Apparent Mathematical Errors in Dominant Calendars

Lunar calendar

235 synodic months * 29.53059 lunations = 6,939.68865
“lunar periods” in 19 years.

365.242424 (ephemeris days) * 19 solar years = 6,939.606056 tropical days.

Difference is 6,939.68865 – 6,939.606056 = 0.082594 days.

1 (leap day) / 0.082594 = 12.107417

Extra Lunar Day every 12.107417 * 19 = 230.040923 years.

29.53059 isn’t static, because of the lunar travel peculiarities it must be a formula.

Julian calendar

365.25 (Julian) * 33 yrs = 12,053.25 tropical days.

365.242424 (ephemeris) * 33 yrs = 12,052.99999 tropical days.

Difference is 12,053.25 – 12,052.99999 = 0.25001 days.

1 (leap day) / 0.25001 = 3.999840006.

Extra Julian Day every 3.999840006 * 33 = 131.9947202 years.

Gregorian calendar

365.2425 (Gregorian) * 231 yrs = 84,371.0175 tropical days.

365.242424 (ephemeris) * 231 yrs = 84,370.9999 tropical days.

Difference is 84,372.0175 – 84,370.9999 = 0.0176 days.

1 (leap day) / 0.0176 = 56.818181

Extra Gregorian Day every 56.818181* 231 = 13,124.9998 years.

Aztec calendar

104 yrs * 365 = 37,960 + 13 = 37,973 + 12 = 37,985 tropical days.

365.242424 * 104 yrs = 37,985.21209 tropical days.

Difference is 37,985 – 37,985.21209 = – 0.21209 days.

1 (leap day) / – 0.21209 = – 4.71497949

Deficient Aztec day every – 4.71497949 * 104 = – 490.3578669 years.

Obviously, the Aztecs added their leap day every eight (8) years and added twelve (12) days after 104 years. This played exponential havoc with their planting schedule, so they ridiculously sacrificed humans. Adding an extra day to a 520 year cycle will help a little, but since they were playing “catch up” with leap days, no matter how accurate their calendar was they were doomed.  126 leap days / 520 years = 0.242307692 = deficient Aztec day every -8,609.271522 years.