Facts about 2025

[andrewducker]

Fact of the day: 2025 is a square year, as its 45*45. The next square year is 2116 (46^2)

45 is also 20+25, so 2025 = (20 + 25) ^ 2. Someone with less children about can run the numbers on how often that's the case.

Of course, 2000 years ago square years were happening every few years. Nowadays you're really unlikely to live through two.

Which led me to wonder when people started counting years using the current method. The answer being between 525 and 730 - with Portugal holding out until the 1400s. Before that was the Era of the Martyrs and regnal numbering ("5th year of King James"). Fun fact, documentation of UK's parliament was still done this way until 1962*.

In any case, that means that the first square number counted in the current year numbering system would be 576 - with the next one being in 625. So if you were born in the century after that you'd have a reasonable chance of living through two of them, if not *that* high, depending on exactly which year you were born in.

Obviously there are many other year counting systems around the world. My favourite regnal one, discovered while going through this, is the Anka Year which skips years ending in 6. And some ending in 0. But not all of them. I'm sure there was a good reason.

*I was ⅔ of the way through writing this (on my phone, while looking after three children) when David Allen Green posted this marvellous look at how the changeover happened.

Comments

[mtbc]

A quick go with an interactive Haskell prompt suggests that it is rather rare:
ghci> [ y | y1 <- [0..99], y2 <- [0..99], let y = 100*y1 + y2, (y1 + y2)^2 == y ]
[0,1,2025,3025,9801]

[asher553]

Very interesting!

[doug]

It’s the sum of the first nine cubes:
1^3+2^3+3^3+4^3+5^3+6^3+7^3+8^3+9^3 =2025

And the sum of three squares:
5^2+20^2+40^2 =2025

And also the square of the sum of the first nine integers:
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)^2 =2025

[mtbc]

Square of the sum of the first n being the sum of the first n cubes is interesting, I had another quick go with Haskell:

ghci> [ (n, s) | n <- [1..20], let s = sum [ p^3 | p <- [1..n] ], s == sum [1..n] ^ 2 ]
[(1,1),(2,9),(3,36),(4,100),(5,225),(6,441),(7,784),(8,1296),(9,2025),(10,3025),(11,4356),(12,6084),(13,8281),(14,11025),(15,14400),(16,18496),(17,23409),(18,29241),(19,36100),(20,44100)]

[redbird]

Having followed the link to the Anka years, and then to the Hindu calendar, I am now wondering who decided to translate paksha, the word for 15-day half-months, as "fortnight." It's not as though most English-speakers use the word "fortnight" very often, and pakshas are never 14 days long.

[andrewducker]

That doesn't seem right at all!

[drplokta]

English speakers in the US don’t use the word “fortnight” very often. It’s everyday usage in the UK.

[redbird]

A fair point.

I've had people tell me that they were surprised when I used the word. I'm sure I gotten that reaction from Americans, and I think at least once from a European who didn't expect to hear the word from me. [If I remember correctly, the surprised person was Irish.]

[bens_dad]

I use "fortnight" and rarely get funny looks for it.

A paksha has 15 tithis, but the length of a tithis may vary from 20 – 27 hours.
A lunar month is just over 29½ (29.5...) days so some pakshas will be fourteen days or they will get out of step with the moon.
I think I saw a mention on Wikipedia that sometimes a day is skipped.

The French equivalent of a fortnight is "les quinze jours" which is 15 days, which is a pashka.
That makes it easier to see that Saturday to Saturday to Saturday is a fortnight and fifteen days !

[redbird]

I see, so the problem isn't translating "paksha" as "fortnight," it's using "day" for "tithi" without specifying that those are lunar days. I'm used to either fixed-length days (always 24 hours) or sunset-to-sunset, where day length varies, but usually not by that much. (Things can get weird north of the Arctic Circle.)

Wikipedia doesn't have much about how tithi-length varies from one tithi to the next, beyond the fact that tithis can begin at any time of solar day or night. Googling mostly gets me a bunch of sites about astrology and the timing of rituals, and skimming a couple of those didn't get me anywhere.

[bens_dad]

I noticed something about each tithi being an equal part (one thirtieth, ie 12 degrees) of the moon's journey around the earth.

That is a little ambiguous since that could be measured against the sun or the fixed stars, or even one of the more subtle definitions, see https://en.m.wikipedia.org/wiki/Lunar_month

[calimac]

From what the footnote was linked to, I thought Green was going to be telling us how Parliament decided to drop regnal years from legislation. Instead, he tells us how the start of the year was standardized at January 1, an event I had never been entirely clear on.

He writes that 'law can compete with lore only so long.' Generalize 'lore' to 'practice' and that's emphatically true: it is, for instance, the reason the US gave up on Prohibition in 1933.