Egyptian civilization

• Mathematics as we know is a product of civilization: the culture of people who live in permanent cities and have to deal with problems related to counting and measuring

The Ishango bone, dating to perhaps 18,000 to 20,000 B.C.

•  A well developed civilization flourished along the banks of the river Nile as early as 5000 BC.  Upper and lower Egypt  were united  around 3100 BC. The Pharaoh Menes became the first pharaoh of Egypt. It was during this period that the `"divine" kingship became well established as Egypt's form of government, and with it, an entire culture that would remain virtually unchanged for the next 3000 or more years.

• The Egyptians grew their crops along the banks of the River Nile on the rich black soil, or kemet which was left behind after the yearly floods. The fertile soil was ideal to grow healthy crops.

• To study of ancient history it is crucial

• To have original documents

• To be able to translate them

• To know how these documents were produced and for which purpose

• The Egyptians wrote  using  Hieroglyphics, hundreds of signs with both phonetic and ideographic values.

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• The Scribes had the monopoly of reading and writing in the ancient Egypt.  They were very powerful members of the ruling class in ancient Egypt.

• They wrote on stone, leather, clothes and papyrus, a paper-like material made out of the reef that grow along the Nile  banks.

• Many of these documents came to us because they were buried in secret chambers of the pyramids, which were the graves of the pharaohs and other notables of ancient Egypt.

• New discoveries are still made.• A New Pyramid was discovered last year! • See the discovery of the KV-63 chamber in 2006. It is

speculated that it could be the tomb of King Tut’s mother

• See also the following video.

•  The translation of the hieroglyphic was made possible by the discovery of the Rosetta stone,  (Ptolemaic Period, 196 BC). Soldiers in Napoleon's army discovered the Rosetta Stone in 1799 AD while digging   near the town of el-Rashid (Rosetta).  The same text is inscribed on the stone three times, in hieroglyphic, demotic (the native script used for daily purposes), and Greek (the language of the administration). The importance of this to Egyptology is immense. Soon after the end of the fourth century AD, when hieroglyphs had gone out of use, the knowledge of how to read and write them disappeared. In the early years of the nineteenth century, some 1400 years later, scholars were able to use the Greek inscription on this stone as the key to decipher them.

• The earliest system of numbers, or hieroglyphic system, was developed around the 2700 BC.  Later a "cursive form" of hieroglyphic was developed, called Hieratic.

Positional versus additive

• For us the value of  of a number depends on the value and the position of the symbols, or digits, that compose the number. Our system is positional. For the Egyptians the value of a number could be determined by adding the values of the symbols used to write the number. Their system was additive

• Shortly after the invention of the hieratic and hieroglyphic numerals, the Egyptians began building pyramids, thus attesting a high degree of mathematical sophistication. This pyramid is the oldest known (approx 2650 BC)

The Rhind papyrus The author of this papyrus is a scribe, A’ h’ Mose, who wrote a treaty on Egyptian mathematics around 1650 BC. A. Rhind is a British gentleman who purchased the papyrus in 1858. This document is 30 cm tall and is made up of multiple parts which in total make it over 5m long. It is now in the British museum