One of my own favorite weirdnesses about ancient mathematics is the Egyptian system of fractions. For some reason they confined themselves to unit fractions (1/2, 1/3, 1/4, 1/5, and so on), with the inexplicable exception of 2/3, and all other fractions were expressed as sums of these -- and you weren't allowed to repeat one. So 3/5 was expressed not as 1/5 + 1/5 + 1/5, but as 1/2 + 1/10.

They developed methods of computation with fractions that got the job done but which seem incredibly roundabout to us now.

]]> <p>Posted July 1, 2003 2:55 PM by Scott</p>For example, from my home page

magicdragon.com

if you click on "Timeline"

you get my Encyclopedia of History of Mathematics combined with History of Science Fiction and History of World Literature and History of Science and Technology.

Go to any Century that I cover. For most of them, I am in the top 5 worldwide according to Google, if you enter in Google: "3rd century",

"4th century", "5th century", and so forth. I have biographic and bibliographic data on major authors, philosophers, mathematicians, scientists, and anyone else who interests me. I have also posted the chronology of estimates of "pi" in the Midle East, Japan, China, India, and so forth.

You can read my chronology (including Math) also in "1st Millennium BC", "2nd Millennium BC", "3rd Millennium BC", "4th Millennium BC", "5th Millennium BC", "6th Millennium BC", and "Cosmic History" goes back into anthropology, biological and geological evolution, and cosmology.

We have another interest in common! And 12,000,000 hits per year on my domain shows that lots of other people do, also.

Don't forget that in the Old Testament, a large circular well is described as being "10 cubits" in diamter, and "30 cubits" in circumference, which make pi = 3.000000

As to Babylon, that friendly merger of Akkadian and Sumerian civilizations was amazingly high-tech. Did you know that one family kept as trade secret the process of electroplating, which they used to make jewelry for the King? We have carefully analyzed the crusted remnants of their wet-cell batteries.

Of course, Bablyon's creation myth was that extraterrestrials who breathed water, had space helmets, and lived for centuries came from a star and taught Earthlings about ceramics, metals, and mathematics... but that's another story.

And don't forget Carl Sagan's weird idea in the novel of "Contact" (started as film treatment) that trillions of digits deep in "pi" is a perfect digitized cicture of a circle, sort of a signature of God...

Sorry I've been out of touch for a month or two. Had to file yet another petition for review to the California Supreme Court, against the Hollwood Producers who ripped me off in 1994-1995, and against whom I won a loandmark Supreme Court case in August 2000. Also, I've been giving testimony to the Columbia Accident Investigation Board (there were SF fans who contributed to the Shutle disaster); attending a wedding at CBS studios with reception on "New York Street" outside set near the intersection of Newhart Street and Mary Tyler Moore Avenue, working on 3 appeals including one to save an historic theatre in Pasadena California, and ever so much more.

Bye for now...

]]> <p>Posted July 1, 2003 4:01 PM by Jonathan Vos Post</p>It makes me wonder if the Egyptians had some set of physical counters — like a set of weights or measuring cups. It’s like a Microsoft interview problem, almost: given 1 cup, 1/2 cup, and 1/4 cup measuring cups, plus a tablespoon, how many of them can you get dirty while measuring out 1 3/8 cup of flour?

]]> <p>Posted July 1, 2003 4:03 PM by David Moles</p>And, of course, Egyptian teachers came up with problems that resulted in crazy long fractions as teaching aids.

Egyptian farm taxes were clever. The flood was measured by Nilometers (one still exists at Elphantine) and the farmers paid a set tax based on that mesurment and how much land he tilled. If a farmer worked hard, and had a better harvest because of it, his tax did not increase -- he was allowed to keep the excess as his own. Conversely, if he didn't work hard, and his harvest was less, he still paid the same harvest. There were many records of farmers pleading for relief from that years taxes, citing crop failures that they could not prevent, no matter how diligent.

We got lucky -- we found what was apparently a papyrus roll used in teaching mathematics, the Rhind Mathematical Papyrus. In short, we found a math book. Handy, that.

Mathematical convention is to leave roots only in the numerator of fractions. However, computation often requires the reverse. Ask any numerical analyst how to solve x^2 - 100 x + 1 = 0. The quadratic formula gives

(100 + \sqrt{9996}) / 2 and (100 - \sqrt{9996}) / 2

but the second one leads to horrible inaccuracies. The subtraction loses 4 significant digits. Fortunately,

2 / (100 + \sqrt{9996})

works fine.

Tell your high school teacher (or your kids' teacher).

]]> <p>Posted July 25, 2003 5:21 PM by Eric Jablow</p>