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The Egyptians have a legend that the end of Osiris's life came on the seventeenth of the month, on which day it is quite evident to the eye that the period of the full moon is over Because of this the Pythagoreans call this day "the Barrier," and utterly abominate this number. For the number seventeen, coming in between the square sixteen and the oblong rectangle eighteen, which, as it happens, are the only plane figures that have their perimeters equal their areas, bars them off from each other and disjoins them, and breaks up the ratio of eight to eight and an eighth by its division into unequal intervals
More generally, 16 and 18 represent solutions (x=4, y=4) and (x=3, y=6) of the hyperbolic equation
xy = 2x + 2y
which in modern terms has an infinity of solutions; Plutarch is saying that (x=4, y=4), (x=3, y=6), and (x=6, y=3) are the only integral solutions. To his positive solutions we would add today three more, at (x=0, y=0), (x=1, y=-2) and (x=-2, y=1): they are symmetrical to Plutarch's set with respect to the two asymptotes, and in terms of geometry represent one null and two imaginary rectangles. In theory, to find any others we are suddenly transported into the very difficult realm of Diophantine equations; but that these are the only five integral solutions can be seen instantly by inspecting the graph. Plutarch's square, and one of his two symmetrical rectangles, are shade
Originally posted by Kantzveldt
When you combine this with the enigmatic carved features interspersed amongst the natural bedrock, which are suggested by some as greatly pre-dating the Inca, due to the extent of the weathering seen upon them and their scattered and fragmentary remnants, then clearly that was the culture teaching advanced irrigation, as the model they left demonstrates...the locals always maintained the oldest structures, those of the highest quality, were of the Gods
Perhaps we observe the principle of that which is above will naturally descend...
Thanks for the interest and replies