I often wonder when I see some of the threads here about the possible role of "trial and error" in Ancient Egyptian maths.

Many of the surviving mathematical papyri don't really give any instruction as such but are a list of pre-done calculations that can be used as a "look up table". It doesn't suggest that many scribes who might be drawing/calculating etc had a particularly good ability at maths.

But they could draw and grids are everywhere in Egyptian tombs etc. Scribes drawing boards have survived with carefully drawn grids. Drawings in tombs are often drafted in red and then a final corrected line is overlaid in black. So there's no reason why a mathematical drawing couldn't be produced in several increasingly accurate steps.

Some time ago I was trying to produce a double spiral feature in 3D for a reconstruction of an Egyptian object. It was a nightmare as I tried to work out how to enter the data. It made me wonder how an Egyptian could possibly have worked it out. So I did it in a more practical way in the form of a cardboard tube with a piece of string wrapped around it. In a few minutes of adjusting the string I had the shape I wanted without the faintest idea of the maths involved. All it took was an initial attempt to get it right and then a gradual adjusting until it was correct. I could have transferred the information by measuring a series of points.

So I produced a really complicated shape with no maths at all. But I'm sure that the number crunchers would have had a field day if the object turned up and could probably find pi, phi and the orbit of Mars if they wanted to.

Dieter Arnold has drawings of a method of producing a right angle that only requires an approximately accurate set-square.



You simply mark the two points produced by flipping the set-square and half the distance between them. You can do that by marking the distance on a piece of papyrus and folding it in half. So an accurate right angle produced with an inaccurate set-square and not even a ruler.

You could measure the 28 divisions around a circumference by similar methods. Draw a circle and lay a piece of string around the circumference. Then divide the string into 28 lengths by repeatedly halving it. Or step around the circumference with something like a pair of dividers and keep adjusting the distance until it fits. It only takes a few minutes. But if you're stuck in front of a computer this sort of practical exercise isn't going to occur to you but the Ancient scribe had the basic tools immediately to hand.

Just because we'd reach for a ruler or calculator today doesn't mean an Ancient scribe would have done the same and just because we think we can see evidence of complicated constructions doesn't mean that the Ancient scribe was aware of any such thing.





Edited 1 time(s). Last edit at 11/23/2009 03:45AM by Hermione.