Egyptian Mathematics and the Greeks. by Alexander Badawy Ⲡⲓϩⲓⲥⲃ ⲛⲣⲉⲙⲛⲭⲏⲙⲓ ⲛⲉⲙ ⲛⲓⲟⲩⲉⲓⲛⲓⲛ ϧⲁ ⲉⲗⲝⲏⲛⲧⲉⲣ ⲃⲉⲧⲉⲟⲩⲓ

The GREEKS report unanimously that Greek science was derived from Egypt. Traveling to Egypt to seek information from the priests became a traditional episode in the life of Greek scholars and philosophers. Orpheus, Homer, Solon, and Thales studied geometry from the Egyptians and among other things introduced the 3:4:5 triangle to Greece.

Thales seems to have applied the empirical rule for finding the taper of a pyramid, already known to the scribe, Ahmose, who wrote the Rhind Mathematical Papyrus in the middle kingdom, to Practical Problems. .

The Egyptian priests, however, were very reticent about teaching these foreign students and those of one temple referred the newcomers to their colleagues at another Temple, on the fallacious pretext that the latter were earlier. According to Porphyry 233-304, Pythagoras was received by king Amasis of Egypt and had to shift from the temple of Heliopolis to that of Memphis, and finally to Thebes; he spent twenty-two years in these temples. He sought mainly to study geometry, for: ‘one finds among the Egyptians many problems of geometry… All the theorems of lines originate from there’ (Iamblichus). He is said to be the first to carry arithmetic beyond the needs of commerce (Aristoxenus), and from a remark from Aristotle we may infer that his procedure was that of numerical symbolism, where numbers were represented by dots in symmetrical patterns, such as the tetrakis, a triangle of four representing the number ten.

This method suggests geometrical problems and the dots representing the Pebbles which Pythagoras used in his demonstrations were ‘boundary stones’ (hence the word ‘calculation’) while the area marked was the field. The word hypotenuse is the ‘cord stretching over against’ surely the cord of the harpedonapate. He studied proportions, namely the most complicated or harmonic ones. Other Greek scholars who studied in Egypt were Oenopides and Democritus. The latter spent five years with the priests to learn of matters dealing with astronomy and geometry. He boasts: ‘I have listened to many learned men, but no one has yet surpassed me in the construction of figures out of lines accompanied with demonstration, not even the Egyptian harpedonaptae, as they call them ’

Strabo reports that he was shown the houses occupied by Plato and Eudoxus. The latter lived thirteen years among the priests at Heliopolis. Plato considered the Egyptians a businesslike people. Aristotle speaks of the origin of mathematics in Egypt. Euclid lived in Alexandria (Third century B.C.) where he founded a school of mathematics. He might have had training at Athens as a Platonist. His method was not Pythagorean but represented numbers by lines.

Both Herodotus (II. 109) and Strabo (XVII.3) ascribe the origin of geometry to the Egyptians’ methods of measuring cultivated land to determine the boundaries.

Whatever the reliability of all these reports maybe it is evident that both arithmetic and geometric disciplines, as further developed by Pythagoras and Euclid, must have originated with Egyptian disciplines. My study of architectural design has shown that harmonic proportions could be reached or at least or at least expressed by the summation series of Fibonacci or by geometric methods based on the use of the proportional 8:5 triangle. Whether the Greeks

succeeded in learning about these harmonic methods from the Egyptian and later passed them on to European architecture as the ‘analogy’ and symmetry’ of Vitruvius, is a matter to be studied.
Article from: Ancient Egyptian architectural design, a study of the Harmonic System. Alexander Badawy. P.49