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Reading Egyptian, Greek. Arab and Medieval unit fraction arithmetic

• Message 1.Β 

  Posted by Milo Gardner (U14346264) on Friday, 19th February 2010

  The British Museum reported this month on Βι¶ΉΤΌΕΔ by discussing the Rhind Mathematical Papyrus that only six Egyptian texts contain geometry information that connect to classical Greek methods.
  
  Had Egyptian arithmetic that decodes Ahmes' 2/n table been reported, as Ahmes discussed RMP 36 with the scaled LCM conversions of 2/53, 3/53, 5/53, 15/53, 28/53 and 30/53, been the topic another set of conclusions would have been reached by knowledgeable Βι¶ΉΤΌΕΔ and BM panelists.
  
  Ahmes selected LCM optimized red auxiliary numbers, linking over 1,000 ancient texts that offer additional arithmetic information that seemed to have been erased by 1585 AD base 10 decimal arithmetic.
  
  Seen as a 3,700 year continuum, from 2050 BCE to a 1637 AD Arab arithmetic text, ancient unit fraction arithmetic explains important ancient number theory details used by Fibonacci in the Liber Abaci:
  
  
  
  and other Egyptian, Greek, Coptic, Arabic and medieval mathematical texts.
  
  That is, gaining vision that takes off Eurocentric blinders and a classical love for Greek geometry, recovering primal Egyptian 2/n table arithmetic methods offers surprising results.
  
  Ahmes and other ancient scribes solved an Old Kingdom binary (Horus-Eye) round-off problem that created a rational number arithmetic metaphor that lasted in several modified forms for 3,700 years.
  
  Planetmath includes 20 discussions of 21st century decoding projects that parse ancient Egyptian, Greek, and medieval texts. Wikipedia includes many of the linked data bases created by decoding projects as well.
  
  Can Βι¶ΉΤΌΕΔ look to update this month's incomplete Rhind Mathematical Papyrus program by preparing a follow-up Βι¶ΉΤΌΕΔ broadcast? If desired, my Skype link, name: Milogardner can assist one or more of your proposed panel members, or Βι¶ΉΤΌΕΔ editors, that wish to further discuss ancient Egyptian mathematics as ancient scribes thought of the topic.
  
  Best Regards,
  
  Milo Gardner

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• Message 2

  , in reply to message 1.

  Posted by Milo Gardner (U14346264) on Friday, 19th February 2010

  The Egyptian Mathematical Leather Roll (EMLR), the RMP 2/n table, and the RMP's 87 problems have been under read and under appreciated for over 100 years.
  
  In 2002 the EMLR's 26 lines of text was published in a journal and in 2005 in an encyclopedia, began a much needed update of the EMLR per:
  
  
  
  The EMLR'S 26 lines of text offers an easy-to-read body of ancient arithmetic information. Its analysis is made available in the hope that staff of the Βι¶ΉΤΌΕΔ and the British Museum consider the informations as a tutorial to update this month's interesting, but at times, unimpressive report of the contents of the RMP.
  
  Thank you for considering several Planetmath and Wikipedia pages in preparing and airing future ancient Egyptian math Βι¶ΉΤΌΕΔ programs. Keep the Βι¶ΉΤΌΕΔ programs coming. We all learn a great deal by reporting the past as it was written by ancient scribes.
  
  Best Regards,
  
  Milo Gardner
  Sacramento, California
  

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• Message 3

  , in reply to message 2.

  Posted by Milo Gardner (U14346264) on Monday, 22nd February 2010

  A broader discussion of Egyptian math is found on the Math-history-list per:
  
  
  
  This thread begins with the 'know-nothing' Βι¶ΉΤΌΕΔ report in the RMP, and progresses to the other document once owned by Henry Rhind, the EMLR. The M-H-L thread proceeds to RMP 38 issues and deeper abstract readings of Egyptian division as inverse to Egyptian multiplication, in a modern sense solving:
  
  1. 320 x 7/22 = 101 9/11
  
  and proving
  
  2. 101 9/11 x 22/7 = 320
  
  My view is that RMP 38 shows that 800 AD Arabic 'false position' logic was not recorded in 1650 BC by Ahmes in RMP 38. Rather, a strong sense that Ahmes recorded an easy method that corrected for grain inventory losses related to pi estimated at 256/81 by using 22/7.
  

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• Message 4

  , in reply to message 3.

  Posted by Andrew Host (U1683626) on Tuesday, 23rd February 2010

  Hi Milo,
  
  Welcome to the boards. You may be interested to know that programme proposals can be submitted on this page:
  
  
  
  As this is a board for the public to discuss History it's unlikely to get picked-up by the right people here.
  
  
  Regards
  
  
  Andrew

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• Message 5

  , in reply to message 4.

  Posted by Milo Gardner (U14346264) on Monday, 1st March 2010

  Andrew,
  
  Thank you for the suggestion. I'll look into sending along a note or two to the Βι¶ΉΤΌΕΔ programmers.
  
  At this time I'd like to complete a classical Greek math thought, cited by Plato per:
  
  
  
  "In context, chapter 8, H.D.P. Lee translation, reports the education of a philosopher containing five mathematical disciplines:
  
  1. arithmetic, written in unit fraction 'parts' using theoretical unities and abstract numbers;
  
  2. plane geometry, and,
  
  3. solid geometry consider the line to be segmented into rational and irrational unit 'parts';
  
  4. astronomy;
  
  5. harmonics, that include music."
  
