User:Milogardner

This is a Wikipedia user page.
This is not an encyclopedia article or the talk page for an encyclopedia article. If you find this page on any site other than Wikipedia, you are viewing a mirror site. Be aware that the page may be outdated and that the user whom this page is about may have no personal affiliation with any site other than Wikipedia. The original page is located at https://en.wikipedia.org/wiki/User:Milogardner.

This is the user page for Milo Gardner, whose login name on Wikipedia is User:Milogardner

Military language and math based

Wealth of Nations

and the USA economy (and political system). A 1970 MBA sharpened modern business threads that connect to ancient monetary and economic systems in subtle ways.

A history of zero project had been contemplated in 1962. One aspect of

history of zero's arrival in Germany was misreported as 1200 AD by Howard Eves

.

In 1988 independent studies re-dated zero's arrival to the West (Egypt and Babylon) by 2,000 BCE. Six months were spent reading math books in local university libraries. It is clear that theoretical zero was used in 2,000 BCE Egypt (nfr) and diffused the idea to classical Greece (two dots), India, and the medieval Arab world.

base 10

decimal system points cited by Eves.

Meeting Noel Braymer in 1989, a retired

RMP 2/n table and Egyptian math became interests that searched for scribal methods that directly calculated scribal mathematics. Military cryptanalysis empowered several studies of hieratic (Middle Kingdom Egyptian) math patterns. A dozen studies over 20 years have cleared up Middle Kingdom math text transliteration errors. Scribal arithmetic patterns have been re-transliterated and translated into modern arithmetic statements in new ways. Gathering an approval from Worcester Polytechnic Institute's history of science department, followed by reviews by David Pingree and two Historia Mathematica experts, three number theory submissions freshly decoded 50 Rhind Mathematical Papyrus 2/n table patterns by modern number theory recorded in least common multiples, one of the new methods. A third rejection recommended that Egyptian number theory be limited to internet discussions. For 15 years internet discussion groups that included David Fowler (mathematician)

discussed ancient Egyptian number theory. Internet discussions identified ancient number theory and history of zero threads as theoretical statements.

In 2004 an

RMP 2/n table

related to LCM construction methods.

Several MK weights and measures and unit fraction patterns have been translated into basic number theory statements. As background, Egypt's 2050 BCE ciphered numerals were replaced by 800 AD when Hindu-Islamic numerals (as used in the first 124 pages of the 500 pages of

Arab mathematics. The Liber Abaci scaled rational numbers n/p by a subtraction method, (n/p - 1/m) = (mn -p)/mp. The medieval method replaced Ahmes (n/p)(m/m) = mn/mp multiplication method that wrote out concise unit fraction series, a context in which weights and measures for over 3,500 years were written in the Ancient Near East

and the medieval world.

2006, 2009, 2010, and 2011 studies were completed in association with Bruce Friedman. The 2006 AWT study reported scribal division as identical to RMP division. Ancient division was inverse to multiplication in the modern sense, invert the divisor n to 1/n and multiply. In RMP 83 Ahmes the RMP scribe used quotient and remainder statements(http://planetmath.org/encyclopedia/AhmesBirdFeedingRateMethod.html in RMP 83. Three bird feeding portions:(1) 2 geese, and a crane ate (1/8 + 1/32)

red auxiliary numbers' scribal secrets connected to the Egyptian Mathematical Leather Roll. RMP 36 reported 5/53 as (60/636 - 1/12) = 7/212 = (4 + 2 + 1)/636 = 1/519 + 1/318 + 1/636 and 3/53 = (60/1060 - 1/20) = 7/1060 = (4 + 2 + 1)/1060 = 1/265 + 1/530 + 1/1060. Tanja Pemmerening's 2002 and 2005 Ebers Papyrus

papers scaled a dja to 1/64 of a hekat, and a 2009 advocacy of interdisciplinary approaches are greatly appreciated.

