Egyptian Geometry and Other Challenges

Rhind papyrus

Would you like to study “the knowledge of all existing things and all obscure secrets”? That is how Scribe Ahmose (also translated Ahmes) described his mathematical papyrus. Ahmose’s masterpiece is now called the Rhind Papyrus, after Alexander Henry Rhind, a Scotsman who was one of the first archaeologists to make meticulous records of his excavations (rather than simply hunting for treasures). Rhind purchased the papyrus from an antiquities dealer in Luxor, Egypt, in 1858.

Ahmose’s writing included a huge table of fractions as well as story problems, geometry, algebra, and accounting. Can you solve any of Scribe Ahmose’s problems?

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Another Egyptian Math Puzzle

Pyramids clip artI have one last puzzle for those of you who are following my Alexandria Jones series on hieroglyphic math and the Egyptian scribe’s method of multiplication by doubling. Here is the “teaser” problem from the cover of the Sept./Oct.1998 issue of my newsletter:

One more Egyptian math puzzle (pdf, 53KB)

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Egyptian Math Puzzles

Pyramids clip artWhat we know about ancient Egyptian mathematics comes primarily from two papyri, the first one written around 1850 BC. Moscow papyrus problem 14This is called the Moscow papyrus, because it now belongs to Moscow’s Pushkin Museum of Fine Arts. The scroll contains 25 problems, mostly practical examples of various calculations. Problem 14, which finds the volume of a frustrum (a pyramid with its top cut off), is often cited by mathematicians as the most impressive Egyptian pyramid of all.

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Alex’s Puzzling Papyrus

(In the last episode, Dr. Fibonacci Jones discovered a torn scrap of papyrus, covered with hieroglyphic numbers. He promised to teach his daughter, Alexandria, how the ancient Egyptian scribes worked multiplication problems using only the times-two table.)

Alexandria JonesBack at their tent, Dr. Jones handed the papyrus scrap to Alexandria. “What do you see?” he asked.

“Well, there are two columns of numbers,” Alex said. “Let me write them down.” She got a piece of notebook paper and translated the hieroglyphs. Papyrus fragment

Click on the image for a larger view. Translate the numbers for yourself before reading on. If you need help, read Egyptian Math in Hieroglyphs.

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Egyptian Math in Hieroglyphs

Pyramids clip artEgyptians wrote in hieroglyphs, a type of picture writing, and in hieratics, which were like a cursive form of hieroglyphs.

Hieroglyphs came first. They were carved in the stone walls of temples and tombs, written on monuments, and used to decorate furniture. But they were a nuisance for scribes, who simplified the pictures and slurred some lines together when they wrote in ink on paper-like papyrus. This hieratic writing — like some people’s cursive today — can be hard to read, so we are only using hieroglyphic numbers on this blog.

Download this page from my old newsletter, and try your hand at translating some Egyptian hieroglyphs:

Then try writing some hieroglyphic calculations of your own.

Edited to add: The answers to these puzzles (and more) are now posted here.

To Be Continued…

Read all the posts from the September/October 1998 issue of my Mathematical Adventures of Alexandria Jones newsletter.

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The Mysterious Temporal Freeze

Pyramids clip artAlexandria Jones stepped into the huge tent that protected her father’s excavation site from the desert winds. She laughed to herself. It was like walking into a circus.

She knelt down to whisper in the ear of her faithful dog Ramus. “In this ring, grad students carefully brush away another layer of sand. In the next ring, the artist sketches every piece as it is found.” She waved her arm. “And over there, our flashiest attraction — drum roll, please — the photographers shoot each shard of pottery from every possible angle. But where is the Master of Ceremonies?”

Alex and Rammy found Professor Jones near the back of the tent, talking to another student. While she waited for her dad, she looked through an assortment of numbered artifacts that were ready to be packed and sent to the museum.

Continue reading The Mysterious Temporal Freeze