The right triangle Petrie was referring to (A Season in Egypt, p. 27) is/was a 4.9-5-7 right triangle, which when multiplied by a factor of 10 becomes a 49-50-70 right triangle, and when multiplied by a factor of 20 becomes a 98-100-140 right triangle. The tangent of the associated slope is = .98, and hence delivers an angle of almost exactly 44*26', and so not the 44*34'40" angle stated by Petrie. (Why or how he made this error I can only guess.)

The Red Pyramid gives the appearance of having been designed to utilize a number of true, and very nearly true, triples - of the sort now labeled as "Pythagorean" triples. I have termed these as being "empirical" triples, in that I do not believe the AE understood the "Pythagorean" theorem as such, but did have a well explored empirical understanding of which right angle lengths appeared to provide a right triangle whose sides seemed for all intents and purposes to each be equal to a whole number of units - such as, for instance, the 49-50-70 right triangle. I see no need to suppose that they suspected that a "Pythagorean Theorem" equality even existed. Much of their approach was based on specific empirical understandings, and not on more rigorous, and general, theoretical formulations.

Lee Cooper