Talk:Ancient Egyptian units of measurement

p i e z Please see ancient weights and measures for previous edit history and discussions wrt this article.

khet

The khet, as far as I can tell from other sources, was a unit of length (v., e.g., Gillings, Mathematics in the Time of the Pharoahs, p. 137). The phrase "Ro or parts of areas are found as strips such as the khet which is 100 cubits long by 1 cubit wide" seems to say that it is an area. —Preceding unsigned comment added by Scorwin (talk • contribs) 14:51, 22 January 2009 (UTC)

Sources [1] [2]. I see mention of a square khet. Dougweller (talk) 10:32, 8 August 2009 (UTC)

I have included a short discussion of the square khet (setjat) in the article. And the strips mentioned above are also discussed now. --AnnekeBart (talk) 13:59, 12 August 2010 (UTC)

As with Greek and some Roman measurements, the Egyptians used the same or similar names for their square units based on their linear ones. That said, yes, the ḫt was a unit of length. — LlywelynII 04:10, 1 February 2017 (UTC)

photographs

Can we get a photograph of an Egyptian ruler? RJFJR (talk) 18:12, 21 June 2009 (UTC)

I have some pictures of the cubit rod of Maya and a picture of the ropes used for measuring length on my own website. But I need further permission from friends to include them here on wikipedia. --AnnekeBart (talk) 14:00, 12 August 2010 (UTC)

Spell it

"h3yt"? Is that transliterated correctly? Or do I need browser support? TREKphiler ^{hit me ♠} 07:22, 29 July 2009 (UTC)

The 3 and y are stand-ins for characters we should be using, although they may require browser support. See Friesian's article on reconstructed Egyptian and its orthography. — LlywelynII 04:09, 1 February 2017 (UTC)

Egyptian Ramen, Cubit and Royal Cubit, digit and Roman cubit

Flinders Petrie, sometimes called the father of Egyptology claimed that the theoretical length of the royal cubit was not exactly 7 palms, but rather the diagonal of a square of 1 ramen on a side. A ramen is 5x4=20 digits, therefore a royal cubit is 20x square root of 2 ~28.28+ digits.

The digit, which he derived in various ways including regularly spaced checkerboards of lines one digit apart is 0.727 inches http://www.touregypt.net/petrie/c20.htm ~1.85 cm and the regular cubit of 6 palms = 24 digits = 44.4 cm = Roman cubit.

This same cubit is found in the tunnel connecting the Shiloach Spring to the Gihon Spring in Jerusalem. The digging of this tunnel is described in the Bible. An inscription in the wall (cut out and brought to Turkey, now on display there) says that the tunnel was 1200 cubits long. The tunnel is 533 meters long, which gives an cubit of 44.4 cm. http://en.wikipedia.org/wiki/Siloam_inscription —Preceding unsigned comment added by Emeslyaakov (talk • contribs) 08:16, 31 May 2010 (UTC) Emeslyaakov (talk) 08:18, 31 May 2010 (UTC)

This must be the "short cubit" or "standard cubit". There were apparently two units referred to as the cubit and did differ in size. --AnnekeBart (talk) 14:02, 12 August 2010 (UTC)

1.5 Roman feet of 296 mm = 444 mm = 6 palm. 12.187.94.103 (talk) 18:54, 23 September 2013 (UTC)

Scaling khar and 'quadruple hekats' to hekats in RMP 42 and RMP 43

RMP 42 calculated a cubit^3 by 3/2 to calculate khar units, meaning that a cubit^3 = 2/3 khar.

RMP 43 began on line 2, diameter 8, height 6, applying a Kahun Papyrus volume formula V = (2/3)(H)[4/3)D]^2 khar, Ahmes input V = (2/3)(6) and wrote 4. Ahmes input [4/3(8)] and wrote 32/3 times 32/3 = 1024/9 times 4 = 4096/6 concluding with 455 1/9 khar. On lines 3 and 4 Ahmes multiplied 455 1/9 khar by 1/20 = 4096/18, writing (22 + 1/2 + 1/4 + 1/180) quadruple hekat ( many read 1/180 as 1/45 (Ahmes poor hand writing)). Clearly on line 5 Ahmes converted 1/180 'quadruple hekat' by 100/180 = 5/9 hekat, recording (1/2 + 1/32 + 1/64)hekat + (2 + 1/2 + 1/4 + 1/36)ro exactly following the Akhmim Wooden Tablet binary quotient and ro scaled remainder. From the above a khar contained 5 hekat, based on Ahmes writing 2200 hekat + 1/2 (100 hekat) + 1/32 (100 hekat) + 1/64 (100 hekat) + 1/180 (100 hekat) = 2275 7/9 hekat. Given that Ahmes noted (22 1/2 1/4 1/180)quadruple hekat, each quadruple hekat contained 100 hekats. Q.E.D. (line 1 of RMP 43 repeated RMP 42 info to show that a 3/2 conversion of cubit^3 to khar were not needed. Milogardner (talk) 02:48, 10 September 2010 (UTC)

1 khar = 2/3 of a cubic cubit (see Clagett)

1 khar = 20 heqat in the Middle Kingdom.

