Talk:Ancient Egyptian mathematics

message: Some dates would be useful in the first paragraph.  In the section on geomesoctry, there are some examples that I think would be useful additions. (1) the use of a 3-4-5 right triangle in surveying to construct a right angle. This is depicted in some surviving drawing, but I don't remember where I saw it reproduced. (2)The formula for the volume of a truncated square pyramid (needed to know how much stone to import to build a pyramidal tomb). It was equivalent to Volume = (1/6)(H)(B + T + 4M), where H is the height, B is the area of the base, T is the area of the top, and M is the area of the cross section halfway up the pyramid. I find it astounding that this formula
 could have been discovered without the use of calculus. (3)They used a formula for the area of a quadrilateral which was incorrect except when the quadrilateral was a rectangle. But it gave a good approximation if the quadrilateral was not too far from a rectangle.  I remember that "A History of Mathematics" by Howard Eves has a very good chapter on Egyptian and Babylonian mathematics.  Aftermath 00:45, 20 Jun 2005 (UTC)
thread_title: Untitled

message: I reverted the edit introducing remainder arithmetic because of verifiability issues: it does not give any references, I asked at User talk:172.194.232.169 for references but did not receive an answer, a Google search suggests that this is a theory of Milo Gardner only published in his blog, and it does not agree with my (admittedly very small) knowledge of the usual theories. -- Jitse Niesen (talk) 00:03, 21 January 2006 (UTC)
replies: text: Wikipedia does not publish original research. Everything has to be verifiably cited to reliable sources. A weblog is not a reliable source. Tom Harrison Talk 17:20, 25 May 2006 (UTC)

text: In brief, it has to be published somewhere else first. Tom Harrison Talk 20:23, 25 May 2006 (UTC)
thread_title: Remainder arithmetic

message: I have added further detail to the geometry section to give a fuller picture of the situation regarding squaring the circle. I have tried to leave you paragraph unaffected in the process.
--Michael saunders 22:16, 18 March 2006 (UTC)
thread_title: Geometry

message: I'm not sure that the solution to problem 25 in the Rhind Papyrus uses the False position method. Wouldn't it more correctly be described as "linear extrapolation?" Tom Harrison Talk 20:39, 6 May 2006 (UTC)
thread_title:  False position 

