All this business about dividing the circumference of circle into 28 units got me wondering about a point that originally occurred to me some time ago. I hope I can get across what I'm on about.

It all started when someone posted a drawing from a Papyrus and overlaid it with some Autocad drawings which he claimed "proved" that the original scribe must have known some fairly sophisticated mathematical concepts. I used a ruler and a compass and reproduced exactly the same drawing with no need for any such knowledge.

So back to the 28 units and a circle. I've found that using a straight edge and a compass I can draw a circle divided into 28 equal segments. The straight edge doesn't even need to be a ruler as I only needed to set up a grid with purely arbitrary units and didn't have to measure anything. I needed to know how to create a right angle but that's well attested for the Old Kingdom. I also needed to know how to bisect an angle but that's easy and can be done purely with the compass or by transferring a distance to the edge of a piece of papyrus and simply folding it in half and transferring it back. So as long as I've got a compass, a straight edge and some papyrus I don't need anything else.

As far as I know there are no surviving compasses from the Old Kingdom but circular disks with clearly marked centring holes and inscribed circles are known from as early as the II Dynasty and some of the stars drawn on the ceiling blocks at Abu Sir have feint circles outlining them and a centre hole which I've seen for myself. So I don't think I've done anything that any Old Kingdom scribe couldn't have done.

So here's the conundrum...

Although I've got a drawing of a circle divided equally into 28 segments I have no way of describing what I've done in terms of Egyptian mathematics. I couldn't even tell anyone else a unit value for each of my 28 segments as I have no way of measuring it or describing that measurement.

I can't tell anyone else what those measurements are without having to resort to modern units and angles in degrees etc.

So as an ancient scribe I've no doubt that I could have left a papyrus for a future archaeologist to find that had a drawing which can't be described or produced using the mathematical calculations available to them. But I didn't need any so it's irrelevant.

So when does evidence from a drawing or structure become evidence of an underlying mathematical knowledge? And when is it just evidence of a scribe with a straight edge and a compass?