
Re: Ariadne's thread
Posted:
Nov 21, 2011 2:55 AM


A period of 260 days was a Tzolkin. 3 Tzolkin or 780 days are a rounded Mars year. Add one twentieth and you get 819 days, a strange period in the Maya calendar. It may have served geometrical and architectonical purposes. Let a rectangle measure 780 by 819 units and the diagonal measures exactly 1131 units, while 1131 lunations are 33399.096... or practically 33399 days.
A period of 360 days was a Tun. 360 lunations are 10631,012... or practically 10631 days. If the diameter of a circle measures 360 units, the circumference measures practically 1131 units, implicit value of pi 377/120.
4/1 (plus 3/1) 7/2 10/3 13/4 16/5 19/6 22/7 25/8
3/1 (plus 22/7) 25/8 47/15 69/22 ... 377/120
15 and 17 lunations counted in the 30 29 30 29 30 29 30 ... mode yield 443 and 502 lunations respectively. 17 15 17 15 17 lunations yield 502 945 1447 1890 2392 days for 17 32 49 64 81 lunations.
502/17 (plus 1447/49) ... 10631/360 ... 25101/850
360 lunations are practically 10631 days. Add 502 days for 17 more lunations and you get 11133 days for 377 lunations. Multiply these numbers by a factor of 3 and you get 33399 days for 1131 lunations.
The Maya were infatuated with time. I could imagine a terrace measuring 780 by 819 units, diagonal 1131 units representing as many lunations, or the Sun Pyramid at Teohituacan as house of time or 'bundle of time':
units 27.1 centimeters ideal base 819 (!) by 826 units 826 Tzolkin are 588 years periphery base 3290 units 3290 lunations are 266 years ideal height 235 units 235 lunations are 19 years
Use a grid of rectangles to measure out the base, 13 x 13 rectangles 60 by 63, diagonal 87, yielding the rectangle 780 by 819, diagonal 1131, and 13 rectangles 46 by 63, diagonal 78.006... or practically 78, yielding the rectangle 46 by 819, together the base 819 by 826, periphery 3290. If you proceed carefully, always checking on the diagonals, you don't have to measures out the whole area, a 'frame' of rectangles will do, allowing to integrate a naturally grown hill that will contribute to the pyramid's volume and safe a lot of work.
Next time: Venus and Mars
Milo, periods of 135 and 270 lunations make sense as one third and two thirds of the 405lunation period, practically 11960 days (5 x 81 lunations of 2392 days as explained above in the line of 17 32 49 64 81 l). If I came across a calendar of 135 or 270 lunations I'd try to reformulate it on the basis of 405 lunations.

