Talk:Rhind Mathematical Papyrus

message: 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
:The proportion of palm to remen is 1:5
:The proportion of hand to remen is 1:4
:The proportion of palm to foot is 1:4
:The proportion of hand to foot is 1:3
The table below demonstrates a harmonious system of proportion much like the musical scales, with fourths and fifths, and other scales based on geometric divisions, diameters, circumferences, diagonals, powers, and series coordinated with the canons of architectural proportion, Pi, phi and other mathematical constants.
In Mesopotamia and Egypt the Remen could be divided into different proportions as a similar triangle with sides as fingers, palms, or hands. The Egyptians thought of the Remen as proportionate to the cubit or mh foot and palm. They used it as the diagonal of a unit rise or run like a modern framing square. Their relatedseked gives a slope. Its convenient to think of remen as intermediate to both large and small scale elements.
Even before the Greeks like Solon, Herodotus, Pythagorus, Plato, Ptolomy, Aristotle, Eratosthenes, and the Romans like Vitruvius, there seems to be a concept that all things should be related to one another proportionaly. 
Its not certain whether the ideas of proportionality begin with studies of the elements of the body as they relate to scaling architecture to the needs of humans, or the divisions of urban planning  laying out cities and fields to the needs of surveyors with their knotted cords. 
In all cultures the canons of proportion are proportional to reproducable standards. 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. Remen are the most common subdivision of land measure
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.
Greek Remen generally have long, median and short forms with their sides related geometrically as arithmetric series 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
* See cubit for the discussion of the choice of division into hands or palms
* See the table below for proportions relative to other ancient Mediterranean units
Roman Remen generally have long, and short forms with their sides related geometrically as arithmetric or geometric series based on fingers palms and feet.
By Roman times the Remen is standardized as the diagonal of a 3:4:5 triangle with one side a palmus and another a pes. The Remen and similar forms of sacred geometry formed the basis of the later system of Roman architectural proportions as described by Vitruvius.
 
