He continues: This book was copied in regnal year 33, month 4 of Akhet, under the majesty of the King of Upper and Lower Egypt, Awserre, given life, from an ancient copy made in the time of the King of Upper and Lower Egypt Nimaatre.
[1] The Rhind Papyrus was published in 1923 by the English Egyptologist T. Eric Peet and contains a discussion of the text that followed Francis Llewellyn Griffith's Book I, II and III outline.
[3] The British Museum, where the majority of the papyrus is now kept, acquired it in 1865 along with the Egyptian Mathematical Leather Roll, also owned by Henry Rhind.
[2] Fragments of the text were independently purchased in Luxor by American Egyptologist Edwin Smith in the mid 1860s, were donated by his daughter in 1906 to the New York Historical Society,[8] and are now held by the Brooklyn Museum.
[6] The first part of the Rhind papyrus consists of reference tables and a collection of 21 arithmetic and 20 algebraic problems.
Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions.
Problems 35–38 involve divisions of the heqat, which is an ancient Egyptian unit of volume.
The quotients are expressed in terms of Horus eye fractions, sometimes also using a much smaller unit of volume known as a "quadruple ro".
Specifically, problem 48 explicitly reinforces the convention (used throughout the geometry section) that "a circle's area stands to that of its circumscribing square in the ratio 64/81."
In other words, the quantity found for the seked is the cotangent of the angle to the base of the pyramid and its face.
[10] The third part of the Rhind papyrus consists of the remainder of the 91 problems, being 61, 61B, 62–82, 82B, 83–84, and "numbers" 85–87, which are items that are not mathematical in nature.
Problem 79 explicitly cites, "seven houses, 49 cats, 343 mice, 2401 ears of spelt, 16807 hekats."
They involve computations regarding the strength of bread and beer, with respect to certain raw materials used in their production.
Its language is strongly suggestive of the more modern riddle and nursery rhyme "As I was going to St Ives".
The last four mathematical items, problems 82, 82B and 83–84, compute the amount of feed necessary for various animals, such as fowl and oxen.
With these non-mathematical yet historically and philologically intriguing errata, the papyrus's writing comes to an end.
Much of the Rhind Papyrus's material is concerned with Ancient Egyptian units of measurement and especially the dimensional analysis used to convert between them.
This table summarizes the content of the Rhind Papyrus by means of a concise modern paraphrase.
These three latter items are written on disparate areas of the papyrus's verso (back side), far away from the mathematical content.
Put another way, the seked of a pyramid can be interpreted as the ratio of its triangular faces' run per one unit (cubit) rise.
Moreover, one of Ahmes' methods of solution for the sum suggests an understanding of finite geometric series.
Ahmes performs a direct sum, but he also presents a simple multiplication to get the same answer: "2801 x 7 = 19607".
Chace explains that since the first term, the number of houses (7) is equal to the common ratio of multiplication (7), then the following holds (and can be generalized to any similar situation):
This is the amount of "grain", (or wedyet flour, it would seem), which is required to make the feed for geese, presumably on the interval of 40 days (which would seem to contradict the original statement of the problem, somewhat).
Suppose that four geese are cooped up, and their collective daily allowance of feed is equal to one hinu.
Suppose that the daily feed for a goose "that goes into the pond" is equal to 1/16 + 1/32 heqats + 2 ro.
Finally a table will be presented, giving daily feed portions to fatten one animal of any of the indicated species.
It seems that the four types of animals consume feed, or "loaves" at different rates, and that there are corresponding amounts of "common" food.
These two columns of information are correctly summed in the "total" row, however they are followed by two "spelt" items of dubious relationship to the above.
These two spelt items are indeed each multiplied by ten to give the two entries in the "10 days" row, once unit conversions are accounted for.