The computations in RPM 41 and 42 shows that they compute the number of heqats from khar by dividing by 20. So 1 khar = 20 heqat.

Your "computations" contradict what all others that I have read write. That means it's original research. Find any writer other than yourself who claims 1 khar = 5 heqat. Then we can use that as a reference. Consistently citing you own work is in violation of wikipedia rules (WP:OR, WP:COI). This has now been pointed out ad nauseum. Read the editing conventions. It still seems to be a continuing problem.--AnnekeBart (talk) 03:19, 10 September 2010 (UTC)

"1 khar = 2/3 of a cubic cubit (see Clagett)" (correct, period!) my apologies to Anneka Milogardner (talk) 20:19, 14 September 2010 (UTC)

RMP 42 reported V = (H)[(8/9)(D)]^2 (cubit^3) and took 3/2 of the cubit^3 (64000/81) to compute 96000/81 khar, meant a formula V = (3/2)(H)[(8/9)(D)]^2 (khar) was used to find (96000/81 khar). Hence a Khar was one and one-half times larger than a cubit^3, and conversely, to convert a khar into a cubit^3 multiply (96000/81) khar by 2/3 to obtain 64000/81 cubit^3 (a point that you or Clagett seem to have muddled), calculation also found in RMP 41 with 640 cubit^3 and 960 khar.

1 khar = 20 heqat in the Middle Kingdom." (not true). Your conclusion assumes that the numerator divided by 20 was scaled to 1 hekat. But Ahmes' numerator was a khar scaled to 5 hekat. Dividing one khar (5 hekat) by 20 meant that a new unit 5 x 20 = 100-hekat was created (that oddly was named a quadruple-hekat by linguists), the exact 100-hekat scaling unit used by Ahmes in RMP 43, LINE 5. as noted above to convert 1/180 (100-hekat) to 5/9 hekat recorded as a unit fraction series:

(1/2 + 1/32 + 1/64)hekat + (2 + 1/2 + 1/4 + 1/36)ro

"The computations in RPM 41 and 42 shows that they compute the number of heqats from khar by dividing by 20". (yes, input the actual numbers and you'll see that the answer created a 100-hekat unit -- since the numerator was a khar = 5 hekat unit.)

True concerning RMP 41, RMP 42 and RMP 43. RMP 41 increased 640 cubit^3 to 960 khar, by D = 9 and H =10

line 1: (9 - 9/9) = 8 x 8 = 64 x 10 = 640 cubit^3

followed by taking 1/2 of 640 = 320, and adding obtaining

khar = 960 khar, as mentioned above.

"So 1 khar = 20 heqat". Not true ... this is the problem that I muddled for one week.

Your "computations" contradict what all others that I have read write. That means it's original research. Find any writer other than yourself who claims 1 khar = 5 heqat.

I'll forward Bruce Friedman's email of yesterday, and see for yourself ... not in my words ... but his words. Thank you for the humble request ...

Then we can use that as a reference. Consistently citing you own work is in violation of wikipedia rules (WP:OR, WP:COI).

The 100-hekat value was also reported by Peet, 80 years ago ... how about that source? Gee, am I really in violation of Wikipedia rules when Peet is cited? Peet was not always wrong, nor am I, or yourself. We all make subtle and not so subtle mistakes.

This has now been pointed out ad nauseum. Read the editing conventions. It still seems to be a continuing problem.

Best Regards, and updated on 9/14/10 to agree with Anneka Bart related to CC and khar scaling. Milogardner (talk) 20:19, 14 September 2010 (UTC)

The responses should leave a record of the original comments by other posters. Editing my posts is not appropriate. Using my comments in a response should be done in quoting it in a separate text below. You seem to be deliberately misinterpreting my comments about WP:OR and WP:COI. And ignoring the fact that by the time you were done the table contents were no longer in line with the column headings.

The text I have added is given a reputable inline reference. --AnnekeBart (talk) 18:46, 10 September 2010 (UTC)

the 100 heqat refers to what is usually translated as the 4-heqat, so Peet doesn't support your khar to heqat conversion. --AnnekeBart (talk) 18:49, 10 September 2010 (UTC)

Regarding this quote:

a formula V = (3/2)(H)[(8/9)(D)]^2 (khar) was used to find (96000/81 khar). Hence a Khar was one and one-half times larger than a cubit^3, and conversely, to convert a khar into a cubit^3 multiply (96000/81) khar by 2/3 to obtain 64000/81 cubit^3 (a point that NEITHER you or Clagett muddled), calculation also found in RMP 41 with 640 cubit^3 and 960 khar.

