The Gregorian calendar, which was created in 1582, includes 97 leap years every 400 years. The Aztec estimate of 365.2420 days per year is actually closer to the genuine number of 365.2422 days than the previous Julian figure of **365.2500 days** or even our present Gregorian value of 365.2425 days....

The Aztec estimate of **365.2420 days** per year is actually closer to **the true figure** of **365.2422 days** than the previous Julian value of 365.2500 days or even our present Gregorian value of 365.2425 days. The Sun Stone was carved by hand during a 52-year period, from 1427 to 1479. Carvings on three other stones also show the position of the Sun at midday on May 1, but these may have been set up after that date. The carver probably took an average over several years.

The Maya developed methods for calculating solar eclipses about 800 years before the Europeans arrived. They did this by counting cycles of length 476.8 days (the tropical year) and using these as markers on the calendar-table. For example, they would note when a certain day in the month reached 0.5 of a cycle or 1/4 of the way through the year, then record the time of eclipse as well as the day itself. This method is exactly like how we calculate solar eclipses today, except that the Maya used a table instead of doing it by eye. They could even tell you when another total eclipse would occur, about 76 years later.

Total lunar eclipses were also observed by the Maya. These events take place when the Earth passes directly between the Sun and Moon, obscuring any glimpse of the lunar surface. Only the far side of the moon is visible from Earth.

To calculate the days of the year, the Aztecs employed **two calendars**. Xiuhpohualli (the first, or solar, calendar) had 365 days split into eighteen months of twenty units each, with a five-day break at the end of the year. The second calendar was a count of the years since the founding of their city by the war god Huitzilopochtli, which began on the day they defeated a rival tribe at Chalcatzingo. This calendar had only 360 days.

The Aztecs didn't need a calendar to know when the new month started. The first day of the month was called 1 Imix, meaning "first day." However, because there were only thirty days in a month, some months had three first days, others had four, and some didn't have a first day at all.

For example, if the date was January 10, 1521, then the month was Iximche. If we divide 1521 by 30 we get 5, but since it's not divisible by three, we add **one more month** and call it Maye.

The shortest month was March, with **thirty-one days**; the longest was September, with thirty-two.

The Aztecs didn't use **a decimal system** like our own. They counted by whole numbers: integers. There were no fractions or decimals.

It is incredibly exact, and Maya priests' calculations were so precise that their calendar correction is 10,000th of a day more precise than the world's standard calendar used today. They possessed two calendar years: the 260-day Sacred Round, or tzolkin, and the 365-day Vague Year, or haab. The difference between these two numbers was always a multiple of 20, with **some exceptions**. These exceptions occurred when the number 20 appeared as a divisor of the year number (as it does **every 120 years**), thus causing a shift either way in **the starting date** of the round. For example, if a given year was a multiple of 4 but not 20, then the start of the next sacred round would fall on the 20th day of that year.

The haab was based on observations of the movement of the moon, stars, and planets. It began on the day after Christmas, the winter solstice, which today falls on December 25. This was important because this was the day they could begin counting forward from. They knew when this happened because there were certain monuments built by the Maya that marked this day every year.

The tzolkin was based on observations of the sun. It began on the day after New Year's, the spring equinox, which today falls on March 21. This was important because this was the only day they had to start counting backward from.