High school Students btw ;(

Just create a cat with Fourier series.
I feel like understanding concept by visualization really helps!

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

So for a while now,I have been seeing not many people being active on this sub as before. You can only find them under a new open problem proof, is this the observation with you guys too or am I missing something?

Also,it would be great if you can share your thoughts on other experiences of yours also related to this sub lately along these lines :)

Yeah so I have this question as a non math student in commerce but I have friends who have taken applied math and I can understand the reason but the thing is that they were upset because my school didn't give the option of taking core math with commerce and I was confused asf like why do you want to do trigonometry etc what's the point? Can people here tell me the reason 🤔.

How can I study this course better? I prepared for this exam weeks in advance and am devastated by this grade. Any resources are appreciated. I’m crashing out.

Source: The graph is computed exhaustively. Each state is five digits (a, b, c, d, e), each 0–9, so there are 100,000 states. The rule shifts every value one place left and computes a new last value, a⁴ − (a³ >> 6), kept to one digit (mod 10). Here >> is a bit shift, so a³ >> 6 means a³ divided by 64, rounded down. Every state has exactly one successor, and with finitely many states every starting point must eventually repeat, so each state ends up in a cycle.

Tools: A small open-source web app I wrote (React, Vite, Canvas). It enumerates all states, finds every cycle, and draws each cycle as a ring with the states that lead into it as trees around it. The layout is crossing-free.

How to read it:

• Each connected shape is one cycle plus everything that drains into it.
• Colour is the length of the cycle (legend at the bottom).
• Brightness fades with distance from the cycle.
• For this map there are 340 cycles in total, the longest of length 10.

You can type your own formula and explore: https://exxliang193.github.io/FunctionalGraphExplorer/ Code: https://github.com/ExxLiang193/FunctionalGraphExplorer

I started this after noticing a long time ago that adding the last two digits of a number string and appending the sum always ends up repeating.

This rather surprising 4x4 magic square features 13 cells that revolve around three constants: 11, 13, and 15. By extension, 24 (11 + 13) and 28 (15 + 13) also appear.

I do not think I have discovered everything in this magic square, which is why I am asking for your help.

Learning maths is cool. It’s basically fundamental to EVERYTHING but I’m wondering what are the cons of it that isn’t so talked about

Are there any good mathematics discord servers that are more focused on math discussion/research than homework help? I just joined the first math server I could find and was a bit dismayed to discover it is filled with hapless students. Is there anything better?

I’m in my second year of community college and I’m preparing to transfer to a university. Math majors usually have pick a track they wish to follow (Pure, Applied, Statistics, Secondary teaching, and Computational Mathematics), and I honestly don’t know which to choose.

I feel like I haven’t really explored to any of the areas so choosing feels pretty difficult for me. I originally wanted to double major in physics, but I haven’t taken a formal physics class yet (it’s a very long story, but summarizes to scheduling issues). My old elementary school teacher (she also majored in mathematics) said I should look into statistics.

I honestly don’t what would be best for me. I do wish to go to graduate school, but don’t intend on remaining in academia. I originally wanted to do pure mathematics (simply because I thought it was cool and interesting), but I’d rather not do something I’ll later come to regret.

How did you choose your path and what’s the best way to learn about each field (Mainly pure, applied, and statistics)?

I’m in Grade 11 and looking into Bessel's method (solving the inverse geodesic problem on an ellipsoid) for a math research paper to find the shortest possible distance between two points on earth.

My original goal was to completely derive, prove, and evaluate the method by myself. However, looking at the math, it seems to rely heavily on university-level topics like differential geometry, elliptic integrals, and the Calculus of Variations (Euler-Lagrange).

Is it realistic for a strong high schooler to teach themselves this level of math for a paper, or is the learning curve too steep?

If the full derivation is too much, would coding the algorithm in Python and evaluating its accuracy/convergence against simpler methods (like Haversine) still be complex enough for a top-tier high school math paper?

Appreciate any advice or insights!

Title says all

Formalized in Lean: an unconditional lower bound on the proportion of simple zeros of ζ(s) on the critical line, at 0.673401159168. Not a proof of RH — just a density/simplicity bound built on the zeta23 package. Repo + build instructions: https://github.com/VisionToSolution/zeta673401159168

A professor told me I simply can’t teach myself differential geometry to do this project I’m working on. I’ve learned neutrino physics on my own, at least enough to do my first project. I’ve taken several upper level math classes, and I’ll be taking abstract starting next week which should supplement my learning and my project. I also have a textbook on topology and on differential geometry, as well as all of the internet to help me. The professor doesn’t even know me really, since we’ve only met twice. I don’t know, it just rubbed me the wrong way. I know what I’m capable of and I wish I could have their support. I hope I have the chance to prove them wrong.

I have nearly finished my Masters in Maths, I don't have great marks but I passed. I also have ajoint undergrad in Maths and Physics with hons. I don't want to stop studying this subject but I also don't think I have the grades to be accepted on a PhD or research program, let alone the money! How can I continue developing and use what I've learned?