To all:

For the past several days it has been discussed how the AE may not have understood the numerical value of the ratio between a diameter and circumference of a circle. To affirm this belief, mathematicians use problem #50 of the Rhind Papyrus as an example.

I was asked by MJ to review this problem and see for myself that the evidence given supports the claim.

My ability to read hieroglyphs is stunningly sad...at best, therefore I must depend on others and their translated concepts/beliefs of what these symbols represent. That in itself has been an issue within the structure of this mathematical problem.

One site explains that it is the surface area of half a basket with diameter of 4-1/2 setat...actually it is the radius that measures 4-1/2...we'll call it a typo for argument sake.

Another site explains that it is not a round "field" because 'ht can only mean "land"...no mention of a basket !

These are completely irrelevant points, but apparently very important to those studying these writing.

That being said then I will continue on with problem #50.

A long quote that "must" be read to understand where this topic will lead us to [www-groups.dcs.st-and.ac.uk]

“...As a final look at the Rhind papyrus let us give the solution to Problem 50. A round field has diameter 9 khet. What is its area? Here is the solution as given by Ahmes.

Take away 1/9 of the diameter, namely 1; the remainder is 8. Multiply 8 times 8; it makes 64. Therefore it contains 64 setat of land.
Do it thus:
1 9
1/9 1
this taken away leaves 8
1 8
2 16
4 32
8 64
Its area is 64 setat.

Notice that the solution is equivalent to taking [pi]; = 4(8/9)2 = 3.1605. This is a remarkable result if one considers the date at which this approximation must have been discovered. The intriguing question is raised as to how such a discovery might have been made. Although we have no way of ever knowing this with certainty, several interesting conjectures have been suggested. In [25] Gerdes gives three ideas which might have led the Egyptians to this result. Two such conjectures suggested in [25] concern African crafts where a snake curve and a set of equidistant concentric rings are often seen. These two geometric designs are widespread in Africa and Gerdes shows how these could have led to a formula for the area of a circle. The third conjecture in [25] relates to a board game "mancala" which was popular throughout Africa and ancient Egypt. The game involves comparing small circles with larger circles and may have provided the motivation for the area formula...”


And now...a comparative problem of Clive's #1

There is a temperature scale named "C" that divides the freezing to boiling point of water into 100 parts. There is a second temperature scale "F" that divided the same range into 180 parts.
The freezing point of scale C is 0
The freezing point of F is 32.
At what temperature will F = C?

That is the answer to problem #50...absolutely nothing to do with pi...!

Best.
Clive