As I write this, we are about to welcome year 2025. What is special about the number 2025? It is a perfect square. Also known as a square number, a perfect square is equal to a natural number times itself. In our case, 2025 =45 x 45 = 45^2. Big deal, you might say. But how many perfect square years have you lived through?
Let’s have a look at the perfect square years immediately preceding 2025. That would be 44^2. Here is a trick for calculating 44^2 without a calculator or long multiplication.
We start by noting that 44+1=45. Since we already agreed that 45^2=2025, we can say that
2025= (44+1)^2=44^2 + 2(44)+1= 44^2 +89. So the last time we had a year that was a perfect square was nearly 89 years ago, in 1936. None of us below age 88 were around in 1936.
When is the next perfect square year? We use the same trick again.
46^2= (45 + 1)^2=45^2+ 2(45) + 1 = 2025+91.
That’s going to be in 91 years. Not to be morbid, but barring major medical breakthroughs, if you are old enough to read this blog, you may not hang around for another 91 years.
Was it always this way— I mean, living through one perfect square year in most people’s lifetime? Certainly not if you lived in the first century AD. The perfect squares in those days occurred with rather high frequency: 1, 4, 9, 16, 25, 36, 49, 81, 100. As time went on, square numbers became more scarce. There was just one perfect square in all of 18th century (what was it?).
So let’s enjoy this special, square year. It’s never been more hip to be square!