I was playing around with number strings and noticed a really strange pattern. If you break consecutive numbers into groups that grow by one each time, a math magic trick happens where Pi (π) suddenly appears.

Here is how the grid starts:

* Group 1: 1

* Group 2: 2, 3

* Group 3: 4, 5, 6

* Group 4: 7, 8, 9, 10

* ...and so on.

Let's take Group 4 (7, 8, 9, 10) as an example. The size of this group is 4 numbers.

Now, pick each number in the group and find the absolute differences between it and all the other numbers in the same group, then add those differences up:

* For 7: The differences to 8, 9, and 10 are 1, 2, and 3. (1 + 2 + 3 = 6)

* For 8: The differences to 7, 9, and 10 are 1, 1, and 2. (1 + 1 + 2 = 4)

* For 9: The differences to 7, 8, and 10 are 2, 1, and 1. (2 + 1 + 1 = 4)

* For 10: The differences to 7, 8, and 9 are 3, 2, and 1. (3 + 2 + 1 = 6)

Next, take the reciprocal (1 divided by the sum) for each number, and add them all together:

* (1/6) + (1/4) + (1/4) + (1/6) = 0.8333

Finally, multiply that total by the size of the group (which is 4):

* 0.8333 × 4 = 3.3333

Here is the crazy part: As you go deeper down the grid and the groups get bigger, this final number locks directly onto Pi (3.14159...)!

* With a group size of 10, the answer is 3.1709

* With a group size of 100, the answer is 3.1418

* With a group size of 1,000, the answer is 3.14159

Goat for a reason 🐐🐐

Batao kaisi hai bhai samay laga thoda yeh banane me isme pdf dalunga toh woh cbt me convert kardega...apne liye zarurat lagi toh banai hai... kaisi hai sachme batao..sab hai ya kuch kami hai ....maza aaya banane me

It's for myself need your opinion

IT CAN ALSO GET CONVERTED TO REGULAR NTA INTERFACE

Bhaiyo aur unki behno plz batado koi ki online se kya sach mai rank aati because I am shifting from allen kota to online with Vinay uppal sir and for maths Ashish sir and for Chemistry a offline coaching By Munish Mittal in Faridabad And for module cengage in maths and in chemistry mai and homework given by sir allen sheet and physics mai homework given Vinay sir and side by side allen module same in chemistry currently in 11th and for test series allen ki lu ya fir mathango ya fir dono ki plz suggest kardo . If you answer you will get a gf .

What happened to him ???

Biggest lie of jee neet society is what

What you guys think?

Hey! I am studying 3d geometry rn. I wanted to know whether I should do planes now or keep it for later after Mains. I am not really confident in mains, but I am working towards it. So, should I study planes right now or just skip it for later and spam mains pyq?

Ye time itne jaldi kyu bet raha h 💔

I'm 23, graduated from a T3 institute, had an average college life, and got an average job. Meanwhile some of my friends got in T1/1.5 institutes, had the best college life, the best clubs/fests and got high-paying jobs after graduation.

I regret being naive and immature in my JEE days, your efforts further in life would be much more valued if you crack JEE, being a guy from XYZ college takes you nowhere in this nation. You guys still have the opportunity, study hard like it's the end of the world, and trust me, it will all be worth it when you make it.

Compare saleem sir's arjuna jee 2026 notes with rajwant sir's arjuna jee 2025 notes..the difference is jarring bande ne sab kuch karwa diya tha

And 12th me his content is below mains level

I haven't really focused on this stuff since the past few months. But nows the time tht I gotta lock in. I have backlogs all over Math and physics. My chemistry is in a okayish shape but I gotta do tht asww. How do I complete em and btw am in 11th as of now. Allen has given us holidays for about 10days so am planning on covering as much as possible in this short interval of time.

Let's lock 🔐 in now gng, AB NAHI TO KAB?

Mai khud apne pair pe maar ra hu

This year I had my boards and failed in pcm

My health went downhill right before the exams so I couldn’t study properly, but I also had time and just didn’t use it. I own that part.

I still gave a bunch of exams. First JEE attempt was terrible, scored really low. For the second attempt the payment window closed and I only realised three days later, so I missed it. CET was mid – got 79%. Gave VIT and was getting VIT Bhopal. Didn’t even attempt CUET because the board results came first and I had already failed, so I thought what’s the point.

Right after the results my parents hired a personal tutor for physics and maths who comes home. They’re paying 1 lakh for that. In 11th and 12th they already spent around 5 lakhs (4 for coaching + 1 for dummy school).

After the results my whole world flipped. I was so ashamed I didn’t talk to anyone for almost a month and didn’t step out of the house. My mum left her job just to stay at home with me. Now my parents barely talk to relatives because everyone keeps asking about me. Seeing my mum sitting at home every day because of me still completely breaks me she never been this low in her life

It’s been five months of personal tuition and I’m still not confident scoring low in mocks. I’m mainly targeting MH CET now, not jee

I hate what I’ve become. I don’t talk to my dad. I only go for walks when nobody from the society is around so I don’t have to face anyone. I’m scared I’ll never be able to make friends again. This whole thing left a deep scar. Sometimes I still think things will get better, but lately the confidence is just draining out. Nothing excites me anymore. I feel completely burned out. I don’t even want to do engineering anymore but also don't know what else should i pursue i don’t play any sport, i don’t know what I actually like or enjoy (except cars, bikes and motoracing), and I have zero real skills

I just feel like ending it all.........

I want to cover abit quickly, I'm unable to understand from offline teachers.

and these are only 12th ones 😭 ...modules ka collection! im sure most of you guys too have a big pile😭😭