Generally the sexagesimal (base-six) or decimal (base-ten) multiples have Mesopotamian origins while the septenary (base-seven) multiples have Egyptian origins.
 Unit Proportions to Greek Remen
Unit                         	Finger              	Culture       	Metric     	Palm     	Hand 	Foot   	Remen 	Pace 	Fathom	
(1 ŝuŝi                      	1 (little finger)   	Mesop         	14.49 mm   	         	.2   	0.067  	0.05  	     	      	
1 ŝushi                      	1 (ring finger)     	Mesop         	16.67 mm   	         	.2   	0.67   	0.05  	     	      	
1 shushi                     	1 (ring finger)     	Mesop         	17 mm      	         	.2   	0.67   	0.05  	     	      	
1 digitus                    	1 (long finger)     	Roman         	18.5 mm    	.25      	     	0.0625 	0.04  	     	      	
1 dj                         	1 (long finger)     	Egyptian      	18.75 mm   	.25      	     	0.0625 	0.04  	     	      	
1 daktylos                   	1 (index finger)    	Greek         	19.275 mm  	         	.2   	0.067  	0.04  	     	      	
1 uban                       	1 (index finger)    	Mesop         	.2         	         	.2   	0.067  	0.04  	     	      	
1 finger                     	1 (index finger)    	Old English   	20.32 mm   	         	.2   	0.067  	0.045 	     	      	
1 inch                       	(thumb)             	English       	25.4 mm    	         	     	0.083  	.067  	     	      	
1 uncia                      	(thumb or inch)     	Roman         	24.7 mm    	.25      	     	0.083  	.067  	     	      	
1 condylos                   	2 (daktylos)        	Greek         	38.55 mm   	.5       	     	2      	.1    	     	      	
1 palaiste, palm             	4 (daktylos)        	Greek         	77.1 mm    	1        	     	0.25   	.2    	     	      	
1 palaistos, hand            	5 (daktylos)        	Greek         	96.375 mm  	         	1    	0.333  	.25   	     	      	
1  hand                      	5 (fingers)         	English       	101.6mm    	         	1    	0.333  	.25   	     	      	
1 dichas,                    	8 (daktylos)        	Greek         	154.2 mm   	2        	     	0.5    	.4    	     	      	
1 spithame                   	12 (daktylos)       	Greek         	231.3 mm   	3        	     	.75    	.6    	     	      	
1 pous, foot of 4 palms      	16 (daktylos)       	Ionian Greek  	296 mm     	4        	     	1      	.8    	     	      	
1 pes, foot                  	16 (digitus)        	Roman         	296.4 mm   	4        	     	1      	.8    	     	      	
1 uban, foot                 	15 (uban)           	Mesop         	300 mm     	         	3    	1      	.75   	     	      	
1 bd, foot                   	16 (dj)             	Egyptian      	300 mm     	4        	     	1      	.8    	     	      	
1 foote(3 hands)             	15 (fingers)        	Old English   	304.8 mm   	         	3    	1      	.75   	     	      	
1 foot, (12 inches)          	16 (inches)         	English       	308.4 mm   	         	3    	1      	.75   	     	      	
1 pous, foot of 4 palms      	16 (daktylos)       	Attic Greek   	308.4 mm   	4        	     	1      	.8    	     	      	
1 pous, foot of 3 hands      	15 (daktylos)       	Athenian Greek	316 mm     	4        	     	1      	.8    	     	      	
1 pygon, remen               	20 (daktylos)       	Greek         	385.5 mm   	5        	1.25 	1.25   	1     	     	      	
1 pechya, cubit              	24 (daktylos)       	Greek         	462.6 mm   	6        	     	1.5    	1.1   	     	      	
1 cubit of 17.6" 6 palms     	25 (fingers)        	Egyptian      	450 mm     	6        	     	1.5    	1.3   	     	      	
1 cubit of 19.2" 5 hands     	25 (fingers)        	English       	480 mm     	         	5    	1.62   	1.3   	     	      	
1 mh royal cubit             	28 (dj)             	Egyptian      	525 mm     	7        	     	2.33   	1.4   	     	      	
1 bema                       	40 (daktylos)       	Greek         	771 mm     	10       	     	2.5    	2     	     	      	
1 yard                       	48 (finger)         	English       	975.36 mm  	12       	     	3      	2.4   	     	      	
1 xylon                      	72 (daktylos)       	Greek         	1.3878 m   	18       	     	4.55   	3.64  	     	      	
1 passus pace                	80 (digitus)        	Roman         	1.542 m    	20       	     	5      	4     	1    	      	
1 orguia                     	96 (daktylos)       	Greek         	1.8504 m   	24       	     	6      	5     	     	1     	
1 akaina                     	160 (daktylos)      	Greek         	3.084 m    	40       	     	10     	8     	2    	      	
1 English rod                	264 (fingers)       	English       	5.365 m    	66       	     	16.5   	13.2  	     	      	
1 hayt                       	280 (dj)            	Egyptian      	5.397 m    	70       	     	17.5   	14    	     	3     	
1 perch                      	1,056 (fingers)     	English       	20.3544 m  	264      	     	66     	53.4  	     	11    	
1 plethron                   	1,600 (daktylos)    	Greek         	30.84 m    	400      	     	100    	80    	20   	      	
1 actus                      	1,920 (digitus)     	Roman         	37.008 m   	480      	     	120    	96    	24   	20    	
khet side of 100 royal cubits	2,800 (dj)          	Egyptian      	53.97 m    	700      	     	175    	140   	35   	      	
