2025—A One-Of-A-Kind Year!

By Aziz Inan

Next year, 2025, is numerically a one-of-a-kind year! Why?

1.      2025 is a perfect square year since 2025 equals the square of 45. The last perfect square year before 2025 was 1936 (44 x 44) that occurred 89 years ago and the one before 1936 was 1849 (43 x 43), which occurred 87 years before 1936. The next two perfect square years after 2025 will be 2116 (46 x 46) to occur 91 years later and 2209 (47 x 47) to occur 93 years after 2116. So currently, there is approximately one perfect square year occurring in each century, but such years will get further apart from one another in the future.

2.      2025 is also special because it equals the sum of the cubes of natural numbers 1 through 9.

3.      Further, the square root of 2025, namely 45, equals the sum of natural numbers 1 through 9.

4.      Moreover, the leftmost and the rightmost two digits of 2025, namely 20 and 25, add up to 45, the square of which equals 2025.

In all four-digit years, there is only one more year that possesses the above four properties.

This year is 3025, to occur 1000 years later in the 4^th millennium. 3025 equals the square of 55. It equals the sum of the cubes of natural numbers 1 through 10. The square root of 3025, namely 55, equals the sum of natural numbers 1 through 10. Also, the leftmost and the rightmost halves of 3025, namely 30 and 25, add up to 55, and square of 55 is 3025.

Other properties of 2025 are as follows:

5. Twice or one-half of the reverse of 2025, namely 5202, also equals a perfect-square number: twice 5202 equals the square of 102 and half of 5202 is the square of 51.

6.      2025 can be expressed as product of two perfect square numbers in two different ways: 2025 = 9 x 225, where 9 = 3 x 3 and 225 = 15 x 15. Also, 2025 = 25 x 81, where 25 = 5 x 5 and 81 = 9 x 9.

7.      If every digit of 2025 is incremented by one, the result, 3136, remains a perfect square number, since 3136 = 56 x 56.

8.      All people born in 1980 will celebrate their 45^th birthday in 2025, which equals the square of 45. When asked about his age, famous Indian-born British mathematician Augustus de Morgan, who lived in the 19^th century, remarked: I was x years old in the year x square. Indeed, De Morgan was born in 1806 and he turned 43 in perfect square year 1849, which equals 43 x 43.

9.      Valentine’s Day in 2025 will be special because February 14 is the 45^th day of 2025.

10.  Lastly, there are 8 month/day/year format perfect square dates and 6 day/month/year format perfect square dates to occur in 2025. Note that 3 of these perfect square dates will be common in both date formats: January 9, September 1, and September 27. The following link provides the list of all perfect square dates in each date format to occur in the 21^st century:

I hope you enjoy perfect square year 2025 particularly since most of us won’t experience another perfect square year in our lives!

(Inan is a professor of electrical engineering teaching in the Donald P. Shiley School of Engineering at University of Portland.)

Also Read: Tune Into These Titles For A New Year, New You!