That is one of the basic mathematical mistakes I'm talking about. There is no muddling here. You just don't seem to understand what is being said. 1 khar = 2/3 cubic cubit (write as CC). So to convert from say X cubic cubits to khar, you use the standard change of unit approach: X CC * 1 khar/ (2/3) CC = 3/2 X khar. I mean, do you really think all the experts are going to get this wrong for more than a century? The smart thing to do when your work disagrees with all the experts is to check your own work. --AnnekeBart (talk) 19:08, 10 September 2010 (UTC)

Please accept this humble apology for writing over your post, rather than citing it in a proper manner. I will not do that again. as well as not properly citing Clagett with respect to CC and khar scaling. Milogardner (talk) 20:19, 14 September 2010 (UTC)

Returning to the serious discussion at hand. Your incorrect conclusion that 1 khar is 2/3 a cubit-cubit was muddled. One khar was clearly 3/2 a cubit-cubit in RMP 41, 42 and 43. Bruce Friedman copied an unknown for an identical false conclusion. To place a khar in the context of a cubit-cubit (actually a cubit^3), considering:

A cubit-cubit was 3/2 of a khar, in your view, as documented by Ahmes. Ahmes in RMP 41 a volume of 640 cubit-cubit was increased by 1/2 to 640, 320, to report 960 khar. Wow, I had misread this fact for one week. Inputting raw data from RMP 43, 455 1/9 KHAR was found. Inputting the same RMP 43 dimensions, H = 6, D = 8 in the RMP 41 formula == 303 33/81 CC ... wow, was I surprised .... and therefore placed in an apology mode. Milogardner (talk) 20:19, 14 September 2010 (UTC)

The same procedure was used in RMP 42 and RMP 43, take 1/2 a cubit-cubit and add the original cubit-cubit to find khar.

You suggested the inverse, 3/2 per

1 cubic cubit = 3/2 khar = 7 and 1/2 single hekats = 3/40ths of a "quadruple hekat"

I agree that 3/40 of a 'quadruple hekat', but where did your 3/2 khar come from? I now see ... wow, was I surprised today! Milogardner (talk) 20:19, 14 September 2010 (UTC)

The following is background information.

V = (2/3)(H)[(4/3)D]^2 khar

But as we know in RMP 41 and 42 Ahmes reported

V = (H)[(8/9)]^2 cubit^3

RMP 41 raw data: D = 9, H = 10

V = (10)[(8/9)(9)]^2 = 640 cubit^3 + 320 = 960 khar

RMP 42 raw data: D = 10, H = 10

V = (10)([(8/9)(10)] = 64000/81 cubit^3

since (10 - 10/9) = 80/9 X 80/9 = 6400/81 (were Ahmes' calculations) with Ahmes taking 1/2 of 64000/81, 32000/81 and added 64000/81 = 96000/81 khar and the KP scribe earlier reported the use of

V = (2/3)(H)[(4/3)D]^2 khar (KP and RMP 43 khar formula)

Added discussion (the correction steps) ... begin with

V = (H)[(8/9)]^2 cubit^3

and RMP 42 shows

V = (3/2)V (H)[(8/9)]^2 khar

scaling both sides by 3/2

(3/2)V = (3/2)(3/2)(H)(8/9)(8/9)(D)(D) = (H)[(4/3)(D)]^2 khar

multiplying both sides by 2/3 completes the formula

V = (2/3)(H)[(4/3)(D)]^2 khar

Hence, a khar from Bruce Friedman's previous analysis Anneka Bart's scaling of a CC to a khar was correct ... and I humbly apologize. Milogardner (talk) 20:19, 14 September 2010 (UTC)

meant that a cubit-cubit was valued at (3/2)(5) = 15/2 hekat, a controversial point that Dr. Bart or others can take up at another time. Milogardner (talk) 20:19, 14 September 2010 (UTC)

Hence, a cubit-cubit, was scaled by Ahmes from a khar by 3/2 (a calculation I accepted today Milogardner (talk) 20:19, 14 September 2010 (UTC). Ahmes calculated in that direction to obtain a khar from a cubit-cubit, he increased a cubit-cubit by 3/2.

Best Regards to all, Milogardner (talk) 20:19, 14 September 2010 (UTC)

The fact that you do not seem to understand that the 1 khar = 2/3 cubic cubits relation gives the exact results found in the problems proves my point. You seem to be very confused about some basic facts. And btw quoting your co-author as a source is not really what is meant when asking for an appropriate reference. --AnnekeBart (talk) 14:21, 11 September 2010 (UTC)

I agree with Anneka's repeated and correct valuations that 1 khar was 2/3 a cubit-cubit within one of nine (9) scribal scaling relationships. A complete list is submitted for Anneka Bart's review and comment:

a. 1 cubit^3 = (3/2) khar = 15/2 hekat

b. (2/3) cubit^3 = 1 khar = 5 hekat

c. (2/15)cubit^3 = (1/5)khar = 1 hekat

issues that can be deferred as controversial and placed in another category, to be discussed later.

