u/QuantumPikachu

Most people know this simple thing:

1 + 3 + 5 + 7 + ... gives square numbers...

Like:

1 = 1

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

So basically the odd numbers are like the layers which grow a square.

But there is another pattern inside the same odd numbers which I dont see talked about much. Instead of adding odd numbers one by one, cut them into groups like this:

1

3 + 5

7 + 9 + 11

13 + 15 + 17 + 19

21 + 23 + 25 + 27 + 29

So the group sizes are:

1, 2, 3, 4, 5, ...

Now add each group:

1 = 1

3 + 5 = 8

7 + 9 + 11 = 27

13 + 15 + 17 + 19 = 64

21 + 23 + 25 + 27 + 29 = 125

So suddenly the same odd numbers become:

1, 8, 27, 64, 125, ......... so on;.

which are cube numbers:

1 cubed, 2 cubed, 3 cubed, 4 cubed, 5 cubed.

That means:

1 | 3 + 5 | 7 + 9 + 11 | 13 + 15 + 17 + 19 | ...

turns into:

1, 8, 27, 64, ...

So the odd numbers are making squares if you read them normally, but they make cubes if you cut them at triangular places.

The reason is simple but kind of nice.

Take the third block:

7, 9, 11

The middle number is 9, which is 3 squared. There are 3 numbers in the block.

So the total is 3 times 9 = 27. That is 3 cubed.

Take the fourth block:

13, 15, 17, 19

The average is 16, which is 4 squared. There are 4 numbers.

So the total is 4 times 16 = 64. That is 4 cubed.

Same thing keeps going...

The nth block has n odd numbers, and the average of that block is n squared.

So the total becomes n times n squared, which is n cubed.

This also explains the famous formula:

1 cubed + 2 cubed + 3 cubed + ... + n cubed

is the same as

(1 + 2 + 3 + ... + n) squared.

Because after using the first n blocks, we have used:

1 + 2 + 3 + ... + n

odd numbers total.

And the sum of the first so many odd numbers is always a square.So cubes are hiding inside the square pattern of odd numbers.

I like this because it is not just a formula trick. It feels more like one sequence has two different geometries inside it:

read the odd numbers one by one, and you get squares.

cut them into growing blocks, and you get cubes.

what do you think guys?

Hey all! I’m going to Forging Better Futures for You and AI on Tuesday 2 June, 18:00, at Gresham College, Barnard’s Inn Hall, Holborn, London EC1N 2HH.

The talk seems to be about how we can think about better futures with AI, beyond the usual doom/utopia framing. Never to this specific type of event, so no guarantees how good it will be.

You can book now as the sale is ending soon i guess, It’s free. I’m into finance, astrophysics, maths, AI, biotech etc. Other interests: long walks, cycling, small cafés and abstract design.
So if anyone wants to come along, comment below or DM me. :)

Thank you!

[https://www.eventbrite.co.uk/e/forging-better-futures-for-you-and-ai-tickets-1777029124949?utm\_experiment=test\_share\_listing&aff=ebdsshios&sg=96a6bb3d3ecb2fbe953a05508a339e804b44447fdc73ab9c649fb6555d7aa3e5260fd721c8d2b3d346fac45e21efbfc901437ade1f9e37c93946056704986d8d3198f9b7f6498f020ec6c9a1ef\]

Hey folks, M27 here. I’m planning to go to Public Talk: Solar superstorms: Are we ready for another Carrington Event? at The Royal Astronomical Society, Burlington House, Piccadilly, London, W1J 0BQ, on Tuesday 19 May, 18:00–19:00.

It looks like a public talk about what could happen if another Carrington-level solar superstorm hit Earth, and whether our Tech, AI etc are actually ready. Tickets are free, you can book now from below Eventbrite link. I’ve never been to this specific event before, so no guarantees, but it sounds like the kind of thing that could lead to a good conversation before or after.

I’m generally into Finance, Astrophysics, Maths, AI, Quantum, Intelligence Curiosity Frameworks, Trading, Psychology etc. Other interests: Long walks, Cycling, Small Cafés, Longevity and Abstract designs. So if anyone wants to join, feel free to comment or DM. :)

Thank you! 🙏🏻

[https://www.eventbrite.co.uk/e/public-talk-solar-superstorms-are-we-ready-for-another-carrington-event-tickets-1987323879220?utm_experiment=test_share_listing&aff=ebdsshios&sg=20363643f114abc242e63753cbd418531b83969a4ea5209522f9d4250195c40371956968871c406a9d12229ff11bb2e80ee56cae634587e17439e964d9f7a7bf609ec60c6de9b4b6e0d26bfb9b]

M27, I am near to National History Museum, If you are interested for an evening walk near to the area for few hours (right now) DM me please.

Interests: Tech, Physics, Astrophysics, Biotech, Intelligence curiosity frameworks, Longevity, Long Walks, Cafes, Cycling

Thank you

Hey folks, M27, planning to go to this ‘Science in a Changing World’ event at Bloomsbury Theatre UCL tomorrow 18:00.

It looks like a talk/discussion about where science is heading and how things like AI, space, medicine, climate, and new technology might change the world over the next few decades. Tickets are £5 and still available. I’ve never been to this specific event before, so no guarantees, but it sounds like the kind of thing that could lead to a good conversation before or after.

I’m generally into finance, astrophysics, maths, AI etc. Other interests: long walks, cycling, small cafés and abstract design, so if anyone wants to join, feel free to comment or DM. :)

https://www.bloomsburytheatre.com/event/2026/05/science-changing-world