Ancient Egypt Math - Part One: Numerals, Hieroglyphics and Hieratic

Ancient Egypt Math - Part One: Numerals, Hieroglyphics and HieraticView of the desert camels and the Pyramids.

An overview on Ancient Egypt and Historical evidence of Mathematics in the Nile Valley

Mystery is probably the right word to define Ancient Egypt. Have you ever heard of the theory that Egyptians and aliens once communicated? If you are a believer, then you have probably also heard the theory about ancient Egyptians and Mayans contacting each other from really long distances. You might be right, because we still have little knowledge about ancient Egyptians. This is because we’re talking about a civilization that lived so many years ago, that makes it difficult to deduct more than a theory of how they actually lived. Even the birth date of the first Egyptian Dynasty has a margin of a mere 400 years! Anyway, we can probably declare this birth between 3400 and 3000 BC along with the unification of the Upper and Lower Egypt made by Menes - or Narmer, we can’t even be sure of this!

Narmer Palette Menes or Narmer killing an enemy Museum of CairoNarmer, maybe Menes, represented while killing an enemy in the Narmer Palette, Museum of Egyptian Antiquities of Cairo

Ancient egyptians started writing and leaving behind documents and monuments, but there are a very few examples available today. These artifacts are the only information we have regarding their way of living, seeing their world and the way they calculated math! We know for sure that they used astronomical timing and orientation, since most of the important buildings have a logical alignment and they used a 365 day calendar divided in 12 months!

Kom Ombo Temple CalendarAn Egyptian calendar at the Temple of Kom Ombo in Aswan Governorate, Upper Egypt

Thanks to some really important finds, such as the Moscow Mathematical Papyrus, the Rhind Mathematical Papyrus and many others we can understand some of the knowledge they had and how they used it. Unfortunately, we only found a small amount of these antiquities, so most of the theories we have can’t be proven.

It is notable how this evidence shows us that their way to calculate was closer to ancient Chinese math than ours and isolated to the Nile area!

Moscow Mathematical Papyrus Pushkin State Museum of Fine Arts A problem shown on the Moscow Mathematical Papyrus, Pushkin State Museum of Fine Arts, Moscow

Decimal Numeral System and Math Signatures

Let’s have a closer look at their math: first we have to understand that at the time ancient Egypt developed their number system, there were a lot of different ways to count around the globe. For example ancient Babylonian used a sexagesimal number system, like our way to count minutes and seconds, while ancient Egyptians used a decimal system, so with base-10 number system like us. Sumerians used multiplication tables, while the inhabitants of the Nile valley understood how to calculate linear algebra and quadratic equations, using the power of 2 to solve complex multiplication.

The writing they used to represent numbers were similar to ancient Romans numerals, but with hieroglyphic alphabet instead of the latin alphabet, and without dividing the decimals by five. For each power of ten they used a different symbol: for the units they used a staff, for the tens a hobble, the hundreds was a coiled rope, the thousands a lotus flower, the ten thousands a pointing finger, the hundreds of thousands a frog, and for the millions a god in adoration. Every symbol was represented many times as needed, so 9 equals nine staffs, 80 equals eight hobbles and so on. The number 999 needed 3 different hieroglyphics each repeated nine times, for a total of 27 signs!

You may think this was a uncomfortable way to write numbers, so did they! That’s why ancient Egyptians invented another way to write numbers, used mostly for documents, using the hieratic alphabet. This was the first numerical system that needed three signs to write complex numbers such as 999. This happened more than one thousand years before Indians used a similar system, and Europe needed another thousand years before adopting the Arabic numerals!

hieroglyphs and hieratic scheduleIn this schedule we can compare some hieroglyphic and hieratic numbers

You may want to ask me how they actually used those signs. How could they use powers of two and multiply? If you think they could use hieroglyphics in column method multiplication, you’re far away from reality! With some patience, I’m going to post the answer to your questions! Stay tuned next week for the second part of Egyptian math on the Atellani Blog, you’re going to calculate like an ancient Egyptian!

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