The Math Behind the Months: Why 90 Days Equals Three Months

Have you ever wondered why there are twelve months in a year and why each month has either 30 or 31 days, except for February which has 28 (or 29 in a leap year)? And why does 90 days equal three months? Let’s dive into the fascinating math behind the months.

The Gregorian Calendar System

First, we need to understand the calendar system that we use today called the Gregorian calendar. It is a solar calendar system named after Pope Gregory XIII who introduced it in 1582. It is widely used around the world and accepted by most modern countries. But why does it have 365 days in a year (and 366 in a leap year) and why is the year divided into twelve months?

The answer lies in astronomical calculations. The Earth takes around 365.25 days to orbit the sun, and this extra quarter of a day per year accounts for the leap year. In the Gregorian calendar system, a leap year occurs every four years, except for years that are divisible by 100 but not by 400. For example, the year 2000 was a leap year, but 1900 was not.

The division of the year into twelve months goes back to the Romans, who based their calendar on the phases of the moon. They noticed that it took around 29.5 days for the moon to complete its cycle from new moon to full moon and back to new moon again. Therefore, they divided the year into twelve lunar months, each with 29 or 30 days.

However, this created a problem because the lunar year is around 354 days long, which is 11 days shorter than the solar year. This meant that their calendar gradually fell out of sync with the seasons. To solve this problem, Julius Caesar introduced the Julian calendar in 45 BCE which had 365 days in a year and added an extra day every four years. But even this system was flawed and needed a correction.

Pope Gregory XIII introduced the Gregorian calendar system to address the problem of the Julian calendar being out of sync with the seasons. He retained the twelve-month structure of the calendar but made some adjustments to the number of days in each month.

The Months in the Gregorian Calendar

In the Gregorian calendar system, there are twelve months, and their names are:

1. January (31 days)

2. February (28 days in a common year and 29 in a leap year)

3. March (31 days)

4. April (30 days)

5. May (31 days)

6. June (30 days)

7. July (31 days)

8. August (31 days)

9. September (30 days)

10. October (31 days)

11. November (30 days)

12. December (31 days)

The months of January, March, May, July, August, October, and December have 31 days, and the rest have 30 days, except for February. The reason for this arrangement goes back to the Roman calendar, where March and December were the first and last months of the year, respectively. January and February were added later, and February was considered the last month of the winter season. Therefore, it was given fewer days than the others.

But why does February have 28 days (or 29 in a leap year)? The answer lies in a historical event in ancient Rome. In 713 BCE, Romulus, the founder of Rome, introduced a ten-month calendar, starting from March and ending in December, which consisted of 304 days. The remaining 61 days were not included in any month and were left as an unorganized winter period. Later, two extra months were added to the calendar, and February was selected as the last month of the new year. Therefore, February had fewer days than the other months to account for the remaining unorganized winter days.

The Math Behind Three Months

Now that we know why there are twelve months in a year and why each month has a specific number of days, let’s focus on the math behind three months. We often say that 90 days equals three months, but is that true?

If we divide a year by 12 months, we get an average of 30.4167 days per month, which is not a whole number. Therefore, if we multiply 30.4167 by three, we get 91.25 days, not 90. However, many people still use 90 days as a rough estimate for three months. Where does this approximation come from?

Although it is not accurate, the 90-day estimate comes from a practical and convenient calculation. When it comes to legal documents, pay periods, rent payments, and other similar transactions, people often use a fixed 30-day month and count three consecutive months as 90 days. It is a simple way to approximate the length of three months and avoid using decimals in calculations.

FAQs

Q. Why does February have fewer days than the other months?

A. February was the last month of the Roman calendar and was given fewer days than the others to account for the remaining unorganized winter days.

Q. Why does 90 days equal three months?

A. Although it is not accurate, the 90-day estimate comes from a practical and convenient calculation where people often use a fixed 30-day month and count three consecutive months as 90 days.

Q. How many days are there in a leap year?

A. There are 366 days in a leap year.

Q. Why does the year have 365 days in a non-leap year?

A. The year has 365 days in a non-leap year because it takes around 365.25 days for the Earth to orbit the sun, and the extra quarter of a day per year accounts for the leap year.

Q. Can we use decimal values for the number of days in a month?

A. Yes, we can use decimal values, but it is more practical and convenient to use whole numbers, especially when it comes to legal or financial transactions.

In conclusion, the math behind the months is based on astronomical calculations, historical events, and practical approximations. The Gregorian calendar system that we use today is a result of centuries of adjustments and corrections to create a more accurate and useful calendar system. Remember that 90 days equals three months is a rough estimate, but it is useful in everyday situations where approximate calculations are needed.