All nine scaled units need to be placed on a Wikipedia documentation list, each double checking the other, issues that can be discussed later. Ahmes listed his scaling steps in RMP 41, 42 and 43, facts that speak for themselves. I'll be searching for appropriate Wikipedia references (including Clagett's corrrect raw data) to detail all nine relationships. Clagett was an editor, and not a mathematician. I thank him for his hard work, but scaling discussion errors are easilY corrected by Clagett's own raw datas. In RMP 43, Clagett cited Gillings, a correct 455 1/9 khar, related to lines 2, 3 and 4, oddly omitting line 5. Clagett, stressed Peet's incorrect use of line 1, a fragment from RMP 42 that in total reported "take (10 - 10/9) = 80/9 times 80/9 = 6400/81 times 10 = 64000/81 cubit^3, and adding 32000/81 cubit^3 = 96000/81 khar, 4800/81 (100-hekat) and finally 480000/81 hekat". Annette Imhausen's use of algorithms, that you advocate may attempts to merge lines 1, 2, 3, 4 and 5 into one calculation. No algorithm exists (that I know of that merge slines 1, 2, 3, 4, 5. Line 1 must be thrown out (again in my humble view, a view that Gillings correctly reported, citing cubit^3, khar and hekat scaling facts from RMP 41, 42 and 43 in one table (the one revised listed above corrteced on 9/14/10). The table, once verified by all parties, does close an important chapter. The time is not at hand to do that. Line 1 fragments of RMP 42 were included in RMP 43 by Ahmes to show that a direct calculation of a khar can be made, without calculating a cubit^3, facts that the Lahun Mathematical Papyrus aptly reports per John Legon and others. Best Regards to all. Milogardner (talk) 20:19, 14 September 2010 (UTC)

Are there any published sources for this reasoning? At the moment this is all looking a lot like WP:SYNTHESIS with material from a lot of different sources being combined in a complex argument. That does seem to be against wikipedia policy. So what published source claims 1 khar = 5 heket?--Salix (talk): 07:26, 14 September 2010 (UTC)

Clagett in RMP 41 began by writing 4800 hekat was contained in 640 CC. Ahmes calculated 4800 hekat by dividing 960 khar by 20 and multiplying by 100, as well as showing a volume calculation from a formula V = (H)[(8/9)(D)}^2 with H = 10 and D =9. Ahmes increased 640 CC by 320 CC and obtained 960 khar. Does not 4800/960 = 5 hekat per khar? Anneka has been shown this 5 hekat = 1 khar scaled data in RMP 42 AND 43, and offers no comment. Does not Clagett's raw data mean anything until a scholar reports the raw data conversion? Suggesting that a 'letter of the law' rule is being applied on Wikipedia, Schack-Schnackenberg and other scholars that worked closely with RMP 41-43 will be consulted. Gillings mentioned that a smaller cubit (f) was used elsewhere. Was a 1/4 smaller hekat in use? As importantly, what has been the history of 'quadruple hekat' a term that has been associated with the 100-hekat unit mentioned by Peet and Clagett whenever a khar was multiplied by 1/20? If a 1/4 hekat size was actually reported in RMP 41, 42 and 43 the scaling problem under discussion would be resolved. Once detailed scholarly RMP 41,42, and 43 CC and khar discussions and conversions to a hekat are located, I'll return, to complete an important scribal story line ... thereby possibly documenting another controversy. Only interdisciplinary teams such as the 2009 group established by Annette Imhausen and Tanja Pemmerening can formally resolve any controversy. That is, my purpose to post to Wikipedia has never been to resolve any of the Egyptian math controversies. I document suggested approaches for interdisciplinary teams to consider. Once the appropriate schools of thought are brought into the same room, and feel energized to resolve a particular controversy, Wikipedia can report formal results. Best Regards, Milogardner (talk) 13:49, 15 September 2010 (UTC)

Fully agree with Salix. Wikipedia is not the place to present WP:original research. We are not qualified to judge its merits. The figure in the literature is the one that is WP:Verifiable. If you think you have good grounds for your figures present a short paper to a journal on it and if it is peer reviewed and accepted then the result can be pur in here, and it wouldn't require any of the above computation to put it here - just a citation. Dmcq (talk) 11:08, 14 September 2010 (UTC)

As other editors have said, Wikipedia is not the place for original research, nor for "documenting suggested approaches for interdisciplinary teams to consider", nor for "bringing appropriate schools of thought into the same room", nor for "reporting formal results". Wikipedia is for repeating results that have already been published in peer-reviewed literature. -- Radagast3 (talk) 12:01, 16 September 2010 (UTC)

I agree with Dmcg and Radagast, pseudonyms for a reason I suspect. "Cherry picking" one aspect of Egyptian math published in the last 20 years, omitting papers that conflict with their positions, as well as omitting older papers dating back 100 years or more, is not the type of scholarship that Wikipedia advocates and supports. There are Egyptian math topics that are controversial. The first one is attested scribal method(s) for writing rational numbers into scaling factors, red auxiliary numbers, 2/n tables, and concise unit fraction series (the central topic of the 2/n table and RMP 1 - 20, and secondary topics in RMP 21-87, and all other hieratic math texts). Does a longer list of controversial issues need to be submitted? Omitting documented scholarly aspects of any on-going controversy reduces the reliability of any group or individual that posts to Wikipedia. Best Regards, Milogardner (talk) 16:48, 16 September 2010 (UTC)

1 '2 khar and 30 hekats in a cubic cubit. 20 hekats in a khar Gillings, chapter 20, p 210. 12.187.94.103 (talk) 18:48, 23 September 2013 (UTC)

