# History and Numbers

## Introduction

The civilization of Ancient Egypt spans some 3000 years of history. In ancient times the country was first unified under a king named Narmer - sometimes called Menes - in ca 3000 BCE. The ruling families of ancient egypt were roughly divided into dynasties. There are all together some 30 dynasties that span the history of this ancient civilization. The fourth dynasty was the ruling family responsible for the construction of the famous pyramids at Giza. The Great Pyramid of Khufu is the topic of many scholarly (and not so scholarly) books. The architects of the time must have had knowledge of mathematics - and more specifically of geometry - in order to construct not only their pyramids, but also the temples they constructed.

We have no mathematical papyri from the time of the pyramids of Giza. There are however some temple reliefs predating that time period by several decades showing rituals associated with planning the temples that accompanied the pyramids. The reliefs show the King marking off predetermined lengths with rope to create the correct dimensions for the temples.

Our present day knowledge of much of the mathematics of the Ancient Egyptians comes from the 12th dynasty. This family ruled Egypt some 1000 years after the pyramids at Giza were constructed. There are two major sources: the Moscow Papyrus - which dates to ca. 1800 BCE - and the Rhind or Ahmes papyrus - which dates to ca 1900 BCE, but is likely a copy from an original dating to ca 1800 BCE.

In addition to these two papyri there are several other smaller fragments as well as tomb inscriptions and notes written on pottery shards (so called ostraca) that give us a glimpse into the mind of the Egyptian scientists.

Experts have cautioned us against drawing too wide ranging conclusions about what the Egyptians may or may not have known. We only have a handful of ancient sources. There is no way to know if we have a reasonable cross-section of Egyptian knowledge of mathematics, or if we only have a glimpse.

## The Egyptian Number System and Mathematical Notation

The Ancient Egyptians used a base 10 number system. The number one was depicted by a simple stroke, the number 2 was represented by two stokes, etc. The numbers 10, 100, 1000, 10,000 and 1,000,000 had their own hieroglyphs.

Higher numbers were assigned their own hieroglyphs. Number 10 is a hobble for cattle, number 100 is represented by a coiled rope, the number 1000 is represented by a lotus flower, the number 10,000 is represented by a finger, the number 100,000 is represented by a frog and a million was represented by a god with his hands raised in adoration.