message: Milo's edits raise a number of issues.
# Primary sources. A long-running guideline is "In general, Wikipedia articles should not depend on primary sources but rather on reliable secondary sources who have made careful use of the primary-source material." (see Wikipedia:Reliable sources). The reason for this is clear: it is not easy to interpret primary sources. This is particularly true in this case, where only few sources are available and they are written in a dead language. Of course, it would be great if all these sources were available to the general public. This does not agree with the mission of Wikipedia, but a sister project called Wikisource collects primary sources. I assume they would be very happy to accommodate for instance the Rhind Mathematical Papyrus, if its text is available.
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Wikipedia's list of authors excludes Archimedes and many in the
mathematical community. Adding Ahmes and other mathematicians of note
as a Scotland University has done online, as I have noted on:
http://historyofegyptianfractions.blogspot.com
may be a major inconvenience to Wikipedia's current point of view, and
practice, of stressing geometry based texts. Oddly Wikipedia had thereby skipped over the scribal arithmetic that empowered Ahmes' geometry! The history of mathematics, and its many texts from around the world seem best left - in detailed descriptions - math problem per math problem
per each important mathematician - to other web pages. Milo
****
# Secondary sources. Milo counters that secondary sources are not reliable either. Indeed, the difficulty in interpreting primary sources suggests that secondary sources may get it wrong sometimes. This may well be the case here. Even if it this is the case, Wikipedia still prefers secondary sources. However, what will often happen in these situations is that secondary sources contradict each other. In the current context, they may give different explanation of how the 2/n tables were constructed.
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Concerning the RMP and its 2/nth table, the number of conflicting
views are too numerous to mention. Scondary sources therefore continue
to  be not helpful to clear up the reading of the RMP and its 2/nth
table. Again, Wikipedia's version of Egyptian math had began and ended with geometry, only a few weeks ago. oddly skipping over large aspects of
scribal arithmetic that empowered scribal geometry. Gillings is a good starting point to open the door to the 'secondarty source' controversies found in the RMP, as cited on Simeon Fraser U. Canada's web page, per
http://www.math.sfu.ca/histmath/Egypt/Ahmes/frametop.html.
I thank Tom, or whomever, for expanding the Egyptian math discussion
to cover numeration, arithmetic (both sides), algebra, geometry and
weights and measures. Adding in all the scribal math as one body of
knowledge allows the ancient scribes to point out their methods, leaving modern secondary sources and their wide ranging opinions aside.
Many scholars, and secondary sources, have tended to choose one subject, or one point of view (i.e additive), as your primary editor keeps returning to 'false position' (using an unproved assumption) that it was used in every algebra problem. I can not find 'false posiition' in any of the scribal shorthand notes, either in MAD and other web pages as cited
by Wikipedia, suggest that it was used. - Again, I challenge anyone to look at RMP 31 - and submit a 'false supposition' version of it. We may have a lively debate, written in numbers. Finally, to my point of view arithmetic empowered the geometry that scribes used to build pyramids,
a supposition on my part. Wikipedia continues to define Egyptian mathematics, as written in the RMP, and for sure the 2/nth table, without citing any of the 80 + old basic secondary source controversial threads
on the subject (ie false position). The current de facto position of Wikipedia only shows the slowly changing scope and slowing improving intellectual and arithmetic integrity of Wikipedia. Wikipedia can
continue to provide samples from four to five alternative views? I have named five of them, for your review: 1. Egyptian math derived from Babylonian sources, a pet notion of Otto Neugebauer and others (minimalist), 2. Algorithms from Babylonian numeration caused Horus-Eye numeration, and that Ahmes used algorithms to create his 2/nth table (far out), 3. Old Kingdom Egyptian math was based in geometry, since the Old pyramid builders' knowledge could not have been based in arithmetic. Oddly the geometric knowledge was lost by the time of the Middle Kingdom (the singular view of Wikipedia, and one of the positions of Otto Neugebauer and his citation that the 2/nth table marked an intellectual decline in Egyptian mathematic, an interesting supposition - but where are the ancient texts that prove it)?, 4. Reading only the hieratic texts, and finding contextual solutions to the Horus-Eye problem, as surely the 2/nth table and Egyptian arithmetic reports, a scribal method that eliminated the rounding off of vulgar fractions - when expanded into Egyptian fractions, by subtraction or division - was required anytime 1/p, 2/p or n/p calculations were made. Middle Kingdom changes in arithmetic definitions of number, and methods associated with scribal division, opened the door to abstract definitions of number (my primary position), and 5. Scribes employed 'false position' 2000 years before it was used in Greek and Arabic texts (an odd add-on to the Wikipedia position) - pedagogical positions that birthed many controversies
80 + years ago. Minimalists tried to close off those debates -and
have failed badly! So, please, ANYONE post RMP #31 examples of 'false position' - off line, or on Wikipedia, and actually cite the hieratic raw data from all the algebra problens in the RMP. If Wikipedia reviewers are willing or able, from: problems #24 to 32 added disussions can follow. Or just cite the scribal step by step solution to RMP # 31: x + (2/3 + 1/2 + 1/7)x =33, since someone forgot to finish it on Wikipeida (I suggest that  this problem can not be done by applying 'false position'!). Show me the beef, as all that I ask! All that has been published on Wikipedia and elswhere in the area of false position is conjecture. Cite the scribal division method, step by step, taken directly from the 1650 BC RMP, used by Ahmes, in these cases and I will show you modern algebra, written in Egyptian fractions, methods that did not use the awkward 100 AD method
of 'false position'.
Another of the critically omitted threads is: why did Ahmes introduce statements and solutions to 80 + problems, by first writing out an optimized 2/nth table of Egyptian fractions? Why not include this thread, along with the five mentioned above? The implications attached to trying to answer the basic question - opens the arithmetic door to several aspects of these math controversies. Note that potential abstract solutions are easily seen in scribal shorthand, introducing three forms of remainder arithmetic, none of which come close to the 'false suppositions' cited by Wikipedia. Stated in other words, whenever an ancient scribe calculated a remainder, by subtraction or division, an exact Egyptian fraction series was written down as part of the final answer, nothing more, nothing less.  Milo
