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LeveL IV
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Rhind papyrus  Empty Rhind papyrus

on Fri Jun 10, 2016 7:01 am
Rhind papyrus  Rhind_10
O μαθηματικός πάπυρος του Αχμός * 1666 BCE. 

The Rhind papyrus is a famous document from the Egyptian Middle Kingdom that dates 
to 1666 BCE.(named after the Scottish Egyptologist Alexander Henry Rhind who went to 
Thebes for health reasons, became interested in excavating and purchased the papyrus in
Egypt in 1858).*Ahmes (more accurately Ahmose Αx-Mός) is the scribe who wrote the
Rhind Papyrus.[The document is dated to Year 33 of the Hyksos king Apophis & written
in the hieratic script.] Ahmes claims not to be the author of the work, being, he claims, 
only a scribe. He says that the material comes from an earlier work of about 1999 BC, 
(dating from the XII-th dynasty)
Nothing is known of Ahmes other than his own comments in the papyrus.
He is the earliest contributor to mathematics whose name is known.
     This Document is the chief source of information on Egyptian mathematics
It begins as follows:

Correct method of reckoning, for grasping the meaning of things 
and knowing everything that is, obscurities and all secrets.

"Αυτό το βιβλίο αντιγράφηκε το έτος 33 τον τέταρτο μήνα της εποχής των πλημμυρών, 
κάτω απτη Μεγαλειότητα του βασιλέα της Άνω και Κάτω Αιγύπτου " Α-ούσερ-Ρέ", 
σε ομοιότητα με παλαιότερα γραπτά της εποχής του βασιλέα της Άνω και Κάτω 
Αιγύπτου "Νέ-μα'ετ-Ρέ. Ο Γραφέας Αχ-μός αντέγραψε ετούτη τη γραφή".
LeveL IV
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Rhind papyrus  Empty Ahmes mathematical papyrus [2]

on Fri Jun 10, 2016 7:22 am
The papyrus consists of a famous table of the numbers 2/n,  where  n = 3, 5, 7, ..., 101
all expressed as a sum of fractions with a numerator 1, and about 
85 assorted mathematical exercises together with their solutions. 
Exercises 56-60 deal with pyramids. Here is the exercise 56.
Note that the term "ukha thebt" refers to the length of one side and the term "peremus"
refers to the height of the pyramid. 

πρόβλημα 56 indicates an understanding of the idea of geometric similarity.
  This problem discusses the ratio
                                        Rhind papyrus  Img6310
The problem essentially asks to compute the Rhind papyrus  Img6410 for some angle Rhind papyrus  Img6510.
Such a formula would be need for building pyramids.
Rhind papyrus  Img7210
Στο πρόβλημα 50 :
The author of the papyrus, gives a rule for determining the area of a circle 
which corresponds to π = 256/81 or approximately 3.16.
(Example of finding the area of a round field with a diameter of 9 khet. 
What is its area?) 
[2ο στην επόμενη σελίδα :]

Rhind papyrus  Egypti10
LeveL IV
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Rhind papyrus  Empty Horus eye fractions

on Fri Jun 10, 2016 7:31 am
Στο πρόβλημα 47:
The author gives a table with equivalent fractions for fractions of 100 quadruple 
"hekat" of grain. The quotients are expressed in terms of "Horus eye fractions". 
The short table gives the values related to the original 100 quadruple hekat; the
quantity "ro" here is a standard ancient Egyptian measure equivalent to 1/320
 of a hekat. (the common unit of volume ~ 4.8 litres)
Horus eye fractions
Rhind papyrus  2726922856 http://mathworld.wolfram.com/EyeofHorusFraction.html

wedjat ,"the Sound Eye" , Horus eye
Rhind papyrus  Images10
also known as 'Τhe Eye of Ra'.
, the pieces of the eye were lost in a battle between Horus and Set  ,
 and restored by the god Τhoth.

[κεφ. 17 from the Book of the Dead : 

"I am he who closeth and he who openeth , and I am but One.  []
It is Osiris who presideth over the account of all that is and all that cometh into being,
that is Endless Time and Eternity.   
Endless Time is Day and Eternity is Night.  []...
I make full the Eye when it waxeth dim on the day of battle between the two Opponents. []
the day upon which Horus fighteth with Sut. []
I lift up the net from the Eye at the period of its distress. []
and it is Thoth who lifteth up the net from it."]
LeveL IV
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Rhind papyrus  Empty black ibis

on Fri Jun 10, 2016 8:20 am
Rhind papyrus  Rpm21-10

[Gardiner Egyptian Grammar ,  Möller - Hieratische Paläographie]

Rhind papyrus  G2810Black ibis ,    
gm. “find

(Painting from: The Book of Coming Forth by Day  {the Book of the Dead})

Rhind papyrus  Pap-th10

"I am Thoth, the skilled scribe whose hands are pure, 
the Lord of purity , who writes what is true"    /spell 42
(The ibis destroyed noxious reptiles and set a standard for cleanliness.)
(Plutarch Isis and Osiris, 75), Elsewhere Thoth is called the "son of Re" 
or "he who came forth from Re"(P.Boylan, Thoth the Hermes of Egypt London 1922)
Mysterious is the name of Thoth as '(son of) the stone (who came forth) from (the two eggshells)'
(Allen, 1974, 219; Book of the Dead [BOD] Spell 134). Another strange announcement is  Thoth 
emerged from the skull of Seth (in 'The Contendings of Horus and Seth'). 
Thoth is called 'the one who emerged from the skull. Thoth's primacy is suggested  in the 
fascinating story told by Plutarch (Isis and Osiris, 12) that Hermes (i.e. Thoth) won five 
extra days for the year by playing a game (senet?) with Selene (moon). These five extra 
days became the birthdays for the deities Osiris, Horus, Seth, Isis, and Nephthys.
Rhind papyrus  Thoth-10
Thoth, was depicted with a symbol combining the Sun’s disk and the Moon’s crescent upon his head. 
His hieroglyphic name Tehuti is usually explained as meaning ‘He who balances’. Thoth is the The Great
Measurer. The god of wisdom and Science . Theinventor of spoken and written language .The God of 
Astronomy , mathematics, geometry,  medicine and botany. The God of measuring , of numbers & 
calendrical order , and a manifestation of Maat the cosmic harmony.

Studies in mythology
Budge, E. A. Wallis (Ernest Alfred Wallis), Sir, 1857-1934
[The Egyptian polymath Imhotep had been deified long after his death and therefore assimilated to Thoth in the classical 
and Hellenistic period.The renowned scribe Amenhotep and a wise man named Teôs were equally 
deified as gods of wisdom,science and medicine and thus placed alongside Imhotep in shrines
dedicated to Thoth-Hermes during the Ptolemaic period.
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