iku side                     	3,600 (ŝushi)       	Mesop         	60m        	         	720  	240    	180   	48   	40    	
acre side                    	3,333 (daktylos)    	English       	64.359 m   	835      	     	208.71 	168.9 	     	      	
1 stade of Eratosthenes      	8,400 (dj)          	Egyptian      	157.5 m    	2100     	     	525    	420   	84   	70    	
1 stade                      	8,100 (shushi)      	Persian       	162 m      	         	2700 	900    	525   	85   	      	
1 minute                     	9,600 (daktylos)    	Egyptian      	180 m      	2400     	     	600    	480   	96   	80    	
1 stadion 600 pous           	9,600 (daktylos)    	Greek         	185 m      	2400     	     	600    	480   	96   	80    	
1 stadium625 pes             	9,600 (daktylos)    	Roman         	185 m      	2400     	     	625    	500   	100  	      	
1  furlong 625 pes           	10,000 (digitus)    	Roman         	185.0 m    	2640     	     	660    	528   	132  	88    	
1  furlong 600 pous          	9900 (daktylos)     	English       	185.0 m    	1980     	     	660    	528   	132  	88    	
1 Olympic Stadion 600 pous   	10,000 (daktylos)   	Greek         	192.8 m    	2500     	     	625    	500   	100  	      	
1  furlong 625 fote          	10,000(fingers)     	Old English   	203.2 m    	2500     	     	635    	500   	100  	      	
1 stade                      	11,520 (daktylos)   	Persian       	222 m      	2880     	     	720    	576   	144  	120   	
1 cable                      	11,520 (daktylos)   	English       	222 m      	2880     	     	720    	576   	144  	120   	
1  furlong 660 feet          	10,560 (inches)     	English       	268.2 m    	2640     	     	660    	528   	132  	110   	
1 diaulos                    	19,200 (daktylos)   	Greek         	370 m      	4800     	     	1,200  	960   	192  	160   	
1 English myle               	75,000(fingers)     	Old English   	1.524 km   	         	15000	5,000  	4000  	800  	      	
1 mia chilioi                	80,000 (daktylos)   	Greek         	1.628352 km	20,000   	     	5,000  	1000  	     	      	
1 mile                       	84,480 (fingers)    	English       	1.628352 km	21,120   	     	5,280  	4224  	1056 	880   	
1 dolichos                   	115,200 (daktylos)  	Greek         	2.22 km    	28,800   	     	7,200  	5760  	4800 	      	
1 stadia of Xenophon         	280,000 (daktylos)  	Greek         	5.397 km   	70,000   	     	17,500 	1400  	3500 	      	
1/10 degree                  	560,000 (daktylos)  	Greek         	10.797 km  	140,000  	     	35,000 	2800  	7000 	      	
1 schœìnus                   	576,000 (daktylos)Z 	Greek         	11.1 km    	144,000  	     	36,000 	288000	28800	24000 	
1 stathmos                   	1,280,000 (daktylos)	Greek         	24.672 km  	320,000  	     	80,000 	64000 	16000	      	
1 degree                     	5,760,000 (digitus) 	Roman         	111 km     	1,440,000	     	360,000	288000	72000	60000 	
: 1 daktulos (pl. daktuloi), digit := 1/16 pous
: 1 condulos := 1/8 pous
: 1 palaiste, palm := ¼ pous
: 1 dikhas := ½ pous
: 1 spithame, span := ¾ pous
: 1 pous (pl. podes), foot :≈ 316 mm, said to be 3/5 Egyptian royal cubit. There are variations, from 296 mm (Ionic) to 326 mm (Doric)
: 1 pugon, Homeric cubit := 1¼ podes
: 1 pechua, cubit := 1½ podes ≈ 47.4 cm
: 1 bema, pace := 2½ podes
: 1 khulon := 4½ podes
: 1 orguia, fathom := 6 podes
: 1 akaina := 10 podes
: 1 plethron (pl. plethra) := 100 podes, a cord measure
: 1 stadion (pl. stadia) := 6 plethra = 600 podes ≈ 185.4 m
: 1 diaulos (pl. diauloi) := 2 stadia, only used for the Olympic footrace introduced in 724 BC
: 1 dolikhos := 6 or 12 diauloi. Only used for the Olympic foot race introduced in 720 BC
: 1 parasanges := 30 stadia ≈ 5.5 km. Persian measure used by Xenophon, for instance
: 1 skhoinos (pl. skhoinoi, lit. "reefs") :=  60 stadia ≈ 11.1 km (usually), based on Egyptian river measure iter or atur, for variants see there
: 1 stathmos :≈ 25 km, one day's journey. May have been variable, dependent on terrain
: For variant, the stadion at Olympia measures 192.3 m. With a widespread use throughout antiquity, there were many variants of a stadion, from as short as 157.5 m up to 222 m, 
: The common Greed stadion is 185 m.
: The Greek root stadios means 'to have standing'. Stadions are used to measure the sides of fields.
In the time of Herodotus, the standard Attic stadion used for distance measure is 600 pous of 308.4 mm equal to 185 m. so that 600 stadia equal one degree and are combined at 8 to a mia chilioi or thousand which measures the boustredon or path of yoked oxen as a distance of a thousand orguia, taken as one orguia wide which defines an aroura or thousand of land and at 10 agros or chains equal to one nautical mile of 1850 m.
Several centuries later, Marinus and Ptolemy used 500 stadia to a degree, but their stadia were composed of 600 Remen of 370 mm and measured 222 m, so the measuRement of the degree was the same.
The same is also true for Eratosthenes, who used 700 stadia of 157.5 m or 300 Egyptian royal cubits to a degree, and for Aristotle, Posidonius, and Archimedes, whose stadia likewise measured the same degree.
The 1771 Encyclopædia Britannica mentions a measure named acæna which was a rod ten (Greek) feet long used in measuring land. Rktect 12:24, 1 August 2007 (UTC)
thread_title:  Remen as a Proportion to other units 

