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the case of a land where pi=256/81 or about 3.1604938 a similar result can be obtained with the different formula that has been suggested by
Zapassky and others where over there the volume of a sphere is given by the quotient of the cube of the circumference divided by six pi (V=c/6π) and in that case the ancient Egyptian volume should come to about 2.386954 liters or about 98.5% of its true volume.
210: = 3 case by showing (64/64)/3 = 21/64 + 1/192 (a modern statement) as written as(16 + 4 + 1)/64 + 5/3 × 1/320 = 1/4 + 1/16 + 1/64 + 1 2/3ro (two-part ancient statement). Two-part statements were also converted by Ahmes to an unscaled hin unit by writing 3 1/3 hin.
241:: 9, 18, 36, 72, and 81, Gillings, page 141) until the vulgar fraction 256/81 was reached, the only relationship that was used in the Egyptian Middle Kingdom. The MMP scribe found the surface area of a basket equal to: (8d/9) = 64d/81, within a cylinder relationship to the hekat. MMP 10 data meant that
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However that may be at least a sphere that has a circumference 523.5 millimeters will actually have a metric volume about 2.42269 liters or roughly half of a hekat or about one sixtieth of a royal cubic cubit to two parts in a hundred. A modern schoolbook formula has volume=4/3 pi r for example. In
337:
Pommerening, Tanja, "Altagyptische
Holmasse Metrologish neu Interpretiert" and relevant pharmaceutical and medical knowledge, an abstract, Philipps-Universität, Marburg, 8-11-2004, taken from "Die Altagyptschen Hohlmass" in studien zur Altagyptischen Kulture, Beiheft, 10, Hamburg, Buske-Verlag,
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was greater than 64. For example, one the 1/320 ro unit was written by Ahmes by solving 320/n ro. Gillings cites 29 examples of two-part statements converted to one-part statements in RMP 82. Ahmes recorded the
261: = 1, a suggestion that does make sense. One royal cubit of the ancient Egyptian weights and measures = 523.5 millimeters. ((523.5 mm)) / 30 = 4.78221176 liters.
370:
Benenson, Itzahk. Some short paper in Hebrew about the noted 2012 pottery volumes studies that looks like it could not possibly have much particulars in it at
356:
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Zapassky E, Gadot Y, Finkelstein I, Benenson I (2012) An
Ancient Relation between Units of Length and Volume Based on a Sphere. PLoS ONE 7(3): e33895.
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to around 3.16. The approximation of π was achieved by squaring a circle, increasingly (i.e. for the denominator in terms of
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to 1/320 units named ro. Quotients and unscaled remainders were obtained for the dja, ro and other units when the divisor
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discussion further shows that the hekat was 1/30 of a royal cubit, an analysis that needs to double checked, against the
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was denoted by Horus-Eye imagery. It has been suggested by
Pommerening that the NK change came about related to the
142:) contained 4 hekat. It was sub-divided into other units – some for medical prescriptions – the
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by showing that five answers were returned to (64/64) when multiplied by the divisors 3, 7, 10, 11 and 13. The
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245: = 2 defined π for use in hekat volumes as 256/81. The 256/81 approximation was also used by
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was recently evaluated by Tanja
Pommerening in 2002 to 1/64 of a hekat (75 cc) in the MK, and 1/64 of an
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Vymazalova, H. "The Wooden
Tablets from Cairo: The Use of the Grain Unit HK3T in Ancient Egypt."
225:, the best known medical text. The hekat unit was defined, in terms of its volume size, in the
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the hekat was one tenth of a khar, later one sixteenth; while the New
Kingdom
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replacing the hekat as the
Pharaonic volume control unit in official lists.
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https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0033895
283:"Ancient jugs hold the secret to practical mathematics in Biblical times"
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also divided a hekat unity (64/64) by prime and composite numbers
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http://www.eurekalert.org/pub_releases/2012-06/afot-ajh060412.php
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https://tauweb.tau.ac.il/news/new-method-discovery-ancient-world
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Hana
Vymazalova evaluated the hekat unit in 2002 within the
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used to measure grain, bread, and beer. It equals 4.8
164:(1/16 of a hekat, or 300 cc) in the NK, meaning that the
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Dover, reprint from
Cambridge, Mass, MIT Press 1972,
345:, Charles U., Prague, pp. 27–42, 2002.
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53:but its sources remain unclear because it lacks
374:retrieved March 21, 2020 at about 11:20 PM EST
291:retrieved March 22, 2020 at about 7:00 AM EST.
366:Egyptian geometry: Determining the value of π
304:retrieved March 22, 2020 at about 7:38 AM EST
193: < 64. The binary quotient used
257: = 2 suggestion, which means that
84:Learn how and when to remove this message
324:Mathematics in the Time of the Pharaohs
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251:ancient Egyptian units of measurement
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388:History of mathematics
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150:(1/64) and
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66:introducing
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