# Ancient Egyptian Math

Just as we have symbols like 1, 100, and 10,000 to represent our numerals, so did the ancient Egyptians. The ancient Egyptians had to be pretty good at math too! Think of all those pyramids, tombs, sphinxes, massive statues, and palaces that they were famous for building. You can’t make any of that stuff without mathematics.

You also need math to trade goods and  measure the land for planting crops. Look at the symbols below to see how the ancient Egyptians wrote their numerals.  Read the numeral from left to  right. The larger numbers always come first.

Let’s work it out! Look at the picture below. What amount does each one represent? Look at the value of each symbol underneath it to help you read this numeral. The numeral is 1,113.

When the society became more complex, computations and records needed to be kept. A need for counting arose and writing and numerals were needed to record transactions in Egypt. Egyptians realised that the science of mathematics offered a solution to all these troubles. They developed a practical approach towards mathematics.

Ancient texts could be written either in hieroglyphs or in hieratic. Hieroglyphic script was developed at around 3000 BC. The earliest fully developed base 10 numeration system was used during 2700 BC. Precision surveying in the construction of the Great pyramid of Giza built in 2650 BC show a notable achievement in engineering.

The two major texts on mathematics of ancient Egypt were the Moscow Papyrus of 1800 BC and the Rhind Papyrus of 1650 BC. The former contains twenty five problems while some ask for equation. It also contains geometric problems.

Rhind Papyrus, a scroll about 6 metres long and 1/3 of a metre wide was written by the scribe Ahmes. It contains eighty seven problems. It also has geometry, algebraic equations and arithmetic series. The Berlin mathematical papyrus was also helpful in studying Egyptian mathematics.

Egyptians used the lunary system of numbers. In this system, a simple line meant one; two lines meant two, three lines three and so on. When it reached 10, a new symbol like an inverted U was used.
The Egyptian number system was additive. Large numbers were represented by collections of the glyphs and the value was obtained by simply adding the individual numbers together.

Egyptians knew addition, subtraction, some division and multiplication. They also used unit fractions. The Egyptian Mathematical Leather Roll is a table of unit fractions which are expressed as sums of other unit fractions. However, Egyptian number system was not suitable for arithmetic calculations.

Geometry was essential for Egyptians as they constructed a number of structures including the pyramids. The Great Pyramid of Khufu from the Fourth Dynasty was a mathematical wonder because it was laid out with geometric precision.

The scribes recorded problems computing the areas of triangles, circles and rectangles. The angle between the base and one of the faces is 51° 50' 35". The secant of this angle is 1.61806 which is remarkably close to the golden ratio 1.618034.

The Egyptians had a well defined civil calendar containing 365 days. The beginning of the year was chosen as the heliacal rising of Sirius, the brightest star in the sky. Eventually the civil year was divided into 12 months, with a 5 day extra period at the end of the year. There were three seasons, each made up of four months. The months were divided into three weeks of ten days each.

Clocks were also used by the people of Egypt. Clocks were of two types; the sun clocks and the water clocks. Sun clocks were formed by means of the construction of Obelisks, tapering monuments. The clock worked much like a sundial, by watching the moving shadows throughout the day.

By doing this, the Egyptians were able to divide the day into morning, afternoon, and night. Water clocks were some of the earliest clocks used. Water Clocks were like pots made of stones, with long slanting sides that allowed water to drip down at a constant rate through a small hole in the bottom.