  My view is that modern classical translators of the works of Plato rebelled against practical versions of his culture's apparent practical mathematics, a sad point continued by Βι¶ΉΤΌΕΔ in last month's RMP broadcast.
  
  However, Plato himself, and classical Greeks generally copied 1,500 older Egyptian fraction abstract unities, one being a hekat unity scaled to (64/64) in the Akhmim Wooden Tablet, and other unities including 10 hin, 64 dja, and 320 ro, thereby not getting lost in fractions.
  
  In conclusion, one meta point is, to fairly decode ancient Egyptian texts in historical context, in ways that clear up classical biases towards Greek geometry, a decoder should consider all five classifications of Greek math (abstract arithmetic, plane geometry, solid geometry, astronomy and harmonics).
  
  When doing so, the abstract side of Egyptian arithmetic and its connections to every day ancientweights and measures come into clear focus, as dominate issues, that expose easy-to-read meta themes that decode the abstract aspects of the RMP, the Kahun Papyus, and other Middle Kingdom mathematical texts.
  
  Best Regards,
  
  Milo Gardner
  

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• Message 6

  , in reply to message 5.

  Posted by Milo Gardner (U14346264) on Sunday, 14th March 2010

  Cross posting from a Βι¶ΉΤΌΕΔ Kahun Papyrus thread, a second reason that Egyptian math is under valued in academia, beyond the 20th century Egyptology minimalists, is that modern Babylonian scholars often report Egyptian math in minimalist ways, per this review:
  
  "Looking forward to the day when Babylonian scholars are challenged on current minimalist views of Egyptian mathematics, Harvard recently made a move in that direction by appointing its first Egyptology (professor) in 68 years:
  
  Harvard To Acquire First Egyptology Professor in Decades | The Harvard Crimson
  
  
  
  After years dedicated to shedding light on the work of the late Harvard Egyptology Professor George A. Reisner, Class of 1889, Peter D. Manuelian will become the first egyptology professor at Harvard since his predecessor's death 68 years ago.
  
  The next move could offer (updated) Egyptian mathematics at Harvard. Currently, Egyptology courses in European and US universities offer reading and writing of hieroglyphic and hieratic script but virtually no hieratic arithmetic (taught by Ahmes or the hieratic texts).
  
  Reading and writing hieratic 2/n tables, the beginning paragraphs of the Kahun and RMP, the EMLR and its 26 lines of text need to be parsed by least common multiples (LCM)s. Understanding the ancient LCM scaling method, as introduced by Ahmes in RMP 14-19, a modern student could easily advance to RMP 36 'red auxiliary number' methods per:
  
  planetmath.org/encyc...
  
  as ancient students followed a well worn study path.
  
  At this point the students of Babylonian and Egyptian math history could be asked to answer the question, Why Study Egyptian fractions:
  
  planetmath.org/encyc...
  
  Any suggested debate between the current array of Babylonian and Egyptian math professors, that think little of Egyptian mathematics, would be brief, with no one required to show up. Future college course outlines of (updated) Egyptian math would be handed out, ending the debate."

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• Message 7

  , in reply to message 6.

  Posted by Milo Gardner (U14346264) on Monday, 15th March 2010

  OOPS, two links in the previous post do not work. Not to bore the reader, only the "Why Study Egyptian fractions" Planetmath link will be fixed:
  
  
  
  Please note that modern Babylonian, and Classical Greek scholars have not reconstructed ancient Egyptian arithmetic theme that connects to Greek, Hellene, Arab, and Medieval arithmetic themes.
  
  During the 20th century, Classical Greek blinders oddly replaced Egyptian fraction arithmetic with Greek geometry and algorithms. Formal algorithms was innovation that did not explode in the Arab world until 800 AD, and Europe by 1585 AD, with the rise of base 10 decimals, a point of view that Babylonian scholars (Friberg, Robson, and Hoyrup) suggest appear in Demotic texts.
  
  Our 21st century Babylonian scholar distractions are easily over come by reading the Egyptian, Greek, Hellene, Arab and medieval texts by meta unit fraction notations.
  
  Again, begin with the Rhind Mathematical Papyrus and its unit fraction notation that scaled rational numbers by:
  
  n/p = n/p(m/m) = mn/mp
  
  with the diviso0rs of denominator mp selected that best summed to numerator mn. Ahmes exposed his often used red number method in RMP 36 by converting 2/53, 3/53, 5/53, 15/53, 28/53 and 30/53, discussed by:
  
  
  
  Jumping to the Liber Abaci
  
  
  
  it is clear that Arabs and Fibonacci converted n/p to unit fraction series by a subtraction method:
  
  (n/p - 1/m) = (mn - p)/mp
  
  with m the LCM and mn-p usually set to unity, one. When unity could not be reached, a second subtraction step was instituted. Another LCM, m', assisted to inspect the divisors of mm'p that best selected summed to the numerator --- as Sigler's 2002 translation of the Liber Abaci explained as Fibonacci's 7th distinction (on page 124).
  
  The issue of Greek arithmetic and its unit fraction notation has not been parsed at this time. Fibonacci actually lists three unit fraction notations, one named after Euclid, so a path to resolve the Greek arithmetic puzzle is open for anyone that is interested.
  
  
  
  

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