Self-discovery Thread

I independently derived the fact that the "new thread" function is a projection from the space of 4chan users onto the space of faggots

When I was in kindergarten I figured out 10X10=100 when I barely knew what multiplication was. All the other babbies were impressed :^)

>>7652828
I guess this was pretty lame, but back when I was in physics 2, I was working through the derivation of the RC time constant, and thought the method used for analyzing the circuit was pretty cool.

So I went to a math instructor and said "Hey, this is pretty cool, given just a relationship between a function and its derivative, you can determine the function! Is there a way to generalize this, it seems really useful."

He told me "Yeah, it's called Differential equations..."

i came up with something to do with standard deviation and rms but i can't remember it now.

Yeah i figured a direct relationship between the fibonnci sequence and the x^2 sequence, its use being a certainty in knowing fibonacci terms wayyy ahead of what you know in betqeen. like if you knoq up to x amount of terms in the series. you can know the x+(roughly)1.618 term

I figured out the third log law when I was 14.

Figured out the expression of a curve's length defined by a function. It was just after highschool.

>>7652828
I only remember this one.
>Skipped a few lectures of Exactly Solveable lattice models
>doing an assignment last minute
>had to show an infinite product is equivalent to this constant
>didn't know what to do
>took the log to turn into a sum
>realised adding a dodgy extra factor looks like a Riemann sum
>turned into an integral using a change of variables
>everything works out

Felt like an absolute baller as it was the first time I'd ever played with an infinite product.

Told my friends, turns out we learnt that in the lectures I missed and was what was expected. I genuinely thought I'd come up with a really neat way to do it. Friends just laughed at me.

When I first started using Maple, I was playing with the prime function, just testing out its limits. On a lark, I punched in a Mersenne number much larger than the greatest known Mersenne prime. After a little while, it came back with "true." We all laughed at the limitation of the algorithm, but I jotted down the number with the intention of seeing why it did what it did. But then the rest of the school year got in the way, and I forgot to go back to it.

Six months later, that number was confirmed as the new record for largest Mersenne prime.

Now, I know that Maple was just using a (pretty strong) heuristic for the test, but if I'd gone and done a more rigorous test on that number... alas....

File: 1447259887337.png (863KB, 1600x1149px) Image search: [Google]

863KB, 1600x1149px

>>7652828
I could not help but notice your png was not optimized anon.
I have optimized your png.
Your png is now optimized.

>>7654720
Then nothing. It'd be added to the list and that's it. They're just primes.

>>7652828
Well its physics and not math. But during my electrodynamics exam I had a brain fart and couldn't apply the Biot–Savart law to a circle, even though I'd done it in the previous question to a square. Needless to say I panicked a bit since this was one of the first and most basic questions, but then I had a moment where I realised that a circle was just a limiting case of regular n-sided polygons, so I started with the square and built up the result for an n-sided polygon, took it's limit. It worked and I got an extra mark for creativity. However two problems:


>At the time I said that it was a general result, however now I'm pretty certain that it only holds for even n.
>I don't really remember how I did it. Something to do with the angle subtended.

Its probably a known result, but I was pleased with myself anyway.

>>7652828
When I was 10, a friend offered to give me a dollar one day. Then the next day, he gave me two dollars. Boy was I happy. The day after he offered me three dollars. And he kept going like that increasing his donation every damn day.
It got me thinking, and I thank the Lord for helping me figure out that he was in fact trying to rob me of 1/12th of a dollar.
The day after, when he tried to pull his stunt again, I punched him in the face.

>>7654933
Hahahahaha very good, very good.

out of my own curiosity I discovered the product integral of a function and proved that the the product integral of f(x) is equal to exp(integral of f(x))

thought I was a genius until I found the wiki page for a product integral

>>7654864
Thanks buddy.

My Calc professor showed us a method for proving convergence of alternating series using derivatives, and I found a way to do it simply by proving the ratio between the n+1 term and the nth term is less than one. I mentioned it to him and he told me to write up a sample problem to demonstrate the idea. He also suggested that you could show convergence by subtracting the n+1 term from the nth term and ending up with a positive number. I've had exams all week so I havnt had a chance to play around with it but I was going to this weekend and show him a write up on monday

>>7654720
A pernicious mersenne number?

>>7654864
Wtf did you change?

>>7652828
>Hey /sci/, have you ever independently discovered a math theorem or concept?

YES

I was thinking about the idea of making game maps more realistic.
Then this idea came to me "why not just use eart map?"
Then 3 seconds later or something like that, this came into my mind "because all maps would them be the same.

I continued to think about it and came with the idea of using earth data to do maps, generating a seed square and generating others based on how likely they are to be adjacent to this other on real earth.

After some amount of time I decided to apply this idea to words and asked the wikipedia it if would easy to create a program like this.

Someone replied, "this program sounds like markov chain generator", then I searched about it and discovered this idea already existed (markov chains).

>>7655421
>I continued to think about it and came with the idea of using earth data to do maps, generating a seed square and generating others based on how likely they are to be adjacent to this other on real earth.

