Wednesday, May 14, 2008

Pi and the Great Pyramid

An article or post written by Assem Deif is a professor of mathematics at Cairo University and Misr University for Science and Technology Pi, Phi and the Great Pyramid Assem Deif investigates the values -- not the symbols -- of the last of the Wonders of the Ancient World Al-Ahram Weekly Online March 27 - April 2, 2008 Issue No. 890 We can forget all the ideas crediting Atlanteans or space aliens with building the Great Pyramid of Giza, and instead imagine ourselves travelling back in time in H G Wells's time machine to try and work out not how the ancient Egyptians built this enormous edifice, because this lies beyond our present understanding, but rather what we can best judge to be its most appropriate proportions. Then, however, there were no electronic calculators, only ropes and rods. Constructing right angles at the four corners of a pyramid is easy. To do it, history tells us that the Egyptians were aware of the ratios 3:4:5 as the side-lengths of a right-angle triangle. Many old kingdom pyramids adhere to these ratios. The Egyptians also knew a rough value of Pi (the value, not the symbol) as the ratio between the circumference of any circle and its diameter. They worked out that 3 _ is less than Pi, and Pi is less than 3 1/7, i.e. Pi lies between the rational number 22/7 and the Babylonian value. This can be done by constructing a circle of diameter AB and laying the latter on its circumference, starting from A, once until C then D then E, to conclude that Pi is greater than 3. The remaining part EA from the circumference is laid down again on the diameter AB, so seven times EA is less than AB which in turn is less than eight times EA, or EA/AB is greater than 1/8 and less than 1/7. Rest of article. Leave it to a professor of mathematics to botch the explanation! I was drifting off into sleep just before I copied and posted the last paragraph here - snore... There has to be a better way of explaining the mathematical wonders of the pyramids and Pi, etc. For instance, WHY does he say it's easy to figure out how to do a 90 degree right angle by using the 3/4/5 method? We actually have NO FRICKING IDEA how the ancient Egyptians came up with this formula, all we know is that they used it to lay out square foundations and that it WORKED! The 3/4/5 method of laying out a 90 degree ("right") triangle was "proven" - much later - by Pythagoras and his "school" of followers in Greece. So, the ancient Egyptians knew it worked, but how did they figure it out to begin with? We don't know - we don't have a clue. Mathematics cannot speak to that quintessimal moment of discovery - when someone along the Nile River figured it out - had that "EUREKA" moment, some 5,000 years ago. For those of you (including yours truly, who made it all the way through college advanced mathematics without having a clue - and what does THAT say about the state of universities back in the 1980's, heh?) one of the few things I remember is that mathematical theory says that a RIGHT angle, that is, an angle that measures 90 degrees (1/4 of a full circle, which is 360 degrees), can be found by utilizing a triangle with the following formula: sides A, B and C of a triangle, with "A" being 3 "units" (whatever your units of measurement happen to be), side "B" being 4 units, and side "C" being five units. I'm sure I'm missing something here, LOL! Now you know why I'm not a mathematician. Using the classic Egyptian formula for figuring out how to make a square (90 degrees) corner of that triangle, the Sheshat Goddess (actually, a priestess representing Sheshat) had a length of rope knotted into twelve equal lengths. A stake was driven into the ground by her consort, the Anubis priest, at a predetermined sacred spot. The Sheshat priestess then looped the rope over the stake such that 3 knots formed one leg of a triangle, which was then staked, and 4 knots formed a second leg of the triangle, also staked. The remaining 5 knots linked together the two sides legs of the triangle previously staked out with the knotted rope, forming the - what I believe is called the hypotenus of the 90 degree right triangle. About all I remember from geometry is 3 squared (9) PLUS 4 squared (16), EQUALS 5 squared (25) - but that was just a Greek way of saying lay out a square corner by doing this...