The numbers 360 and 400 were used in degrees and grads because they

were equally divisible by so many different small numbers:

such as 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, ............ etc.

Time is also divisible by small numbers ( 24 hours, 12 hours, 60 minutes

, 60 seconds ), as was degrees, minutes, and seconds of ARC.

These were very practical consideration prior to calculators and computers.

They still serve the practical consideration of standardization of a method

of doing something like surveying and telling time.

Michael, thank you for your comments. To the Mayans on level three of the Dresden and Madrid, considering all 120 LCMs of 260, 360, 364, 365, 584, 585, and 780 by unique combinations: LCM (a,b), LCM ( a, b, c), LCM (a, b, c, d), LCM (b, c, d, e,), LCM(a, b, c, d, e , f), and LCM (a, b, c, d, e, f, g) computes 86 in multiples of 18, 980 days = 1 calendar round (CR) per:

1-CR (1), 2-CR (2), 3-CR (2), 6-CR (4), 7-CR (2), 9-CR (3), 14-CR (4), 18-CR (28), 21-CR (2), 42-CR (4), 63-CR (4) and 126-CR (30)

attests to Mayan calendar round LCM math.

18,980 / 365.26 = 51.963 years...... 18,980 / 365 = 52 years.

I suspect, but have not been able to prove, that the Mayan calendar is based on the

repeated astronomical alignments of the outer planets relative to one another,

and the Mayan observers.

Long term climate changes should be based on the effect the alignment of the

planets have on the Sun and thus effect Solar energy output, which in turn

effects climate patterns, rainfall patterns, and crop yields.

If the Larger planets all line up on one side the pull on the Sun is greater,

and the Solar output should also be greater. if the planets are all dispersed at

90 degrees or 120 degrees apart the pull on the Sun will be more even, and the

result will be a quieter Sun, less Solar output and cooler Earth temperatures,

fewer Sun spots.

It is the cooler Earth temperatures that are the problem as they result in longer winters, and shorter summers, and crop failures which result in human warfare

over food, or the lack of it.

The orbital periods of the four Gas Giants and the periodic alignments once every few hundred years should determine Solar " Global " Maximum and Minimum outputs

of energy in a multi-hundred pattern.

The periods of the inner planets alignments occur too often, and their masses

are too puny to effect the Sun. The Outer planets are far more massive, and their

mutual alignments occur less often, but have a larger effect for a longer duration

of several years.

This could all be correlated to tree ring data ( annual precipitation ) in

semi - arid locations.

For example China's Dynasties all lasted until the crops failed for several

years in a row, then the Dynasties were replaced.

Michael,

To my eyes, global warming had nothing to do with six planets and our moon lined up on Feb. 1, 1951 BCE ... as seen from China. Anyone can see the event on programs like Stellarium:

Advanced cultures around the globe created abstract mathematics to model the cycles of planets, and other astronomical events. Several cultures, including our own, have predicted planetary cycles and events in exacting ways. Chinese math, for example, modeled a ”string of pearls” event such that planetary alignments focused on Feb. 1, 1951 BCE and other times when fewer planets aligned. Chinese mathematical astronomers birthed the Chinese remainder theorem a generalized indeterminate equation method aligned calendars and predicted astronomical events including solar and lunar eclipses.

This paper introduces LCM math that was independently developed by Mayans in base 13 and base 20. Mayans aligned calendars in n-calendar rounds by LCM tests in multiple planetary and lunar cycles. The modular math tests followed implicit features of CRT-like math paired, tripled and quadrupled 117, 260, 360, 365, 584, 585, and 780 cycles, and other planetary cycles and groupings scaled to n-calendar rounds(CR). One CR = 18980 days.

The linear math followed the sun, equinoxes and solstices across the horizon that began at the summer equinox. Nominal planetary cycles were often alighned in terms of solar and lunar equinoxes.

In 2012 four super-numbers have been dated to 419 AD. The long count dates were painted on a wall near Tikal, Guatemala reports the LCM (584, 585):

1. 341640 = 2920(117) = 1312(260) = 949(360) = 936(365)= 585(584) = 439(780)= 18(18980) = 9(37960) = 6(56940) appears 6-times as LCM (a, b, c) and 5-times as LCM (a, b, c, d).