>something after that and before the wikipedia part

I saw this idea was impossible to be done and quit about it, I actually tried to test it with chess board data instead of world data.

Then after it I decided to apply the idea to words and discovered markov chain existed.

In some way world data markov chain is not so stupid/impossible, it would be able to be done with heightmap as some example.


The problem is how averaging of percentage works, and so earth heightmap would need to have at least one height "tile/pixel" that can be adjacent to all others height tiles.

If world dont have this (that is the case), you will have the chance of having a situation where the chance of the height X (X being any possible height) being generated will always be 0

>>7652828
In 4th grade, I had this thing for writing down squares. From noticing that in between each square was an odd number, and with little to no knowledge of algebra I figured out that x^2 +2x + 1 = (x+1)^2 and x^3 + 3x^2 + 3x +1 = (x+1)^3

I thought it was pretty neat at the time.

>>7652828
when I was 12 my friend told me his older brother taught him something and wanted to challenge me during the 15 minute break.
He asked me to find a formula for the sum of all integers between 1 and n.
It took me a few minutes in my head to find (n^2+n)/2, I remember having the idea by computing the sum for n=7 and n=10 (which yields 55).

>>7654904
why does /sci/ denigrate number theory? Once you get out of high school you will realize that there is more to maths than calculus.
>>7654720
Cool discovery bro. I want to get into primes one day. Is it all computers these days? Im currently working on discovering on representing Gelfond's Constant as an infinite sum of algebraic numbers. Obviously if you use the taylor series it will give you a string of pis which is transcendental of course. My autism does not like this, I prefer algebraic numbers, much more relateable.

>>7653615
lol

>>7652828

When I was a junior in HS I was doodling in German class and started dividing successive consecutive Fibonacci numbers by each other. I recognized what they were tending towards from a kid's science book I had, though I didn't understand the property of the number itself. Since I'd known the quadratic formula for a few years I walked it all back and figured out the significance of the number (and its "duals", being its various negatives and reciprocals). Once I had that part, I took my recently-learned trig and came up with something simple but endlessly fascinating:

[math] \phi = 2 \sin(54^ \circ ) [/math]

I had it all scrawled on the same piece of paper; I saved that scrap for years.

>>7655765
I checked with my calculator and this does not equal the golden ratio.

>>7655778
Try again then

For a few weeks id be trying to prove whether or not the speed of light changes between Casmir plates. After reading a few papers and doing so miscellaneous googling, I found that someone had beaten me to the punch.

https://en.m.wikipedia.org/wiki/Scharnhorst_effect

I've been playing around with the idea that this is the actual reason the meme drive works (instead of plates fucking with the vacuum, it's the weird resonance effects in the cavity). I have no way of proving it until I take a course in/teach myself SR and maybe GR, but I'm gonna try to run it past a prof at some point.

>>7655415
He just gave you your picture back with a better resolution. Stop freaking out and start thanking.

>>7652828
>have you ever independently discovered a math theorem or concept

Complements back when I was in the 2nd grade, wasn't until my 2nd year in college that I learned about them in class.

>>7655787
lolz it was in radians my bad.

>>7655722
>Once you get out of high school
There is your answer to your "why"

>>7655778

I wrote the post to which you replied. For the record, this post >>7655787 is not me.

Only one of two things is going on. Either you didn't reset your calculator to handle degrees (most likely), or you are referring to one of the other "duals" of the golden ratio to which I referred above. The RHS of my earlier post is precisely 1.618... , or, the positive number x with the property that x is to one as (x+1) is to x. re-arrangement of this equality gives the quadratic x^2 - x -1 = 0, which also has the negative root -0.618... The negatives of these roots correspond to some similar quadratic, but the defining property of "phi" persists through all of these, plus/minus some fluff about signing.

>>7655415
Filesize.

>>7655765
post a pic of the scrap of paper, or else this didn't happen

>>7655722
>why does /sci/ denigrate number theory?
To be fair, I wouldn't say that collecting prime numbers is the most interesting part of number theory

This may sound stupid but whatever.
As a kid trying to learn linear equations for the first time Ive found Bisection method on my own.
I just estimated the solution and if it wasnt it Ive tried something else and compared the results...

>>7656552
yeah, this

>>7656552
>>7657877

As is implied in the last sentence of my previous post, I tossed the paper out several years ago; once every few years I go through my personal papers (anything from billing statements to old homework) and toss out whatever doesn't make sense to hang onto anymore. I did hang onto it for a few years, though.

I'm flattered that you think enough of what I described to suppose that I might be lying about figuring it out for myself, but I did. Another poster ITT also talked about observations about the golden ratio, pentagrams, etc.

Another thing that I conjectured before this (and also conveniently can't prove :^) was an observation about a standard sum for magic squares, which turned out to be true. I only /conjectured/ it based on the 3x3 and 4x4 case though, I did not /prove/ this thing, it was just another self-discovery like OP was saying. I looked this thing back up, it's called a /magic constant/.

I'm not hot shit, but I've always liked math and had aptitude for it, which is why I went on to major in it.

when I was in 2nd grade I came up with inter-universal teichmüller theory in my head