Five mathematical quirks about 2025

It's a square year, for starters

As we head into the second quarter of the 21st century, here are a few mathematical curiosities about the year we’ve just started. (Just in case you want some fun facts to help work off the New Year festivities.)

1. It’s a square year

2025 is equal to 45 squared, which makes it a square year. The last time this happened was 1936 (or 44 squared), so make of that what you will.

2. It’s the square of a triangular number

45 isn’t just any old number. It’s a triangular number. Picture a pool table, with the balls arranged in rows: 1, 2, 3, 4. In this situation there are 10 balls in total. Continuing the pattern gives 15, then 21, 28, 36, and finally 45. The last time this happened was 1296, which was the year Chiang Mai was founded.

3. It’s also the sum of two triangular numbers

If we were to set up a massive game of pool, adding row upon row of balls until we had 44 rows in total, we’d have 990 balls. If we added a 45th row, we’d have 1035. Together, these two triangular numbers add up to 2025.

4. It’s a harshad year

If we add up the digits of 2025, we get 9 (i.e. 2+0+2+5). And 2025 is divisible by 9, which makes it a so-called harshad number. But don’t get too excited about this one, because 2024 was also a harshad year (as it divides by 2+0+2+4=8).

5. It can be calculated using powers and multiplication from the digits 1 to 5

I’ll give you a minute to think about this one. How can you make 2025 using the digits 1, 2, 3, 4 and 5 only once with only multiplication or powers (e.g. squares, cubes etc.)?

Had a guess?

One option is as follows:

\(1 \times 3^4 \times 5^2 = 2025\)

And with that, I’ll leave you to your New Year!

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Cover image: DESIGNECOLOGIST via Unsplash

Note: edit made to point 3 following a helpful comment below.