message: needs to go--M a s (talk) 12:56, 8 March 2008 (UTC)
replies: text: Whose original research? If the user(s) who wrote this read it in someone else's paper (e.g., http://www.mes3.learning.aau.dk/Plenaries/Powell.pdf), and never themselves looked at the papyrus with their own eyes, then it can't honestly be called original research now, can it? CompositeFan (talk) 13:39, 17 September 2008 (UTC)
thread_title:  all the stuff about influences is OR - No, it's just unreferenced 

message: I rewrote part of the article because I find the following sentences too biased:
* "Scholars from the 1880 to 1980 period claimed to have decoded the 2/n table, a task that was not completed until 2008. The intellectual basis and applications of Ahmes' red auxiliary numbers had been misunderstood for over 100 years."
* "In 2008 one LCM method was proven to have created the RMP 2/n table."
There is no reference to this development that took place in 2008. And there has not passed enough time to show that this new proof is now generally accepted by the community. Such strong language is simply not suitable for Wikipedia without strong evidence that the consensus has shifted and now accepts the new proof. I also took out term Red auxiliary numbers for the same reason. It's not clear what that means, but they are usually called unit fractions. The only reference for the term "Red auxiliary numbers", according to the Wikipedia article, is Gardner's 2006 article in Gaṇita-Bhāratī. That's not enough evidence to change the language. -- Jitse Niesen (talk) 18:35, 29 October 2008 (UTC)
thread_title:  2008 results 

