Math Lair - The Mathematics of Ancient Egypt

"It was among the Egyptians that geometry is generally held to have been discovered. It owed its discovery to the practice of land measurement. For the Egyptians had to perform such measurements because the overflow of the Nile would cause the boundary of each person's land to disappear."
-Proclus, 5^th century A.D.

The story of mathematics starts at least 5,000 years ago in Ancient Egypt. Tradition holds that the first geometers were Egyptian. As the annual flooding of the Nile river wiped out all boundary markers, it was necessary to figure out each year where one property ended and another began.

Building the Pyramids would also require mathematical knowledge. Some of the pyramids also contain interesting relationships which, although they are usually accidents or coincidences, are interesting to realize. For example, the ratio of the length of one side of the Great Pyramid of Cheops at Giza is approximately ^π/₂. The Greek historian Herodotus wrote that the pyramid was built so that the area of each lateral face would equal the area of a square with side length equal to the pyramid's height, in which case the ratio above will automatically approximate π.

The advent of an agricultural society in Ancient Egypt led to a class of priests and scribes who were able to spend some of their time working on mathematics. Fortunately for us, some of the scribe Ahmes' work has been preserved in the Rhind papyrus. This work deals with many different problems that the ancient Egyptians would have encountered.

The papyrus is able to give us a fairly good picture of the state of Egyptian mathematics. The measurement of figures and solids plays an important part of this papyrus. There are no theorems as we would call them; everything is stated in the form of a problem, and not in general terms but using actual numbers (for example: "measure a rectangle the sides of which contain two and ten units of length").

There is also a section of arithmetical problems, which is headed "Directions for knowing all dark things". The first part contains directions for expressing as unit fractions numbers of the form ²/_(2x+1). The ancient Egyptians, with the exception of ²/₃, only dealt with unit fractions; see my Egyptian Fractions page for more details.

Ahmes also writes about multiplication, which he accomplished by repeated adding, and he also posed some algebra problems, which is interesting considering that the ancient Greeks paid little attention to algebra.

I don't go into further detail here on Egyptian mathematics, but you can check out my Egyptian Fractions page.

Egyptian Mathematics