Hand vs Span of Hand

Half of a cubit is called a "hand" in the Units of Length table, but other sources I have seen call half a cubit a "span of the hand" or "span." I also see reference to other sources say that a hand is 5 fingers. History of measurement calls it "span of the hand" and http://www.britannica.com/EBchecked/topic/933255/large-span refers to half a cubit as a "span" and defines a "hand" as 5 digits. Can someone help clear this up? --Onmywaybackhome (talk) 16:47, 21 September 2010 (UTC)

The Turin cubit-rod clearly shows the hand (with thumb) above the fifth digit, immediately after the palm (without thumb), as do I believe other extant cubit-rods. I'm a total layman here, but every other source I've looked at today gives a hand as five digits, a value not far different from its present value. Is it possible that there is some mistake here? Justlettersandnumbers (talk) 18:00, 3 July 2011 (UTC)

The hand is 5 fingers rather than 4 fingers and 1 thumb. Egyptian rulers systematically use fingers (18.75 mm), palms (75 mm), hands (100 mm), spans (131.25 mm), feet (300 mm), remen (375 mm(, cubits (450 mm), royal cubits (525 mm) and ells (600 mm). The inclusion of hands makes the Egyptian standard commensurable with the Mesopotamian standard where 4 palms and 3 hands = 1 foot; 6 hands = 2 feet = 1 ell = 1 Mesopotamian great cubit. 4 spans = 1 royal cubit. The division of the ruler into palms of 4 fingers, hands of 5 fingers, spans of 7 fingers, feet of either 14, 15,or 16 fingers depending on whether you are using 2 spans,3 hands or four palms is related to calculation by the use of unit fractions.12.187.94.21 (talk) 14:15, 17 July 2013 (UTC)

henu or hinu

The section Ancient Egyptian units of measurement#Volume, Capacity and Weight mentions a unit "henu" in the text and "hinu" in the table. Are these the same unit? Is there a preferred spelling?--Salix (talk): 19:34, 24 September 2010 (UTC)

The Egyptian language has no vowels, but pronunciation is sometimes indicated with a consonantal spelling hnu. Whats interesting about squares and volumes is that they have sides and edges which are lengths squared and cubed. We read in the table that one hinu is about half a liter, but another way to think of it is in terms of how many cubic inches it contains. If we take one liter = 64 cu inches then its side is its cube root or 4 inches. That's 4/3 Egyptian palm of 75 mm (four fingers of 18.75 mm) and also one hand of 100 mm (with five fingers of 20 mm). The metric system is essentially the same system used in Ancient Egypt and Mesopotamia and the Egyptian system relates to the Mesopotamian system as palm to hand.

If you have to make a container that holds a volume of grain its convenient to come up with a system that allows larger containers to be close to whole number multiples of the unit with whole number sides; in other words to double the cube. Two liters is 128 cu in so the cube root of 128 is close to 5" (5.0396841995794926590688424291129). If you were measuring with Egyptian rulers that were hand made its doubtful that your precision would be anywhere close to +/- .04" less than the width of a human hair. Skipping over gallon measures for the moment the cube root of 512 cu in or 8 liters is 8" or two hands. Three hands gives a volume of 1728 cu" or 27 liters with a side of one foot.

Gallons appear to be measured with cylinders rather than cubes. One common definition was a cylinder with a height of 6" and a diameter of 7", a clever variation on the artificial limit of doubled cubes.

The area of a diameter of 7" (using Pi = 22/7 and the formula area of a circle = Pi r^2), is 38.5., so the cylinder contains 231 cu in, and is a wine gallon. Modern measures preserve this system for the Gallon and other definitions of volumes. 12.187.94.63 (talk) 13:14, 11 August 2013 (UTC)

Every language has vowels. Prehellenic Egyptian simply didn't transcribe them. The variant spellings are variant guesses, but should be generally replaced by the known consonant values, with the proposed reconstructions given once, possibly in a footnote, and only with citations. — LlywelynII 04:04, 1 February 2017 (UTC)

1 Royal cubit = 7 palms x 4 fingers = 28 fingers

A Standard cubit/Biblical cubit is the measurement of everyone's forearm from the elbow to the tip of your middle finger. Everyone's standard cubit is 6 palms x 4 fingers. The exact measurement of the standard cubit came from the measurement of the pharoah's cubit. The ancient Egyptians practiced sacred geometry with its premise "As above, so below."/"On Earth as it is in the heavens." Because the Egyptians observed 7 moving objects in the heavens and 4 don't cast shadows on Earth, as well as the lunar months being rounded off to 4 7-day weeks (7.4 days), and the lunar year + 7 day week + 4 days = solar year, the Egyptians added a palm to the standard/Biblical cubit to produce 1 Royal cubit = 7 palms x 4 fingers. Notice that by using Simple(6,74) English(7,74) Gematria(8,74), GOD=7_4 with G the 7th letter, a circle can be 15 or zerO, and D is 4. 'The key'= 74=T20+H8+E5+K11+E5+Y25. cubits=74=C3+U21+B2+I9+T20+S19. heavens=74=H8+E5+A1+V22+E5+N14+S19. objects=74, shadows=74, months=74. - Brad Watson, Miami (talk) 19:54, 27 September 2012 (UTC)