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# Neutral point of view. If we have secondary sources contradicting each other, we try to describe all sources from a neutral point of view. This means that the interpretations from all sources are mentioned, with their arguments, while giving the greatest weight to the interpretation that is accepted by most of the professionals (Egyptologists and maths historians, in this case).
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I wish this was the case. Giving the greatest weight to the oldest set of professional Egyptologists and math historians, using the additive point of view, going back 80 years or more, should not be continued, without
citing a few of the alternatives. Concerning Egyptian mathematics, NPOV is not being followed. Current policy, the stressing of minimalist views from outdated authors like Otto Neugebauer (Exact Sciences in Antiquity - where Egyptian fraction was said to be a 'sign of intellectual decline') should not continue since there is no abstract side of number possible
within Neugebauer and his group's view. By only citing the additive views of Peet, Chace, Neugebauer, et al, a de facto policy of excluding 100% of the alternative views, especially the recently well documented analyses published after 2002 (Vymazalova, et al) grossly distorts the subject to young and old readers alike. Remainder arithmetic definitions of scribal division, one of the most reasonable of the altenatives only adds to our understanding of the ancient texts. Why not consider Occam's Razor, that the simplest method is most likely the historical method, per Sarton, whenever the secondary source was published? Following this history of science policy, remainder arithmetic would clearly jump to the top of the the simplest method list, and so forth! Get a real debate started and see your readership rise. Best Regards, Milo Gardner
***
# References. This aspect puzzles me a bit. Using references is standard in academic texts, and the article that Milo wrote for the Non-Western Encyclopedia of the History of Science, Medicine and Tenchology shows that he knows some of the references in the field and how to cite them. I don't understand why he doesn't do the same for his contributions to this article.
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I'd have begun to edit your current list of Wikipedia outdated
references, many going back 80 years. The list cries out to be
brought upto date to include the discoveries made after 2002,
a critical year in the history of decoding Egyptian fractions
(as I have sent a separate email to Jitse, on this topic). A
small number of references going back to F. Hultsch 1895 (per Science
Awakening), Daressy in 1901, and so forth have been added. From this broader context of the history of the 2/nth table and weights and measures a few added changes will be suggested to the narrative itself, leading to the 2002 era. Milo
# False position. When Tom said above "I'm not sure that the solution to problem 25 in the Rhind Papyrus uses the False position method," he means that it does not use the iterative method for nonlinear equations. Instead, in the standard interpretation, it uses a method called sometimes the "rule of false position", akin to linear interpolation. It seems that Milo has misunderstood what Tom wanted to say.
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I am saying the Tom does not understand the primary ancient Egyptian
text that he is discussing. Ahmes, the RMP scribe includes shorthand footnotes to define and prove his problems, using a form of writing that we commonly call proofs. Ahmes' problem was that his shorthand excludes many logical steps, something mathematicians often do today. Reading fragmented 'proofs' from any era causes confusion for everyone that reads bits and pieces of data. In the case of Ahmes, scholars had not correctly guessed the mental side of Ahmes' thinking that had been omitted. Oddly, scholars, rather then mentioning their translation problems, have commonly filled in several different classes of logical gaps, often taken from thin air, with one overly simplified additive versions scribal math. One overly complex version of scribal math is 'false position' while - at the same time, poorly discribing scribal division as being based in an inverse relationship to scribal multiplication. Scholarly 'assumptions'
therefore have commonly been based on assumptions, several wild ones as teh RMP 2/nth table discussions report, rather than rigorously applying the scientific method of hypothesis, testing and proof.
To resolve Ahmes' logical step omissions, other hieratic texts
need to be cited, a step that Wikipedia listed scholars secondary
sources often avoid. In the case of Egyptian ' False Position' the method could NOT have been used by Ahmes. The methodology did  not appear until 100 BC, or as documented 200 AD+ in Arabic texts.
So why is Tom and others pushing for 'false position' to have been
used by Ahmes in 1650 BCE? The issue is, there is not one confirmed definition or use of Egyptian division in the RMP. So why cite it?
There were only logical gaps created by Ahmes shorthand discussions
that are very difficult to decode. Yes, false suppositions abound when all the scribal versions of proposed scribal division are placed in the context of the 2/nth table, Egyptian algebra or Egyptian weights and measures decoding efforts by modern scholars. Differing definitions appear in each of these three scribal areas of mathematics. Yet, to avoid discussing these three different number based realities, several 'false' definitions continue to be offered one simple (logical to Wikpedia), and minimalist gap filling idea, by otherwise professional Egyptologists and math historians. One irony is that the current 'minimalist' term stressed by Wikipedia's current list of references is named 'false position', a term that is more logically reported as 'false supposition'.  Milo
****
Concluding, Milo obviously knows a lot about Egyptian mathematics. I'm sure he can make a valuable contribution to Wikipedia. However, Wikipedia has policies, which parallel the policies in academic encyclopaedia. Be careful to add references to a reliable source (most importantly, not a blog) and give a fair summary of all points of view, giving due prominence to the dominant point of view.
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I'd be happy to do that, slowly at first, if reviewers do not continue
over-reacting by totally removing my references and comments, prior
to their complete entry. Milo
***
Perhaps it is better to start with describing the sources themselves. Our article on the Moscow and Rhind Mathematical Papyri is inadequate and could easily be expanded.
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I'd be happy to add an Akhmim Wooden Tablet article, one of the ancient
texts that is needed within everyones' references - whenever Egyptian
mathematics is discussed. For those that would like a peek at the
subject, log onto http://glyphdoctors.com and enter through the
public door, and query "Akhmim Wooden Tablet", and 53 articles will
be offered for your review.  Milo
***
I expect that there are less issues with a subject ties to primary sources. -- Jitse Niesen (talk) 11:56, 4 June 2006 (UTC)
thread_title:  Milo's contributions 

