Soon it will be 2025 and that reminded me of an arithmetic trick that used to impress my students, when I was a maths teacher.
Suppose you want to square a number ending in 5, for example 85. Take the first digit, 8, and add 1 to it to get 9.
Now work out 8 x 9 = 72, then put 25 (it's always 25) at the end, giving 7225
And sure enough 85 x 85 is 7225.
This works with any number that ends in 5, for example 1152 is 13225, although doing the calculation in your head obviously gets progressively harder.
What has this to do with 2025? Well 2025 is a square you see; using the method above we find 452 = 2025. This may seem unremarkable, after all, aren't there plenty of square numbers (infinitely many in fact)?
But they get further and further apart the further we travel along the number line – so for example by the time we reach a million only (1,000/1,000,000) x 100% = 0.001% of numbers up to that point are squares. In the long run the proportion of squares gets closer and closer to zero.
And the next square year after 2025 will be 462 = 2116, another 91 years off.