In 2012 Aveni, et al, data reported the remaining super-numbers:

2. 1195740 = 10220(117) = 4599(260) = 3285(364)= 3276(365)= 2044(585)= 1533(780) = 63(18940) = 21(56940) meant LCM (260, 364, 365, 585) = LCM (364, 365, 585,780).

3. 1765140 = 6789(260) = 4836(365) = 2263(780)= 93(18980) = 31(56940)

4. 2448420 = 9417(260) = 6708(365) = 3139(780) = 129(18980)= 43(56940)

The linear door to Mayan time encoded four long count dates as least common multiple (LCM)s. Related classes of quotients and remainder appeared 800 years later in Dresden Codex almanacs.

smaller grouping of planets and our moon align in about 200 years a par, as discussed by ,,, as Maya math also anticipated ,,,

simply stated ... so anyone can confirm the LCM math ..seven frequently used Mayan calendrical elements were approximated by lunar and planetary periods: 260; 360; 364; 365; 584; 585 and 780. To resolve the variety of least common multiples of 2 or more of these periods, we must consider all possible non repeating combinations. For 2 elements there are 21 possible, for 3 there are 35, for 4 there are 35 again, for 5 there are 21, for 6 there are 7 and for seven there's only one [LCM = 2,391,480 = 126 *18980] . Total LCM options from the unique sets above = 21+35+35+21+7+1=120 = 5! How many of the 120 possible are divisible by a calendar round of 18,980 days? Use the list button at the bottom to make the LCM analysis more efficient. Use the LCM calculator to make this easier. http://www.alcula.com/calculators/math/lcm/

18,980 / 120 = 158.1666667

( 3 x7) + (5x7) + (5x7) + (3x7) + ( 1 x 7 ) +1 = 120 = 5!

( 17 x 7 ) + 1 = 120 = 5!

if you express this as weeks it is 17 weeks

A year is thus 17 + 17 + 17 +1 = 52 weeks

52 x 7 = 364 days Years are ( 364 + 1) = 365 days except when we add a

day every fourth year and skip adding it every ( ? ) hundred years. This is

far newer than Mayan times.

18980 days / 365 days = 52 Years

and

3 ( 17 weeks ) + 1 day = 52 Weeks / 1 year

780 / 260 = 3

If I remember right LCM stands for Lowest Common Multiple ( Multiplier )

the 360, the 364 and the 365 are then earth days

18980 / 260 = 73

18980 / 360 = 52.72222222

18980 / 364 = 52.14285714

18980 / 365 = 52

18980 / 584 = 32.5

18980 / 585 = 32.4444444

18980 / 780 = 24.3333333

The to that divide evenly in 18980 are 260 and 365

If we double the 18980 to 37960 then three numbers

divide evenly: 260, 365, and 584

37960 = 260 (146) = 365 (104) = 584 (65)

If we tripple the 18980 to 56940 the three numbers

again divide evenly: 260, 365, and 780

56940 = 260 ( 219) = 365 (156) = 780 (73)

This is :

56940 = 260 ( 73 x 3) = 365 ( 52 x2 ) = 780 ( 73 x 1 )

Notice that any number that has N.14285714 is

actually N plus 1/7 th because 1/7 th is 0.142857,142857,142857,........

The comas added for emphasis to show the repeating pattern.

Notice that 364 is actually 52 and 1/7 th

so that 18980 x 7 = 132860

132860 / 364 = 365

132860 days / 365 days per year = 364 years

Any way, a few eons ago when I worked Archaeology,

I remember their temples were rebuilt every 52 years,

by covering the old temple up with a new stone covering.

Since 2012 was supposedly the end of a super cycle, you

can subtract 52 from it repeatedly to find the years that

rulers lived, and temples were rebuilt.