For the billionth time, gematria is not a reliable source, and you have to cite reliable sources for additions. Ian.thomson (talk) 21:21, 27 September 2012 (UTC)

Egyptian measures are documented by artifacts to include rulers marked in fractions of fingers, fingers, palms, hands, spans, feet, remen, ordinary and royal cubits; architects measured drawings, calcuations and construction diagrams with dimensions given in standard units, the Rhind papyrus and Egyptian mathematical leather roll, studies by Egyptologsts to include Sir Allen Gardiner, mathematicians like Gillings and Milo Gardiner, Historians going back to Herodotus, all of which demonstrate the Egyptians used unit fractions and a special fraction of 2/3 to simplify commensurable measurement and calculation of standards of body, agricultural, architectural, and artistic proportions.12.187.95.16 (talk) 16:12, 28 June 2013 (UTC)

There were many different cubits in use in international business between Mesopotamia, Egypt, Greece, Rome, Persia and eventually Europe. Generally all of them had long and short forms and were based on multiples of sub unit body measures such as fingers, palms, hands, spans, feet, remen, short cubits, long cubits and ells, and also as multiples of the foot related to linear, square and volumetric agricultural measures such as feet, yards, fathoms, rods, cords, perch, furlongs with both body and agricultural measures used as the basis of squares to provide areas and cubes to provide volumes and combined into systems of architectural and engineering proportion following the Egyptians concept of inscription grids and the Greeks concepts of golden sections and other sacred geometry. Egyptian rulers were subdivided in ways that allowed them to measure other systems. For example with Egypt and Rome measuring in fingers and palms and Mesopotamia, Greece and Persia measuring in fingers and hands, a foot of 300 mm could be four palms and sixteen fingers or three hands and fifteen fingers. The Roman standard for a foot might be 296 mm and the Greek standard for a foot might be 308.4 mm but both could share stadia of 185 m with the Greek thousand or mia chilios (aroura) of 1000 orguia or 4800 feet being 8 stadia of 600 feet and a Roman miliaria or thousand paces being 8 stadia of 625 feet and both combined as a degree of 75 miles or 600 stadia of 5000 Roman or 4800 Greek feet and 111 km. Whats more degrees could be divided into 400 stadia of 277.5 m , 500 stadia of 222m (Persia) , 600 stadia of 185m, (Herodotus)or 700 stadia of ~158.6 m (Eratosthenes). (I have tried to use generic English terms like foot rather than confuse by switching between units like Roman pes,and Greek pous, and explaining the common etymology.)The remen wass commonly used for land measure but also for public buildings. The proportion of foot to remen can be either 4:5 making it the hypotenuse or 3:4 making it the side of a right triangle. If the remen is the hypotenuse of a 3:4:5 triangle then the foot is one side and the quarter another so the proportions are 3:4 quarter to foot, 4:5 foot to remen and 3:5 quarter to Remen. The quarter is 1/4 yard. The foot is 1/3 yard. The remen may also be the side of a square whose diagonal is a cubit The proportion of remen to cubit is 4:5. In ancient cultures the standards are divisions of a degree of the earths circumference into mia chillioi, mille passus, and stadia.

Stadia, are used to lay out city blocks, roads, large public buildings and fields

Fields are divided into acres using as their sides, furlongs, perches, cords, rods, fathoms, paces, yards, cubits, and remen which are proportional to miles and stadia

Buildings are divided into feet, hands, palms and fingers, which are also systematized to the sides of agricultural units.

Inside buildings the elements of the architectural design follow the canons of proportion of the the inscription grids based on body measures and the orders of architectural components.

In manufacturing the same unit fraction proportions are systematized to the length and width of boards, cloth and manufactured goods.

The unit fractions used are generally the best sexigesimal factors, three quarters, halves, 3rds, fourths, fifths, sixths, sevenths, eighths, tenths, unidecimals, sixteenths and their inverses used as a doubling system. 2/3 is a special non unit fraction. (Gillings)

Greek Remen generally have long, median and short forms with their sides related geometrically as arithmetric or geometric series based on hands and feet.

The Egyptian bd is 300 mm and its remen is 375 mm. the proportion is 1:1.25

The Ionian pous and Roman pes are a short foot measuring 296 mm their remen is 370 mm

The Old English foot is 3 hands (15 digits of 20.32 mm) = 304.8 mm and its remen is 381 mm

The Modern English foot is 12 inches of 25.4 mm = 304.8 mm and its remen is 381 mm (15")

The Attic pous measures 308.4 mm its remen is 385.5

The Athenian pous measures 316 mm and is considered of median length its remen is 395 mm

Long pous are actually Remen (4 hands) and pygons

The proportion of palm to remen is 1:5

The proportion of palm to foot is 1:4

The proportion of hand to foot is 1:3

The systems are inter related as explained by Vitruvus from body measures up to degrees of the Earths equatorial circumference

across all the major empires of antiquity because they measured property and were defined legally in contracts.

