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Milo (Sacramento, CA)

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 The Greeks and the Irrational (Sather Classical Lectures) by E R DoddsEdition: Paperback Price: £17.92

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2.0 out of 5 stars Greek math roots that extended to Egypt were not well understood in the 1950s, 16 Jan. 2014
"The Greeks and the Irrational" takes the reader back to the 1950s and a time when classical Greek math was reported as taking large steps to improve older Egyptian mathematics. The 1950s was a golden era that European and US universities shut down their Egyptian math departments , with the retirement of Prof. Reisner, Harvard was the last to close its department. Irrational numbers were reported as only known by Greeks like Archimedes.

The 1950s was the time that I worked as a military code breaker, assigned to Germany and Lebanon to decode Russian and Arabic texts.:

Last year fragments of Greek square root were reassembled by the request of a researcher. Several surprises came into view.

Unresolved aspects of Archjimedes' ESTIMATION OF PI problem were reported by Kevin Brown and E.B. Davis with upper and lower limits;

(1351/780)^2 is greater than PI is greater than (265/153)^2

A. Archimedes calculated the higher PI limit(1351/780)^2 by:

1. step 1. guess (1 + 2/3)^2 = 1 + 4/3 + 4/9 = 2 + 3/9 + 4/9, meant 2/9 = error1

2. step 2 reduced error1 2/9

by dividing 2/9 by 2(1 + 2/3)

steps that meant

2/9 x (3/10) = 1/15

such that

(1 + 2/3 + 1/15)^2, error2 (1/15)^2 = 1/225 = error2

knowing (1 + 11/15) = 26/15

3. step 3 reduced error2 = 1/225 by dividing by 2 x (26/15) = 52/15

1/225 x (15/52) = 1/15 x (1/52) = (1/780)^2 = error 3

reached

(26/15 - 1/780)^2 = (1351/780)^2 in modern fractions

recorded a unit fraction series that began with step 2 data and subtracted 1/780

(1 + 2/3 + 1/15 - 1/780)^2

as Archimedes would have written

(1 + 2/3 + 1/30 + (13 + 6 + 4 + 2)/780)^2 = (1 + 2/3 + 1/30 + 1/60 + 1/+ 1/195 + 1/390)^2

B . The lower limit 265/153 modified step 2, used

1/17 rather than 1/15, (1+ 2/3 + 1/17) = (1 + 37/51)

such that (1 + 111/153)changed to (1 + 112/153) = 265/153.

The decoded raw data shows that Ahmes in 1650 BCE and the scribe that wrote the 1900 BCE Berlin Papyrus solution to two second degree equations had used the same square root method.

As an aside, today Harvard has refunded its Egyptian mathematical chair. There are critical rational steps that Harvard may be considering to update the classical Greek views of the 1950s. For example, will Harvard revisit the rosay "The Greeks and the Irrational" Dodd narrative and offer corrective suggestions for us all? I for one vote yes.

Best Regards,

Milo Gardner
Sacramento, Caiifornia
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