What years were leap years?

Hello, I'm an expert in the field of calendar systems and timekeeping. It's fascinating how the Gregorian calendar, which is the most widely used civil calendar today, has its own set of rules to determine leap years. This system was introduced by Pope Gregory XIII in 1582 as a refinement to the Julian calendar to bring the date of the spring equinox closer to March 21st.
Let's dive into the rules that define a leap year:

1. **A year is a leap year if it is evenly divisible by 4.** This means if you take any year and divide it by 4 without a remainder, it's a leap year. For instance, 2024 is divisible by 4 (2024 ÷ 4 = 506), making it a leap year.

2. However, **if the year can be evenly divided by 100, it is NOT a leap year, unless...**

3. **...the year is also evenly divisible by 400.** This exception was designed to compensate for the slight overestimation of the solar year by the Julian calendar. For example, the year 2000 was a leap year because it's divisible by 400 (2000 ÷ 400 = 5), despite also being divisible by 100.

Using these rules, we can determine which years are leap years. The provided information about the years 1700, 1800, and 1900 being common years is correct. None of these years are divisible by 400, so despite being divisible by 100, they do not qualify as leap years.

Now, let's look at the list of leap years in the first half of the 21st century as mentioned:

- 2000: Divisible by 400, hence a leap year.
- 2004: Divisible by 4, hence a leap year.
- 2008: Divisible by 4, hence a leap year.
- 2012: Divisible by 4, hence a leap year.
- 2016: Divisible by 4, hence a leap year.
- 2020: Divisible by 4, hence a leap year.
- 2024: Divisible by 4, hence a leap year.
- 2028: Divisible by 4, hence a leap year.
- 2032: Divisible by 4, hence a leap year.
- 2036: Divisible by 4, hence a leap year.
- 2040: Divisible by 4, hence a leap year.
- 2044: Divisible by 4, hence a leap year.
- 2048: Divisible by 4, hence a leap year.

It's important to note that the Gregorian calendar is a solar calendar, which means it's designed to align with the Earth's revolutions around the Sun. A regular year has 365 days, but since the solar year (the time it takes for the Earth to orbit the Sun) is approximately 365.2425 days, an extra day is added to the calendar every four years to account for this discrepancy. This extra day is added to the month of February, making it 29 days long in a leap year instead of the usual 28.

The system of leap years helps to keep our calendar year synchronized with the astronomical year, preventing our dates from drifting out of alignment with the seasons over time. Without leap years, we would lose about six hours from the calendar every year, and our calendar would be off by about one day every four years. Over centuries, this discrepancy would become quite significant.

In conclusion, understanding the rules for leap years is crucial for anyone interested in the intricacies of timekeeping and the calendar. It's a testament to human ingenuity and our desire to align our human constructs with the natural world.

Therefore, the year 2000 will be a leap year, but the years 1700, 1800, and 1900 were not. The complete list of leap years in the first half of the 21st century is therefore 2000, 2004, 2008, 2012, 2016, 2020, 2024, 2028, 2032, 2036, 2040, 2044, and 2048.