The Year 2025 Is Special…

People hear may (or may not) know or care that the number 2025 has special properties, apart from being announced as a Jubilee year.

2025 is the square of 45, which is a triangular number. This means that 2025 is both the sum of the first nine cubes, and the sum adding the numbers 1 through 9, then squaring that.

That is:

1^3 + 2^3 + 3^3 + … 8^3 + 9^3 = 2025

(1+2+3+ … +8+9)^2 = 2025

{isplaystyle um _{k=1}^{n}k^{3}=eft(um _{k=1}^{n}kight)^{2}.}

This identity is sometimes called Nicomachus’s theorem, after Nicomachus of Gerasa (c. 60 – c. 120 CE).

You don’t care, of course. This last happened in 1296. It won’t happen again for a thousand years. But if you did, Nichomachus’ proof that the sum of the cubes equals the square of the sum is given below.

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