message: The inclusions of Book I, II and III are welcome additions. Overall the Wikipedia editorial pedagogy lacked humility in several areas. First, Peet's view of Book I, II and III needs to be expanded to include other scholars. Book I, II and III contents were improved upon by Griffith, an outline that Peet followed, a combined topic discussed by Spalinger in 1990. 
In the current version there were not 40 RMP algebra problems, nor 20 arithmetic and 20 algebra problems. There were 10 algebra problems (RMP 25-34). The scribal algebra included scholarly discussions of 'trail and error' an open topic that scholars like Howard Eves reported false position related to scribal division for many years. Today, is it known that scribal algebra problems and/or the conversions of answers to Egyptian fraction series 'trail and error'? I hope that Wikipedia editors agree that humility is required to report the existence of this class of scholarly reviews of the RMP.
Second, Book I followed the 2/n table with six labor management problems (RMP 1-6). The labor management topic was "confirmed' by the Reisner Papyrus. The next grouping of RMP 7-20 included discussions of red auxiliary numbers; followed by RMP 21-24, set apart by Ahmes (Spalinger), as RMP 31 was set apart by Ahmes(Spalainger).
RMP 35-40 discussed hekat problems that were converted to 320 unit units (Clagett, 1999). RMP 40, 64 and a Kahun Papyrus arithmetic progression discussion was discussed by Robins-Shute (1987) and by John Legon (1992).
There are additional under reported math contents of Book II and III. Are Wikipedia editors interested in reporting these unsolved issues? I'd be happy to mention a small number of them, if requested.
Best Regards,Milogardner (talk) 16:28, 5 October 2010 (UTC)
thread_title:  Book I, II, III 

message: From the introduction "The British Museum, where the [Rhind Mathematical Papyrus] papyrus is now kept ... The Rhind Mathematical Papryus is now at the Brooklyn Museum"? Aarghdvaark (talk) 13:10, 1 November 2012 (UTC)
replies: text: The British Museum has two pages on it   these seem to indicate that the majority are held there. The Brooklyn Museum's page  just has a few fragments. There is a comment on the Brit Mus page about the papyrus being broken up into two parts with part missing from the middle.--Salix (talk): 13:48, 1 November 2012 (UTC)
replies: text: Thanks Aarghdvaark (talk) 14:13, 1 November 2012 (UTC)
thread_title:  Where actually is it kept? 

message: The article text makes it sound like Book III contained 84 problems.  I believe that 84 may be the total number of problems in books II and III.  Could someone verify this?
--Heath 198.82.20.227 (talk) 16:07, 29 August 2013 (UTC)
thread_title:  Number of problems? 

message: The Content section needs to be broken out of the table format. It is borderline unreadable as currently set. My feeling is that this section is simply too long, and too detailed, full stop; but maybe reformatting will be enough. Regulov (talk) 06:56, 18 August 2019 (UTC)
replies: text: The cruft was probably added long ago by Milogardner, topic-banned from Egyptian mathematics for his disruptive contributions in 2010 and eventually indefinitely blocked a year ago. Anyway, if you take a machete to it I certainly won't complain. —David Eppstein (talk) 07:41, 18 August 2019 (UTC)
thread_title:  One table to rule them all. 

message: The links to The British Museum article don't work anymore. The correct ones are https://www.britishmuseum.org/collection/object/Y_EA10057 for the first section and https://www.britishmuseum.org/collection/object/Y_EA10058 for the second section. Unfortunately I am having trouble editing the infobox  links so maybe somebody else can fix that. BananaBaron (talk) 02:23, 22 December 2022 (UTC)
thread_title:  Links to The British Museum don't work 

message: Somehow a translation of the introductory sentence made its way into a standard math text: "Primer of Modern Analysis" – SJ + 16:28, 3 March 2024 (UTC)
replies: text: Odd. That is really what it says on the book, not a bizarre cataloguing mishap: . It appears not to contain anywhere an explanation for why that is its subtitle. (Instead, the preface ends with a quote from Newton.) —David Eppstein (talk) 03:01, 4 March 2024 (UTC)
thread_title:  trivia: Directions for knowing all dark things 

message: The error is more than one percent . 194.153.110.5 (talk) 13:28, 10 March 2024 (UTC)
replies: text: Incorrect. It is approximately 0.6%. 0.6 is less than 1. —David Eppstein (talk) 16:44, 10 March 2024 (UTC)
thread_title:  Discussion