By Hossam M.K. Aboulfotouh
ABSTRACT
For nearly a century there is an ongoing debate about, have the ancient Egyptians known any case of the Pythagorean Theorem and that the triangle 3-4-5 is right-angled? According to the opinions of most scholars, there is no written evidence regarding this dispute. Hence, this paper shows the written evidence in a prob-lem on land survey in the so-called Rhind Mathematical Papyrus-RMP of circa 1550BC, which has been sep-arated by the early scholars into two problems: RMP#53 and RMP#54. The paper shows that RMP#53-54 is one problem on reckoning the dimensions of a triangular plot of land with sides 6-8-10 and its sections, where the triangle’s height is a radius of a circular horizon that increases by adding one-tenth of the trian-gle’s hypotenuse. Besides, it shows that the reckonings of RMP#55 are based on the same triangle sketch of RMP#53-54. The paper proves that the ancient Egyptians knew this triangle almost thousand years before the days of Pythagoras. The paper also shows that the ancient Egyptians did not only use the unit fractions but have also used complex fractions.
