Customer Reviews

Architecture and Mathematics in Ancient Egypt

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Several reviews of this book, published elsewhere, stress
the contents of Rossi's analysis were more focused toward
the skeptical side of Egyptian math and construction methods.
Rossi, therefore is being fairly depicted as publishing new information within unproven paradigms.

On the math side, Rossi mentions Fibonacci's algorithm
and phi, two paradigms that clearly were not used in ancient
Egypt, though many like to suggest that they were. The
Fibonacci algorithm idea was introduced after 1891 and J.J.
Sylvester's skeptical views of the RMP's 2/nth table, are
reference point to 1202 AD and the Liber Abaci, but not
a reference point of Egypt. Egypt used more subtle ideas
like http://egyptianmath.blogspot.com and http://akhmimwoodentablet.blogspot.com .

Yet, Hultsch in 1895 clearly showed that Ahmes in 1650 BC
easily wrote out 2/p series into short and concise unit
fraction series using a very simple partitioning method
(as Ahmes wrote out n/p answers in his 'false position'
algebra problems, ie. 5/19 written out in a long awkward
series using 1/12th as the first partition, as he did for 2/19,
as describe a couple paragraphs below. Ahmes wrote 5/19

per, 5/19 - 1/12 = (60 - 19)/(12*19) = (38 + 2 + 1)/(12*19)

or, 5/19 = 1/6 + 1/12 + 1/114 + 1/228).

Clearly modern scholars (two being Robins-Shute) have often suggested that 'false supposition' was used by Ahmes, hinting
that Ahmes guessed at his answers. Ahmes never guessed! Ahmes'
answers were always exact when he worked with rational numbers.

Moderm scholars were the ones that had guessed, and missed, finding Ahmes deeper methods. Interestingly no scholar, until
very recently, has claimed to have read Ahmes' shorthand
notes. Modern scholars had sadly filled inlogical gaps left
by Ahmes with their own intellectual guesses - many of which
have been proven to be wrong (as Rossi had not learned, since
he referenced none of the controversial Eguptian fraction and weights and measures issues).

Bruins also discovered the Hultsch method in 1945, and today
the method is named the Hultsch-Bruin method. It says that

2/p = 1/A + (2A -p)/Ap

where A, a highly divisible number selected in the range

p/2 < A < p

with the divisors of A uniquely added to (2A -p)
thereby solving (2A-p)/Ap.

Example,

2/19 = 1/12 + (24 -19)/(12*19)

= 1/12 + (3 + 2)/(12*19)

= 1/12 + 1/76 + 1/114

with the (4 + 1) alternative being discarded
since its last denominator was too large.


Rossi also mentions that Egyptian division may have followed
an inverse operation of its multiplication 'doubling' method.

Here also Rossi did not seen the simple remainder arithmetic
found in RMP #62 where 100/13 = 7 + 9/13 = 7 + 2/3 + 1/39.

Generally Ahmes and all scribes divided by this Q = quotient
and R = remainder method. The Akhmim Wooden Tablet even
shows a special method for grain and volume division where
a hekat unity 64/64 was divided by n, with n < 64, as

(64/64)/n = Q/64 + R/(n*64)

Even more interesting, Ahmes also used this method to
divide 100 hekat by 70, with his final form matching
the Akhmim Wooden tablet's special use of ro = 1/320th
of a hekat, by:

(6400/64)/70 = 91/64 + 30/(70*64)

and introducing ro = 1/320 of a hekat,

= (1 +16 + 8+ 2 + 1)/64 = (150/70)* 1/320

= 1+ 1/4 + 1/8 + 1/32+ 1/64 + (2 + 1/7)*ro

I'll not go on and discuss Rossi' view of Egyptian
architecture being the above her standard Cambridge
skeptical comments.

Overall, many accept Rossi's view as informative,
and I do as well, in limited areas. However, on the
math side of Rossi's quick use of a Sylvester's and
other recent skeptical techniques, all disproven years ago,
shows that her Cambridge training needs to be expanded
to read the Egyptian mathematical texts. Clearly Ahmes
and his brother/sister scribes are the only experts
that should guide our understanding of Egyptian math.