Here’s some interesting mathematical stuff for those of us who are so inclined.
This was published yesterday in the Sydney Morning Herald’s “Column 8” which is a kind of repository for Believe-It-Or-Not type trivia
Our next calendar year 2025 is a mathematical wonder
1) 2025, itself is a square, 45 x 45 = 2025.
2) it is also a product of two squares, 9² x 5² = 2025.
3) it is also the sum of three squares, 40²+ 20²+5²= 2025.
4) and remarkably it is also the sum of the cubes, of all the single digits, from 1 to 9, 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³= 2025.”
>>>>>>>
A bit dusty for this yet Mousey
Instead of the Oh Wow reaction I was expecting from my son, he revealed an unexpected streak of mathmo nerdery:
Hm, I think given 1), 2) is trivial. If it is true that
(x * y) * (x * y) = z
then necessarily it is also true that
(x * x) * (y * y) = z
E.G. 10² = 100 so 2² * 5² = 100 because 10 is two times five
4 is true because 2025 is the square of a triangular number, i.e. 45 is equal to 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9. And the square of a triangular number is always equal to the sum of the cubes of its parts
Although the last year that was the square of a triangular number was 1296, so I guess we’re lucky to be alive for one
A dullard writes: I agree.
chin drop
Not counting doubles and triples, 2025 is also the last two-darter “year” until 2050 i.e. you can throw a 20 and a 25. After 2050 it won’t happen again until the year 2501.
All right, it’s not as impressive as Mousey’s.
Treble 20, treble 19, double 954 – easy!
Amazing stuff, Mouse.
Thank you, Mousey.
I find myself really fascinated by maths these days. I wonder how my life might have turned out had I not had shit maths teachers for a couple of years at secondary school.
If this kind of thing is of interest, I can recommend the books by Kyle D Evans (who is also the singer & guitarist of The Dawn Chorus).
Do they explain why calculus is so important, and more importantly how to do it? That is where me and maths parted company .
And I’ve forgotten how to do long division too – I blame calculators.
Never stayed in school for the sixth form, so never did calculus. Completely clueless on that score.
In my school days I found mental arithmetic really hard. Scoring at darts and tallying how much space was left on mixtape cassettes improved my performance no end, after I’d left school.
Astronomy, architecture, engineering etc. I did a pile of it at university, pretty complex stuff. Confess I have hardly used it since though. I never properly studied statistics which would be more useful in my current job
They’re aimed at kids with an interest in Maths (Kyle’s day job is as a secondary-school teacher) so they’re a bit more “how many rivets are in the Forth bridge?” than “this is how you solve quadratic equations”.
When the Offsprings were little, I showed them how to do column addition/subtraction (“carry the one”). Then, when they went to Primary school, I was hauled up in front of the Head, because I had told their Maths teacher they didn’t need to learn the “chunking” method, as they could already add up and take away.
I was disrespecting the teacher and confusing the Offsprings, apparently.
Both Offsprings later passed A-level Maths.
Here in Singapore at Primary school they use a visual system called “models” (which is admittedly pretty good) to solve algebra problems.
I was similarly told off by the teacher for teaching them to solve using traditional algebra, which they hadn’t learnt yet.
Chunking is/was an attempt to bring Chinese-style Maths teaching to the UK. The basic idea being: don’t rely on a calculator. If you’re adding 20 something and 30 something, the answer is unlikely to be hundreds or thousands (which is easily done with a slip of a finger on a calculator).
Being an accountant, I surprisingly use this a lot.
Nearly 30 times just over 50 is very likely to be about 1500.
I also used the “(n+1) x (n-1) = n squared -1” trick to great effect the other day when someone wanted to know what 160 times 1800 was, and I knew it was 288,000, not a calculator in sight.
Whilst there were some genuinely astonished faces in the room after a tap or two on a calculator, party invites have, equally astonishingly, not been forthcoming.
In my experience, your average Joe has a dislike of even basic maths bordering on pathological, yet there are few more beautiful things, as the OP shows. Doing maths like the above can get you looks that would’ve had you burned at the stake a few years back.
I can recommend Alex Bellos or Matt Parker’s books, for a nice fun maths-y read. I bought myself Sir David Spiegelhalter’s new one for Christmas. I’m saving it for my holiday in March.
On a unit square grid, a circle of radius 26 with origin at the centre of a square encloses exactly 2025 squares. But then everyone knows that.