Play with the year

Happy 2025!

2025 is a great number for Maths:

• It’s a square (45²), the sum of two squares (27² + 36²), the product of two squares (9² × 5²), and the sum of three squares (40² + 20² + 5²).

• It’s the sum of the cubes of the first nine positive integers (1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 83 + 93).

• Equivalently, it’s the square of the sum of those integers (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)². (This is Nicomacus' Theorem).

• It’s one of only three four-digit numbers whose halves can be split, summed, and squared to produce the original number: (20 + 25)² = 2025.

• It’s the sum of the entries in a 9×9 multiplication table.

• July 24, 7/24/25, will be a “Pythagorean day,” because 7² + 24² = 25².

• When asked his age, Augustus De Morgan used to say, “I was x years of age in the year x².” (He was 43 in 1849.) People born in 1980 will be able to make the same cryptic response starting next year.

Source: Futility closet.