Bruce's Hieratic (Middle Kingdom) Math of Egypt HOME page.

CREATED: JANUARY 2000

LAST MODIFIED: JUNE 29, 2003

I love math and math loves me.  Sometimes I dream in math.  

Currently I am working to decrypt the Hieratic RMP.

The Rhind Mathematical Papyrus is a fascinating document (1650 B.C.E.)

copied from an older papyrus circa 1850 B.C.E.

The following is a reproduction of the characters from a geometrical portion of the RMP.

I have invested considerable time eliminating smudges from bad copies and splicing

and resizing and even going to the pixel level to clean this up further!  

However, for access to a real color picture of the actual document go to this RMP link.

I Suggest you print out a black/white and red copy to compare to the color RMP link.

The Rhind Mathematical Papyrus was acquired by Henry Rhind who moved to Egypt upon his Doctor's request.

 As the (self-appointed?) purchaser of Antiquities for Scotland, he acquired this papyrus in 1858.  

The RMP contains many mathematical equalities (known as the 2/n table - more later) and examples

of certain geometric exercises (see the image above).  

The papyrus also contains a coded message that is damaged and only partly understood.  

A note  is included by the scribe who wrote it, that he, Ahmes (or Ah-Mose), was copying from a much

older text (presumably worn and faded).  Ahmes has preserved for us a great store of information!

Unfortunately the scroll has many errors and omissions.  In many areas the papyrus is unclear and damaged.

 It is conceivable that the papyrus Ahmes was preserving contained some of these errors from the outset.

The scroll, carelessly torn into two large portions, is now in the British Museum in London.  

Some fragments of the scroll were purchased separately and are kept by the Historical Society of New York.

I wonder why?

 

I intend to use this website to host a forum for amateur discussions of Egyptian Math.  

I am working to re-decipher the content of the RMP and become familiar with the layout and content.  

Later, I will review this data more closely and get deeper into the number theory aspects.

 

As a novice I researched mathematical papyri on the web and at my local library. (Mostly fruitless).

I tried to purchase books that had images of the RMP. (I got a few crumbs).

I contacted Milo Gardner's VERY HELPFUL  number theory site.:

http://www.ecst.csuchico.edu/~atman/Misc/horus-eye.html  

As a Cryptanalyst his focus is almost entirely on number theory.  

Milo Gardner appears to be the most knowledgeable of the RMP number theorists.  

He is dedicated to the creation of helpful algebraic identities that were likely used to generate

the original 2/n tables of the RMP.

 

In November of 1999, I was fortunate to visit Cairo, Egypt.  At the Cairo Museum there is an extensive library.  

I was aided by Maha, the Curator.  She helped me follow the path of similar research done by others.

I had set aside 2 days for the Museum.  Mostly I was in the library.

I copied portions of many papyri and got to work.  

I identified many numbers/ unit fractions and numerical relationships.  The blind stab approach.

Once back in NY I could not find any better source material!

I pursued one book that seemed likely to be most helpful;

The RMP, as translated by Thomas Eric Peet, 1923.  This book was procured with great effort.  

Many thanks to Alice at The Periodicals Service Company in Germantown, NY.  

 

My efforts:

I have largely deciphered or reasonably guessed at the content of the REDUCED PAGE BELOW.

This reduced image is not the RMP. IT IS THE EMLR!

Clearly a duplication of most of the content is present.  It looks like a practice ditto!
The most complex addition I have identified is:
1/16 (=) 1/400 (+) 1/150 (+) 1/50 (+) 1/30 (I call it COLUMN II, Q#9)
or in more familiar terms:
75/1200 = 3/1200 + 8/1200 + 24/1200 + 40/1200 which is correct.

On the papyrus itself the line immediately above this one, (COLUMN II, Q#8) has eluded me.
It looks like (sort of)
1/8 (=) 1/100 (+) 1/35 (+) 1/15 (+) 1/25

262.5/2100 = 21/2100 + 60/2100 + 140/2100 + 84/2100 but, 262.5/2100 = 305/2100 is not correct.  

Please forgive my fractional numerators, but this is inherent in middle kingdom math and you should quickly get used to it!

This equation is also out of form, as unit fractions were generally written in ascending order (denominators).
I suggest that the line should read:
1/8 = 1/210 + 1/35 +1/15 +1/40
262.5/2100 = 10/2100 + 60/2100 + 140/2100 + 52.5/2100
It does not look egyptian but at least it is an equality!
An alternate guess that I created on the subway:
1/8 = 1/55 + 1/15 + 1/35 +1/6600!  This is not what I see on the papyrus!
See analysis on the QUEST page.

(COLUMN II, Q#10)  the apparent answer is wrong!
It looks like (sort of) 1/6 (=) 1/150 (+) 1/50 (+) 1/25
again the familiar: 50/300 = 2/300 + 6/300 + 12/300 but, 50/300 is not equal to 20/300
I think the error lies in the answer.  20/300 = 1/15!  More later...

E mail ME: brucefriedmandcg@aol.com    be sure to note "Egypt" or "math" in the title of your email.

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