message: What point was it that was to be cited to Britannica? Tom Harrison Talk 23:28, 14 June 2006 (UTC)
replies: text: Thanks; based on Britannica Online, I think we can say that the first ciphered system was the Egyptian hieratic. I would rather cite something other than Britannica, if some other work is available. I'll look in Menninger's Number Words and Number Symbols next time I get to the library. Tom Harrison Talk 17:42, 17 June 2006 (UTC)
thread_title:  Britannica citation 

message: There's been a suggestion to merge Ancient Egyptian multiplication here. Did anyone have an opinion on whether it should be merged or not? Tocharianne 02:58, 9 January 2007 (UTC)
thread_title:  Merge 

message: If anyone reading this can speak French, I propose, reading the text "Egyptian Geometry", by Theophile Obenga, and adding some of his commentary to this page. He certainly qualifies as a specialist.
User talk:seqoyah bey
* Obenga may have studied Egyptology (though real degrees are conspicuously absent in his resumé), but he's certainly not a specialist or a reliable source. His writings are (as mentioned in the Wikipedia article) politically motivated. There are two themes, first trying to prove that all Africans, including the Egyptians are strongly related, and second, that the Egyptians were very scientifically advanced (which they were absolutely not), to come to the conclusion: Western civilisation owes everything to black Africa. This is politics, or "feelgood science", or crackpottery. Riyadi (talk) 12:34, 9 June 2017 (UTC)
thread_title:  Accurate Egyptian Geometry Sources

