
Re: Ariadne's thread
Posted:
Nov 22, 2011 3:05 AM


One Venus year is longer than 583 days but slightly shorter than 584 days:
583/1 (plus 584/1) 1167/2 1751/3 2335/4 2919/5 3503/6 4087/7 4671/8 5255/9 5833/10 6423/11 7007/12
One Mars year is longer than 779 days but slightly shorter than 780 days:
779/1 (plus 780/1) 1559/2 2339/3 3119/4 3899/5 4679/6 5459/7 6239/8 7019/9 7799/10 8579/11 9359/12 10139/13 10919/14 11699/15 ... 17159/22
If the Maya astronomers made very careful observations over long periods of time, and if they were able to establish that 12 Venus years are slightly longer than 7007 days, and 15 Mars years slightly longer than 11699 days, they could have drawn up a further pair of excellent sequences:
584/1 (plus 7007/12 7591/13 14598/25 21605/37 28612/49 35619/61
780/1 (plus 11699/15) 12479/16 24178/31 35877/46 47576/61
61 Venus years are 137 Tzolkin minus 1 day 61 Mars years are 183 Tzolkin minus 4 days 46 Mars years are 138 Tzolkin minus 3 days 31 Mars years are 93 Tzolkin minus 2 days 16 Mars years are 48 Tzolkin minus 1 day
The Babylonians knew a Mars year of 12,59;57,17 days, 779 days 22 hours 54 minutes 48 seconds. If they found this value by means of number sequences then like this:
779/1 (plus 780/1) 1559/2 ... 17159/22
780/1 = 10920/14
10920/14 (plus 17159/22) ... 2807837/3600
2807837/3600 = 12,59;57,17
They would have chosen too big a valuie from the first sequence and been seduced by the divisor 3600 in the second sequence that goes along with the Babylonian number system.
A Venus year lasts 583.92 days, a Mars year 779.936 days. The Maya astronomers counted 584 days for a Venus year, and, I assume, 780 days or 3 Tzolkin for a Mars year. However, in their most advanced calculations, they could also have derived the above results, pleasing in their Tzolkin form.
Next time: saving the honor of the Babylonian mathematicians

