Count Like an Egyptian: A Hands-on Introduction to Ancient Mathematics

DAVID REIMER
Pages: 256
https://www.jstor.org/stable/j.ctt5vjvdr

1. Front Matter
(pp. I-IV)
(pp. V-VI)
3. PREFACE
(pp. VII-VIII)
4. INTRODUCTION
(pp. IX-X)

Far too many decades ago, I was sitting in a junior-high Spanish class. The topic of the hour was the conjugation of verbs, but one of them didn’t follow the standard rules. This bothered my budding mathematical sensibilities, which required that all things follow well-regulated patterns. I asked the teacher why this word was different, and she simply responded “That’s just the way it is,” to which I replied, “Well, Spanish is stupid.”

As her face turned red, I immediately realized my mistake. She was upset for a variety of good reasons, one of which was the comment that came...

5. COMPUTATION TABLES
(pp. XI-XVI)
6. 1 NUMBERS
(pp. 1-12)

In the primal waters at the dawn of time, the Egyptian god Ptah brought himself into being. This bearded god had skin blue as the night sky, and he carried a scepter whose form combined the Egyptian symbols of stability, dominion, and life. In his heart, Ptah conceived of the world, and his tongue turned his thoughts into words. At the sound of his voice, the universe changed. The amorphous eight gods of the Ogdoad, including the primeval waters, darkness, chaos, and the invisible power, came together. There they formed the primeval mound, the first piece of the earth. The...

7. 2 FRACTIONS
(pp. 13-21)

Egyptian society was concurrent with a number of great Mesopotamian empires; however, those empires rarely lasted more than a couple of generations, being brought down by barbarians or a warlord with a desire for an empire of his own. Although it was a great civilization, Mesopotamia suffered from constant turmoil and abrupt change. Although equally as large, Egypt was more of a nation than an empire. For almost three thousand years, Egypt remained relatively stable. There were a few “intermediate” periods consisting of either internal strife or foreign influence, but these were small compared to the thousands of years of...

8. 3 OPERATIONS
(pp. 22-54)

“Beginning of the teaching, explaining to the heart, instructing the ignorant, to know all that exists, created by Ptah, brought to being by Thoth, the sky with its features, the earth and what is in it, the bend of the mountain, and what is washed by the primeval waters . . . .” So begins the Onomasticon of Amenemipet.

Egyptian children destined for the scribal class entered school at the age of five. They had to start early because they had so much to learn. In the modern world, we take reading for granted. We have to learn only twenty-six...

9. 4 SIMPLIFICATION
(pp. 55-79)

Students simply do not appreciate how much time teachers put into their classes. Little do they realize that the hours they spend in class are matched by hours outside. Good teachers labor over every problem they explain in class. The order, difficulty, and complexity of each exercise is carefully planned. Apparently little has changed in almost four thousand years.

We can learn a lot about ancient mathematics by looking at texts from a pedagogical point of view. Far too often historians of mathematics select one interesting problem and analyze it to death. By taking these problems out of context, they...

10. 5 TECHNIQUES AND STRATEGIES
(pp. 80-120)

The four cardinal points of the compass were extremely important to the Egyptians. The human world ran north-south along the Nile. Trade, raw materials, and people continuously moved up and down the river. The life-bringing flood came from the south and worked its way to the north. Throughout their entire lives most Egyptians rarely moved significantly in any other direction.

Death was another matter entirely. At this time, Egyptians hoped to join their gods, who moved east to west when embodied as the sun, moon, and stars. The entrance into the netherworld was in the land of the setting sun,...

11. 6 MISCELLANY
(pp. 121-143)

Like father, like son. Khufu, a powerful pharaoh of the Fourth Dynasty, like his dad, Sneferu, had a thing for big pyramids. Sneferu made three separate pyramids, including the famed-but-disastrous bent pyramid. The lessons learned were not lost on the next generation. Khufu needed only one main pyramid built correctly the first time. While he used less stone than his father, it was all devoted to one structure, the Great Pyramid of Giza.

This mammoth structure remained the tallest man-made object for more than four thousand years, when it was replaced by the relatively flimsy Eiffel Tower. The pyramid was...

12. 7 BASE-BASED MATHEMATICS
(pp. 144-181)

Stop reading this chapter! For God’s sake, aren’t you listening! I know you’re still reading and I’m beginning to get annoyed. I have half a mind to turn this book around and go home. You’d be left with a hundred or so blank pages and who would be sorry then?

I’m faced with a dilemma. Most authors try to write to please their audience. Up to this point I’ve tried fairly hard to work a little color and humor into a book that might otherwise consist of little but a few dry mathematical procedures. I’ve tried to make the mathematics...

13. 8 JUDGMENT DAY
(pp. 182-208)

We generally consider the grave as our final resting place. For an Egyptian, being placed in a tomb was merely the start of a great journey; the goal was to reach the land of the setting sun. Theka, a form of the deceased’s soul, had a head start since all tombs were built on the western side of the Nile for that very reason. To begin the journey, the ka would open the false door within the tomb. To the living, the door seemed merely painted on the wall, but to the dead, it opened to the underworld. On...

14. PRACTICE SOLUTIONS
(pp. 209-234)

Many Egyptian problems have more than one solution. You should not automatically assume that if your answers don’t look like the following solutions that they are wrong. If you have a calculator, find a decimal approximation for your and my solutions and see if they are the same....

15. INDEX
(pp. 235-237)