As we mentioned in the previous two articles, the Ancient Egyptians attained a sophisticated level of mathematical knowledge as early as 2000 BC, a date close to the building of the pyramids era.
This week, we will concentrate on the most famous mathematical papyrus known as Rhind Mathematical Papyrus (RMP) which was found in the middle of the nineteenth century in Luxor and sold with a lot of other things to a British tourist named Alexander Henry Rhind.
The papyrus was purchased by the British Museum in two parts. Only the second part is on display. Some fragments from the ‘region of the break’ are now in display in the Brooklyn museum, USA. The total length of the papyrus is more than 5m and its width is 32cm. It has writings on both sides. It starts with a title page (like any standard book) followed by a table for calculating fractions and then 60 problems, mostly geometrical ones.
On the back of the papyrus, an additional 27 problems are displayed, mostly pure mathematics. The problems are separated by black lines and every problem has a title in red ink, then a statement about the problem and finally the solution. In the case of geometrical problems, they are generally accompanied by a sketch indicating the dimensions. The geometrical problems address normally practical things like calculating areas of lands or the volume of pyramids, etc.
Like any cover page, the title page of the manuscript contains a title, date, author (scribe) and most surprisingly an intellectual property statement. The title is in red and reads as follows: “Correct Method of Reckoning, for Grasping the Meaning of Things and Knowing Everything That is, Obscurities (missing part) and all Secrets”.
The dating is given as follows: “Written in the fourth month of inundation season in year 33 of the reign of King Auserre (Apophis)’. This King’s reign began in 1585 BC, so the papyrus must date to 1552 BC.
The statement reflects the way the Ancient Egyptians created their calendar which will be the subject of the next article. The intellectual property statement is as follows: “Similar to work done in the old times, copied from work written down in the reign of king Ny-Maat-Re (Amenemhat II)”; a wonderful statement indicating that the papyrus was copied from another one that existed 400 years earlier. Finally, the title page gives the name of the scribe who copied the papyrus.
Now let us look at one example, calculating the area of a triangular piece of land. Here is the title of the problem (in red ink): “Example of calculating the area of a triangular piece of land”. Then comes the statement of the problem: “Assume you have a triangle of height 10 khat and a base of 4 khat. What is its area?”
The khat is a measurement of length equivalent to 100 cubits. The solution then is given: “Take half of the base 4 and this gives 2, so that you can square the triangle. Then you multiply 10 times 2, this will give you the area”.
As we can see, the problem is very well stated and structured. The solution is as we know it today and as was given a thousand years later by the Greeks. This is just one of the 87 problems in the RMP.
