Milogardner~frwiki

Several of the oldest Egyptian fraction statements were unreadable to 20th century scholars. Two hard to read weights and measures passages in the 1900 BCE Akhmim Wooden Tablet (AWT) and 1650 BCE Rhind Mathematical Papyrus (RMP) were parsed and decoded in a 2005 study (http://www.mathorigins.com/image%20grid/awta.htm). The study was based on finding a fresh decoding path, as discussed on: http://planetmath.org/encyclopedia/WhyStudyEgyptianFractionMathematics.html. Unreadable aspects of the RMP 2/n table have also been parsed in a 2008 study (http://rmprectotable.blogspot.com/) by finding a fresh decoding path. The 2005 study revealed one of two scribal quotient and remainder division methods. The method was defined by five AWT statements and proofs, and applied over 40 times in several RMP problems. The division method includes RMP 83 data: (three bird feeding portions) 2 geese and a crane each ate (1/8 + 1/32) hekat + 3 1/3 ro; a set-duck ate (1/32 + 1/64) hekat + 1 ro, and a set-goose, dove and quail each ate (1/64) hekat + 3 ro. Ahmes, the RMP scribe, was asked, how much grain did the seven birds eat? (answer 5/8 of a hekat). The three 2005 readable portions of a hekat (a volume unit) were 1/6, 1/20, and 1/40. The three portions were created from divisions of 64/64, a unity. Ahmes created the 1/6 portion by: (64/64)/6 = 10/64 (a quotient)+ 4/384 (a remainder), rescaling the remainder by multiplying it by(5/5) obtaining 20/1920. The scaled remainder,(20/6)*(1/320) was included in an intermediate step (1/6 (8 + 2)/64 + (20/6)ro). The readable (1/8 + 1/32)hekat + (3 + 1/3)ro statement replaced 1/320 number with word ro (http://planetmath.org/encyclopedia/AhmesBirdFeedingRateMethod.html). The unity (64/64) substitution was reported by Hana Vymazalova in 2002. Ahmes' rational number divisors n were limited to 1/64 < n < 64) in the seven bird-feeding examples, and 29 RMP 82 examples. Ahmes created a second division method by dividing sub-units by a rational number n of any size. For example, the second method wrote the subunit hin (1/10) as 10/n hin, and the subunit dja (1/64) as 64/n dja, (per Tanja Pemmerening in 2002). Additional hekat sub-units remain to be scaled and fully parsed. The 2008 2/n table study showed that least common multiples (http://planetmath.org/encyclopedia/Arithmetics.html) read all 51 RMP 2/n table and 26 Egyptian Mathematical Leather Roll series. Minor differences between ancient and modern LCMs are reported by Russian scholars that studied Egyptian aliquots parts (http://egyptianmath.blogspot.com/). Five ancient Egyptian theoretical ideas are used in modern arithmetic: prime numbers, rational numbers, Least Common Multiples, quotients and remainders, and arithmetical progressions.

Several personal qualifications to work on math projects were obtained in college. Studies of medieval mathematics, history of mathematics (Eves), Theory of Equations (Borofsky), history of number theory (Ore), and European/US history of economic thought, dating to the Hanseatic League, ending with capitalism's economic history define the core courses. Military code breaking skills, learned in the 1950s, assisted several of the last 20 years' math history projects that have parsed Egyptian math texts. About 20 years ago I assisted a retired SRI International electrical engineer, Noel Braymer, to submit RMP 2/n table number theory findings for publication. Little did I know, about six years ago, AWT and RMP abstract patterns would merge to spark academic debates. During the last three years 4,000 year old theoretical methods amplify and explain 3,000 years of practical Egyptian fraction arithmetic statements. The Liber Abaci is a theoretical text that explains (in its first 124 pages of Sigler's translation) the hows and whys of the 2,800 year old Egyptian fraction math.

CONCLUSION: It turns out that an Old Kingdom binary problem was corrected by Middle Egyptian scribes 4,000 years ago. Replacement unit fraction methods created a unified commodity based monetary system (Heqanakht papyri) by applying optimized LCM remainders. Ahmes practiced optimized LCMs in RMP 21, RMP 22, and RMP 23 in red auxiliary numbers. LCMs were less optimally used in the Liber Abaci (LA). Fibonacci, the LA scribe, documents seven LCM threads, with five converting rational numbers as the RMP 2/n table, and the EMLR scribes had done. Increasingly 21st century AD Egyptian fraction papers are merging 2000 BCE arithmetic into 1202 AD and modern arithmetic. Occam's Razor points out eight(8) Egyptian Mathematical Leather Roll LCMs, 14 optimized red auxiliary numbers LCMs used by Ahmes, and other classes of LCMs by Ahmes and Fibonacci per http://mathforum.org/kb/message.jspa?messageID=6492421&tstart=0. Newly decoded Egyptian fraction methods include arithmetic progressions in the Kahun Papyrus, RMP 40, and RMP 64. The methods connect modern, medieval, and Greek arithmetic to Middle Kingdom arithmetic, algebra, weights and measures, and theoretical monetary units.

BIO: http://milorgardner.blogspot.com/2008/08/milo-gardner-personal-info.html