In MMP 10, RMP 41, RMP 42 and RMP 43 reported the area of a circle formula that solved for Diameter (D) by replacing radius (R) with D/2 and pi with 256/81 such that: A = [(8/9)D]^2 cubit^2. In RMP 42 Ahmes multiplied height (H) to compute Volume (V) a cubit^3 unit. By increasing the cubit^3 value by 3/2 a khar unit appeared. In RMP 43 and the Kahun Papyrus scribes scaled A^1/2 = (8/9)D by 3/2 and obtained V = (2/3)H[(4/3)D]^2 khar. In RMP 44 1500 khar/20 = (75) 400-hekat. In RMP 47 400-hekat times 1/10, and 1/20 = (10) 4-hekat and (5)4-hekat, respectively, and 100-hekat times 1/40, 1/50, 1/80, and 1/100 reported binary (Q/64)hekat quotients and (5R/n) ro remainders were understood by Clagett (1999). Clagett did not report an understanding of 100-hekat multiplications, facts reported by 1/30, 1/60, 1/70 and 1/90 discussed by: http://mathforum.org/kb/message.jspa?messageID=7259234&tstart=0 . A Dec. 6, 2010 New York Times article reported puzzle implications of four Egyptian texts per: http://www.nytimes.com/2010/12/07/science/07first.html?ref=science written in an economic context citing wage payments.

The 2011 update of the AWT, EMLR and RMP 2/n table corrected

Kahun Papyrus, 25 in the Moscow Mathematical Papyrus, two in the Berlin Papyrus, two in the Reisner Papyrus, and the remainder in Ebers Papyrus

-type prescriptions recorded shorthand LCMs and red auxiliary numbers that applied the scribal longhand method. The longhand scribal method solved a wide range of issues.

About 1,500 later the 300 BCE Greek Hibeh Papyrus (http://planetmath.org/encyclopedia/HibehPapyrus.html) mentioned 27 Greek festival days within an Egyptian civil calendar, and other topics. The length of each festival day and night was encoded to Egyptian unit fraction series that applied LCM 1, 2 and 4. A 500 AD Coptic text (http://www.mathorigins.com/image%20grid/ACHMIM_GR_001.htm) reported the Egyptian-Greek-Coptic LCM arithmetic in the Akhmim Papyrus (http://mathforum.org/kb/message.jspa?messageID=7485114&tstart=0), a ciphered number system that scaled rational numbers n/17 and n/19 by LCM 2, 3, 4, 5, 6, 10, 12, 30, 60 and 120, as needed. The 2,800 year old numeration system ended in 800 AD with the rise of Arabic numerals.

A related approach was applied by Fibonacci's rational number conversion method, the simplest of three Arabic notations. One of the Arabic notations was named after Euclid. Ahmes (the RMP scribe)scaled rational numbers n/p by LCM m to mn/mp selectrf the best divisors of denominator mp that summed to numerator mn calculated 2-term. 3-term, 4-term, or 5-term series. Fibonacci's n/p conversion method also used a related LCM m method that scaled (n/p - 1/m) = (mn -p)/m with numerators (mn-p) set to unity that reported 2-term series. When (mn-p) could not be found a second LCM m was subtracted from the remainder that calculated a 3-term exact unit fraction series (i.e 4/13 = 1/4 + 1/18 + 1/468), unit fraction system that ended in 1585 AD with

base 10

decimal system.

In summary, Middle Kingdom Egyptian and Fibonacci arithmetic systems were finite. Middle Kingdom arithmetic defined economic and theoretical arithmetic methods that empowered scribal wage payments (made in hekats of grain, and other commodity units) that were extended to the medieval era (with minor modifications). Middle Kingdom Egyptian arithmetic was confirmed in the 21st century AD by decoding the EMLR, RMP (http://ahmespapyrus.blogspot.com/2009/01/ahmes-papyrus-new-and-old.html) and other texts. Egyptian scribes used

arithmetical progressions, and later Archimedes square root http://planetmath.org/squarerootof3567and29

that reduced square root approximation errors to 4- 6 places.

BIO: http://milorgardner.blogspot.com/2008/08/milo-gardner-personal-info.html links 24 ancient Egyptian, three classical Greek, two medieval and Mesoamerican topics (http://planetmath.org/mayanseasonalalmanac) are also published in Planetmath's math encyclopedia. A 12/6/2010 New York Times Science section article reported four Egyptian math paper puzzles per: http://www.nytimes.com/2010/12/07/science/07first.html?ref=science. In 2011 an interview captures personal snapshots of my life: http://www.eimacs.com/blog/2011/11/milo-gardner-cryptanalyst-code-breaker/ .