Mesopotamia used 600 sos of 180 m = 108 km

Egypt used 10 itrw = 700 "3ht or fields" (of 3 kht of 100 royal cubits) = 110.25 km

Persia used 20 parasangs of 30(furlongs = 185 m) = 111 km

Phoenicia used 500 stadions (of 750 feet = 185 m) = 111 km

Ptolomy and Marinus of Tyre measured in the Persian/Phoenician stadia

Eratosthenes measured in the 700 3ht of Egypt.

The Greeks used 600 stadions (of 600 pous of 308.4 mm) = 111 km

The Romans used 600 stadiums of 625 pes (of 296 mm = 111 km

All of those are accurate divisions of a degree as defined by Ptolomy

Ancient Europe used the same standards because it did business with the same people. 12.187.94.100 (talk) 11:41, 7 August 2013 (UTC)

Removed another editor's rude shunting of 12...'s comments. Formatted. — LlywelynII 04:01, 1 February 2017 (UTC)

Additions and corrections

Added to units of length nbiw and nwh from Gardiner "Egyptian Grammar" Section 266, p199; corrected hiero on itrw to agree with Gardiner from the same section, corrected finger measure to read 18.75 mm instead of rounded 18.8 cm, added hiero for hand and fist; and changed order to run from smallest to largest length.12.187.94.103 (talk) 13:23, 23 September 2013 (UTC)

Edited areas to agree with Gardiner, left alone the last three units which don't agree with Gardiner ("t3" generic land) to check other sources such as Gillings, and Faulkner. There are differences between the Old Kingdom, Middle Egyptian and the New Kingdom caused by a difference in how fields were plowed, planted and left fallow. I'll check Wilkenson on this and Loprieno. 12.187.94.103 (talk) 14:27, 23 September 2013 (UTC)

Could you please add reliable references for the edits you just did on the article? Otherwise the edits might (rightfully) get reverted. Iry-Hor (talk) 14:50, 23 September 2013 (UTC)

As above) Sir Allen Gardiner, "Egyptian Grammar", 3rd Edition, 1994 Griffith Institute, ISBN 0900416351

Richard J. Gillings, "Mathematics in the Time of the Pharoahs",1972, MIT, ISBN 0262070456 (hardcover)

Checked Wilkenson,Vol 1 of 3 vol set; Loprieno, "Ancient Egyptian"; Faulkner Middle Egyptian couldn't find "t3" earth opposed to sky, land opposed to water, land in the geographical sense, ground, flatlands as opposed to hillcountry, where it doesn't have the unspecified generic sense of land in the old kingdom or middle Egyptian; Faulknerp 294 has tsSh "boundary"; t(3)sh for "the limits of". Gardiner is the principal source of the hiero used by Wikipedia and for that matter Manuel de Codage. 12.187.94.103 (talk) 18:26, 23 September 2013 (UTC)

I am not the one you should try to convince: instead, you need to cite these references in the text of the article for every claim you make in the article. Note, Gardiner's book can only be used as a ref on the hieroglyphs themselves and I doubt anyone will argue that the hand hieroglyph was a drawn as a hand. I mean that it is rather the meaning and value of the units of measurement which needs to be backed by references. Also, given that some suspect this is all numerology and/or original research, you need to be very clear in your citations and (if possible) provide perhaps one or two google books excerpts viewable online to allow the rest of us to check the references in question. This would certainly be a big step to convince editors that your statements are correctly sourced. P.S: I own both the Falkner and the Gardiner so I will personally check these references if required. Iry-Hor (talk) 19:52, 23 September 2013 (UTC)

Gardiner includes a section on measures (section 266 measures of length p 199, measures of area p 200) The measures are also given on the Turin cubit already included in the article so you can read the name in the first register and the values in the second just by looking at that. I corrected some errors in Gardiner numbers which corrects the hiero so it references the right glyphs. Egyptian measures are well documented in Faulkner and Gillings as well. 12.187.94.103 (talk) 21:39, 23 September 2013 (UTC)

The values presently in the article come from Digital Egypt which is referenced in the article but has no references or correct information on its own site. 12.187.94.103 (talk) 00:04, 24 September 2013 (UTC)

Right so edit the article and to avoid other editors reverting your edits, simply put a reference for each claim made in the edits. It's that simple. Iry-Hor (talk) 07:54, 24 September 2013 (UTC)

I edited the article and added the references above as per your instruction 12.187.95.149 (talk) 08:04, 24 September 2013 (UTC)

These are not really my instructions, it's wikipedia's instructions. Also if you create yourself an account, other editors would be less prone to doubt your edits. Iry-Hor (talk) 08:29, 24 September 2013 (UTC)

In addition to references I linked some graphics from Wikipedia commons. The discussion on the linked pages includes some elaboration from the reference "Ancient Egyptian Construction and Architecture" which was already mentioned but not cited under the length section

A text found at Saquara dating to c 3000 BC or 5000 years BP has a picture of a curve and under the curve the dimensions given in fingers to the right of the circle as reconstructed to the right. It was presumed the horizontal spacing was based on a royal cubit but the results if based on an ordinary cubit are different. It appears the value for PI being used is 3 '8 '64 '1024. which at 3.141601563 is slightly better than the Rhind value.

