“9+16=25” (Egyptian triangle)

010

Canvas on cardboard, 50х70 cm (19.7”x23.6”)

Oil

Arithmism

Kyiv, 2012

Egyptian triangle is the most simple right-angled triangle having whole-number values for legs, hypothenuse and square. The ratio of its sides is 3:4:5. It is a good demonstration of Pifagorean theoreme: indeed, the squares on the hypothenuse (25) is obviously equal to the sum of the areas of the two squares on the legs (9 and 16). It is lso believed that this acquintance with this very triangle inspired Pifagor to pur forward his famous theoreme. It must be noted, however, that historians who normally are ignorant of any science other than history, especially if mathematics is concerned, might be wrong.

One way or another, there are many indications that Pifagorean theoreme in general and Egyptian triangle in particular had been well-knowd nd widely used long before Pifagor and far away from Egypt – in Mesopotamia, in Indus valley, and in ancient China. Tree of human knowledge seems to be deeply rooted in practice. No sooner than a need to erect buildings and structures emerged, then man by empiricicm came to understand the crusial importance of right angles. But how to mark off right angle if there are no surveying instruments?

It does reveal that the answer is quite simple. Take a rope and divide it into 12 equal intervals. Choose the part consisting of 5 interwals so that this part is situated just between the other two ones equal to 3 and 4. Straighten and fix it with two stakes on a plain surface. Then strain the ends and make them meet to form a triagle – right triangle, Egyptian...

«Do it the way it goes». Famous ancient Egyptian proverb, still extant in our days. Normaly we think of it as just of wise consideration: «if it works this way, then it is right». But we should remember cultural and historical context of ancient Egypt. All the works were managed by priests who were members of  closed caste of watchers of ancient knowledge. Thus, «do it the way it goes» in Egyprian context must have meant «do it and do not ask unnecessary questions». Which means that the priests knew not only how to do it, but also why, and this knowledge was concealed from exoteric profanes.