A solar leap cycle of 351 years contains 85 leap days and thus overall 128200 days or 1538400 twelfth-of-a-year months. Its mean year length is 365.242165 days or 365 days, 5 hours, 48 minutes and 43 seconds. It deviates from the mean Tropical year by one day in more than 40000 years.

The most intriguing fact about this leap cycle is that it encompasses three lunisolar leap cycles of 117 years or 1447 lunations each.

But that is quite approximative; for improved precision on the lunar cycle one should take four 351-year periods with 517 intercalary months. The resulting mean lunar month is 29.5306651 days or 29 days, 12 hours, 44 minutes and 9 seconds.

## Cycle mysteries

Seven days make one week, seven times seven lunations make 1447 days.

We know that there are 1447 lunations in 117 years.

${\displaystyle {\frac {\sqrt {117\times 365.242}}{7}}\cong 29.531}$

The square root of the approximate number of days in 117 years is approximately the number of days in seven lunations.

What a strange coincidence! Why are these numbers, 7, 117 and 1447 repeating like that?

Note too that:

${\displaystyle 1447=4\times 360+7}$

And 360 is the number of degrees in a circle, or the number of days in a year for the ancient people of Sumer. Their system of counting gave us hours, minutes and seconds in addition to angle degrees.