message: Some of the well known formulas for PI make use of continued unit fractions.
(PI2)/8 = 1/12 + 1/32 + 1/52 + ...
(PI2)/24 = 1/22 + 1/42 + 1/62 + ...
Euler's Formula
(PI2)/6 =  (n = 1..) 1/n2 = 1/12 + 1/22 + 1/32 + ...
One example of Egyptian continued unit fractions can be found at Saquarra where an architect lofted a circular arch using a series of measured grid coordinates spaced a unit dimension apart. The finger is a fraction of a series of standardized related proportions to other units such that its a fraction of a palm (1/4), a fist (1/6), a foot (1/16), a remen (1/20), an ordinary cubit (1/24), a royal cubit (1/28) and a nibw (1/32). I think that makes it easy for an ordinary working man to calculate how many staves he needs to make a barrel or an arch.
 1/n 2
n=1     = 1 + 1/4 + 1/9 + 1/16 + ... = (1/6) PI 2
 1/n 4
n=1 = 1 + 1/16 + 1/81 + 1/256 + ... = (1/90) PI 4
 1/n 6
n=1 = 1 + 1/64 + 1/729 + 1/4096 + ... = (1/945) PI 6
In practical terms we are familiar with 3 '7 as a good aproximation to PI but dividing something in seven parts is harder than dividing it in eight parts. A working man's aproximation 3 '8 '64...
rather rapidly becomes good ground for conjecture and further development.Rktect (talk) 11:21, 17 August 2008 (UTC)
thread_title: Egyptian continued unit fractions

message: Second section (the overview), fourth paragraph, first line - nonsensical.  —Preceding unsigned comment added by PurrfectPeach (talk • contribs) 22:20, 14 October 2009 (UTC)
thread_title:  Problem 

message: This article has steadily degraded over a period of years to the point where it is now completely unintelligible.  The last good version seems to be this one from 2006.  I suggest restoring this version, and then merging in any new content that is worth keeping. Sławomir Biały (talk) 23:54, 11 July 2010 (UTC)
thread_title:  Proposed cleanup 

message: The intorductory section of this article reads like a bad joke. I couldn't read this gibberish further.  —Preceding unsigned comment added by 217.159.199.228 (talk) 21:50, 18 August 2010 (UTC)
thread_title:  constructive criticism 

message: Before my recent edit, the lead read as follows:
:Egyptian mathematics refers to the style and methods of mathematics performed in Ancient Egypt.
This phrasing exhibited a failure of the use–mention distinction.  Egyptian mathematics doesn't "refer" to those styles and methods.  If anything, it is those styles and methods, though replacing "refers to" by "is" would leave an awkward sentence.
I changed it to
:The term Egyptian mathematics refers to....
but this has now become unfortunately indirect; the article is supposed to be about Egyptian mathematics, not the term Egyptian mathematics.  So this is not a great solution either.
My worry about making the sentence more direct, with Egyptian mathematics rather than the term Egyptian mathematics as the subject, is that it would appear to exclude modern Egyptian mathematics.  So I don't currently have any good solution.  I leave this note as a starting point, hoping that someone can figure out a fix that addresses these concerns. --Trovatore (talk) 20:16, 11 September 2010 (UTC)
thread_title:  Use–mention 

message: :Feel free to state your position on the renaming proposal by beginning a new line in this section with *Support or *Oppose, then sign your comment with ~~~~. Since polling is not a substitute for discussion, please explain your reasons, taking into account Wikipedia's policy on article titles.
* Support.  Title ignores modern mathematics done in Egypt.  That might be acceptable if "Egyptian mathematics" were widely understood as a name meaning something different from its component parts, but I don't think that is the case. --Trovatore (talk) 22:49, 8 April 2014 (UTC)
thread_title: Survey

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thread_title:  External links modified