calling, when your behavior is as ridiculous as it has been is really beyond any boundaries of civility. I don't even care if I get reprimanded for voicing my opinion. You are an absolute waste of time. --AnnekeBart (talk) 00:36, 3 October 2010 (UTC)

It is interesting that you raise civility, and emotional issues. Your side of an intellectual debate raises 'ignorance', conspiracies, and rhetorical issues that are not based in ancient mathematical facts. Those are your name calling words not mine. I only discuss and offer to discuss ancient math reported by scholars and scribes. You have refused both classes of opportunities to discuss any set of scholarly and scribal facts that you desire.

You may realize that the largest controversy connected to Egyptian mathematics opens when Ahmes and the Kahun Papyrus recorded 2/n tables that scholars could not read. The scholarly record over-flows with proposed analysis on this topic. All 200 scribal problems in about ten hieratic texts used 2/n table arithmetic written in ciphered rational numbers that replaced an awkward Old Kingdom numeration system (source: Boyer). But how was the information presented in the tables created? And more importantly was there an intellectual basis for the arithmetic tables that infers or validates that rational numbers n/p were generally converted by scribes to concise unit fraction series? These are questions that Sarton and the History of Science community have been asking for a long time, open intellectual topics that you appear to claim certainty by closing off a needed debate before a number based debate begins.

Your debating position may begin and end by saying no to ancient Egyptian fraction math containing intellectual content that led to proto-number theory. That is a strong position that requires evidence to be produced. For many years Otto Neugebauer, "Exact Science of Antiquity" was offered as a standard for your school of thought ... paraphrasing Otto slightly ... I know how Ahmes created the 2/n table (little hard evidence presented). The scribal use of Egyptian fraction marked a step backward taking a wrong turn in history. Otto oddly concluded that Egyptian fraction math marked intellectual decline, when the reverse is likely true, compared to earlier times.

Did Otto mean to infer that Egyptian and Babylonian cursive rounded-off numeration algorithms were superior to Egyptian fraction 2/n tables and mathematics? How can that be? Did not the Old Kingdom Egyptian Eye of Horus arithmetic and weights and measure systems always throw away a 1/64 unit rounding off to 6-terms? Did not Middle Kingdom scribes correct Eye of Horus round-off errors by adding back ro remainders in exact ways in hekat division (Vymazalova, 2002)?

I again offer an olive branch. Open a real debate by offering hard evidence. For example, I would like to debate a commonly held belief that scribes used false position for a division (algorithm). Do you agree with that long held scholarly suggestion? Howard Eves offered it within a range of interesting ancient math problems in my undergrad history of math class almost 50 years ago. Eves forgot to rigorously connect scribal 2/n table division with medieval single false position a 800 AD root finding method. I await your updated information on this important matter. Best Regards, Milogardner (talk) 12:57, 3 October 2010 (UTC)

I'll disclose a few debating points. During a future discussion of Arab single false position, and Egyptian scribal division issues, medieval cultural background sheds weak or strong light on a larger number theory subject, depending up one's point of view. As you may know Fibonacci wrote the Liber Abaci by applying seven rules (distinctions) that did generally convert rational numbers to unit fraction series. His base 10 numeral method(s) may have been close to ciphered numeral methods used by Arabs, Greeks and Egyptians, or may not have been.

One of Fibonacci's rules set (n/p - 1/m) = 1 as often as possible. When (n/p-1/m) = 1 could not be obtained, i.e. 4/13 - 1/4 = 3/52, rule seven allowed a second LCM to be chosen. Completing the calculation 3/52 - 1/18 = 2/468, meant 4/13 = 1/4 + 1/18 + 1/468, written from right to left possibly following Arab, Greek and even older Egyptian notational styles.

You are correct to be skeptical. What has Fibonacci's 124 pages of rational number conversions to unit fraction series in the Liber Abaci have to do with Ahmes or the Kahun Papyrus 2/n table construction method(s)? No scholar (that I have read) has documented an equivalent set of rules that line up with Fibonacci's seven rules (distinctions per Sigler's 2002 translation). The academic record is almost blank on reporting scribal rational number conversion rules beyond debatable 2/n table suggestions.

What scholars have documented are two forms of scribal division. Your school of thought may opt for the single false position rule suggested by Howard Eves. But other scholars indirectly report Ahmes inverting divisors to a fraction and multiplying. For example, Clagett reported that Ahmes in RMP 38 multiplied one hekat (320ro) by 7/22 reporting a unit fraction series; and multiplied by 22/7 returning 320 ro. Was Ahmes reporting that scribal division was at times an inverse to multiplication in the modern sense, an not connected to scholarly false position scribal division proposals? Milogardner (talk) 19:47, 3 October 2010 (UTC)
 * Milo, please stick to the topic. This talk page is for discussion of improvements to the RMP 2/n table article, only. Fibonacci's work was at best very indirectly informed by the mathematics of this table, and says nothing about the table itself. It is off-topic. I am getting the impression that the recent RFC has made absolutely no impression on you — your longwinded talk diatribes, original research, and failure to stay on topic have continued unabated. —David Eppstein (talk) 19:50, 3 October 2010 (UTC)

Why? How can it be used?
The article ask how this table was computed.

But it does not answer the question to know why such table was existing. How can it be used? — Preceding unsigned comment added by 77.199.96.122 (talk) 21:31, 7 September 2016 (UTC)

2/35 = 1/30 + 1/42 ?
2/35 = 1/30 + 1/42 ? — Preceding unsigned comment added by 77.199.98.194 (talk) 21:52, 15 September 2016 (UTC)
 * Yes. Or if it's simpler for you this way, 12/210 = 7/210 + 5/210. —David Eppstein (talk) 22:20, 15 September 2016 (UTC)