2012 , 1960, 1908, 1856, 1804, 1752, 1700, 1648, 1596, 1544

1492, 1440, 1388, 1336, 1284, 1232, 1180, 1128, 1076, 1024

972, 920, 868, 816, 764, 712, 660, 608, 556, 504, 452, 400,

384, 296, 244, 192, 140, 88, 36, -16, -68, -120, -172, -224, -276,

-328, -276, -328, -380, -432, -484, -536, -588, -640, -692, -744,

-796, -848, -900, -952, -1004, -1056, -1108, -1160, -1212, -1264,

-1316, -1368, -1420, -1472, -1524, -1576, -1528, -1680, -1732, -1784,

That is 73 cycles of 52 years = 1,385, 540 days = 73 x 52 x 365

That is -1784 = (73 x 52) = -1784 + 3796 = 2012

73 x 52 = 3796 and 3796 / 364 = 10.42857143 which is

3/7 = 0.428571,428571,428571.......

so 10.42857143 is actually 10 and 3/7

we can explore the repetitive cycles by finding sevenths:

1/7 = 0.142857, 142857, 142857......

2/7 = 0.285714, 285714, 285714,..........

3/7 = 0.428571 , 428571 ,428571,.....

4/7 = 0.571428, 571428, 571428,...

5/7 = 0.714285, 714285, 714285,.....

6/7 = 0.857142, 857142, 857142,....

notice that the same six digits are cycled and that 3, 6 , and 9

never show up, only 1,2, , 4,5, , 7,8, are ever used in multiples of sevenths.

117 = ( 16 and 5/7 th) x 7

260 = ( 37 and 1/7 th) x 7

360 = ( 51 and 3/7 th ) x 7

364 = ( 52 and 0/7 th ) x 7

365 = (52 and 1/7 th ) x 7

584 = ( 83 and 3/7 th ) x 7

585 = ( 83 and 4/7 th ) x 7

780 = ( 111 and 3/7 th ) x 7

In fact every number that exists can be divided by

7 to get a result of (N and n/7 ths) x 7 = original number.

Thanks Michael, looks Mayan to me. There are 86 n-18980 cycles.

Michael, 86 n-CR combinations of 120 LCMs of 260, 360, 364, 365, 584, 585, and 780 by LCM (a,b), LCM ( a, b, c), LCM (a, b, c, d), LCM (b, c, d, e,), LCM(a, b, c, d, e , f), and LCM (a, b, c, d, e, f, g): reports an interesting distribution;

1-CR (1), 2-CR (2), 3-CR (2), 6-CR (4), 7-CR (2), 9-CR (3), 14-CR (4), 18-CR (28), 21-CR (2), 42-CR (4), 63-CR (4) and 126-CR (30)

18-CR appears 28 times and 126-CR 30 times ... wonder why?

Michael, look at these long count numbers from the Madrid Codex confirming Mayan views of Jupiter ... several Madrid data points were scaled to lunar, earth, Venus and Mars cycles and explicitly to Jupiter (399, 1432) per long count numbers:

4.4.4.4 = 30824 = 76(399) = 7(4332)

6.6.6.6 = 45486 = 114(399)

7.7.7.7 = 53067 = 133(399)

8.8.8.8 = 61648= 152(399) = 14(4332)

11.11.11.11 = 83391 = 209(399)

13.13.13.13 = 98553 = 247(399)

I looked up Synodic Orbital Periods and Jupiters was 398.9

All of the Larger Planets have Synodic Orbital Periods

between 398.9 and 365.1.

We have to think that they could only see Venus, Moon, Mars, Jupiter, and

Saturn with the naked eye.

Mercury, Uranus, and Neptune require telescopes.

It makes sense that they would round the numbers to whole numbers, and

since Jupiter is brighter and near a whole number (399) it would be chosen

for a calendar.

Michael, thanks for commenting ... decoding Mayan that report synodic and sidereal cycles and LCMs has been a fun project, now 18 months old.

Michael, thanks for commenting ... decoding two Mayan texts, the Madrid and Dresden, report planetary synodic and sidereal cycles and LCMs has been a fun project, now 18 months old

Another fun project is searching the values of the length of a foot, a yard, a meter,

a Vara, and also standards of weights, ounces, pounds, stones, grains, and standards of liquid measures too.

Google searches work best.

I have a friend that spent 10 years running down the length of a cubit ... in, end he failed ... standards change over time ... politicians hide their details ...

The four long count numbers on a wall in Gualemala were all mod 780 ... one of several LCM cited on the wall : http://planetmath.org/mayansupernumberarithmetic