The circumference of the circle is 1200 fingers and the diameter of the circle is 191 x 2 = 382

3 '8 '64 '1024 x 382 ~= 1200.0

The side of the square is 12 royal cubits and its area is 434 square feet.

The area of the circle is 191^2 x 3.141601563.

The algorithm suggests working with coordinates and numerical analysis to define a curve.

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

3

3 + 1/2y^3 is 3 '8, = 3.125

3 + 1/2y^3 + 1/2y^6 is 3 '8 '64,= 3.140625

3 + 1/2y^3 + 1/2y^6 + 1/2y^10 is 3 '8 '64 '1024 = 3.141601563

For purposes of comparison(3 '7 = 3.142857143) 12.187.95.149 (talk) 08:57, 24 September 2013 (UTC)

What you just stated makes absolutely no sense. Proof ? There were no text by 3000 BC. There were certainly signs already in use, but the first texts date from much later. Don't invent stuff or check your sources please, this makes me wonder about the rest of the edits ! Iry-Hor (talk) 20:11, 24 September 2013 (UTC)

First its from a published reference "Ancient Egyptian Construction and Architecture" which I referenced. Here it is as a Google Book. "Ancient Egyptian Construction and Architecture" Here is the referenced graphic Architects Curve What you see there was already referenced on the page as an artifact from Saqarra, but without the graphic. Its Fig. 53 p. 52. Figure 54 p. 53 is a scale drawing of it. The Graphic I referenced is in Wikipedia commons and is used in two other articles which have the text I copied to the talk page. As to your comment that it makes absolutely no sense, I paraphrased the caption "The algorithm suggests working with coordinates and numerical analysis to define a curve". Thats just basic math, so I gave an example of how Pascals triangle may be used to generate PI with a series formed by the third diagonal; 1,3,6,10.

As to your comment "there was no text c 3000 BC. Its a measured drawing of a curve entitled "An architects drawing defining a curve by co-ordinates. Probably 3rd dynasty. Saqarra. (from Annals du Service, xxv, p.197)" The measurements look similar to those on the Turin cubit with 5 vertical columns of dimensions under the curve given p.52 as follows

1 1 cubit, 3 palms, 1 digit (41 digits)

2 2 cubits, 3 palms (68 digits)

3 3 cubits (84 digits)

4 3 cubits, 2 palms, 3 digits (95 digits)

5 3 cubits, 3 palms, 2 digits (98 digits)

As to your instruction "Don't invent stuff or check your sources please, this makes me wonder about the rest of the edits" Apparently you just aren't very familiar with measured third dynasty drawings, and don't read pre dynastic palettes...page 51 gives three other examples. 12.187.95.149 (talk) 01:00, 25 September 2013 (UTC)

Another Google Book reference to it that lets you scroll through it page by page page by page12.187.95.149 (talk) 01:11, 25 September 2013 (UTC)

Again you have serious problems with the chronology. 3000 BC is mid-first dynasty and I continue to say that there were no extend texts at the time. There were years labels for examples, but no extend text. The thrid dynasty is much later from c. 2670 BC until 2610 BC and the fifth starts around 2490 BC !! The books you cite, date the inscriptions from the 3rd or 5th dynasties NOT the 1st. Furthermore, it would be difficult to do an entire book about architecture during the 1st dynasty given the paucity of architectural remains from this period. This shows that you don't simply cite sources, but also that you (perhaps not deliberately) interpret them to the point of actually modifying what they say !! P.S: Predynastic palettes are rarely inscribed with signs: only those from Naqada III have recognizable signs and none have an extend text. Even Narmer's palette does not have a text. Iry-Hor (talk) 09:35, 25 September 2013 (UTC)

Iry-Hor, what do you think then should be changed, reverted or simply deleted? We've had OR problems in the past here. Dougweller (talk) 11:19, 25 September 2013 (UTC)

Sorry I just noticed your question. I don't know for the moment. I do have the Gardiner and Faulkner but not much time on my hands right now. I will take a look asap. Iry-Hor (talk) 13:25, 28 September 2013 (UTC)

Sources for future article expansion

• Hirsch, Antoine Pierre (2013), Ancient Egyptian Cubits: Origin and Evolution (PDF), Toronto: University of Toronto.

 — LlywelynII 14:52, 18 January 2017 (UTC)

Nonsensical section on Egyptian treatment of fractions (I think)

Commented out below:

It's mostly but not entirely cited to "MTP" and may have relevance to a history of fractions article of some sort. It doesn't belong here in its present form. — LlywelynII 16:30, 1 February 2017 (UTC)

I have to apologize. I didn't notice that another sock of User:Rktect had added that and was participating here. See these edits[3] mainly by IP socks of the same person. Any edits by this person can be removed on sight as block evasion. Doug Weller talk 17:07, 1 February 2017 (UTC)