Is there anyone on /sci/ who isn't a student? I've

>>8420147
No. /sci/ is getting deleted soon anyway so who gives a fuck.

Donate or die.

>>8420147
Nope. This board used to be for neets and wagecucks who liked to do math in their spare time. The reddit invasion brought with it tons of autistic undergrads.

I...I enjoy the complicated things. But it's too early for much of a turn out.

>>8420147

I'm a PhD student so that's like the least annoying type of student at least.

>>8420228
That's probably because you guys are rarely out.

>>8420194
I'm a wagecuck who likes to do math in their spare time. We're still here we're just drowned out by the newfags.

>>8420147

I am currently not a student in the conventional sense that you meant it, i.e. I am not currently enrolled in a school or uni of any kind, I am not taking formal official classes with formal official grades, etc. I did however complete a bachelor's with a math major, several years ago.

>>8420194

I am part of the former category, (was NEET for a few years, am now a wagecuck again), and I've been rediscovering math over the past few years since I've actually had some spare time to myself. The things that I've been interested in are pretty low-tier but here they are. I've developed simple ideas or easy research projects, self-taught them, and "created product" in the form of /sci/ threads. In other words I've written at length about what I've learned, which helps to internalize the ideas.

At the moment I'm more interested in the /history/ of mathematics. Here are some archived threads that I've driven to some state of completion.

My little projects have been:

solving the cubic, https://warosu.org/sci/thread/7529602

solving the quartic, https://warosu.org/sci/thread/7613239

Writing up a short exposition of the Rhind Papyrus, an ancient (and sometimes confused) example of Egyptian mathematics. First I made this old thread to get my arms around the document, and some months later I massively overhauled the wiki with a modern paraphrase of the document (the bottom 80% of the page), and corrections to existing issues with the page.

https://warosu.org/sci/thread/S8027713

https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus#Content

Future projects will include actually reading Cardano's Ars Magna to understand the tedium of his various cases (which are superfluous from the modern standpoint), and going through Euclid.

>>8421093
Kek, I was there for the cubic one.

Im air force.

But i do university part time too so i guess i fall into the school group

>>8420147
OK so you haven't known 4Chan for long enough or just haven't really figured it out that the majority of people here aren't open minded people looking for discussion, it's just annoying shitposters, bait, opinionated assholes, elitists, retards, etc. And none of those people allow for a good discussion. This also kinda has to do with everyone being a student because anyone older than that doesn't have time for this shit and is probably more mature.

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>>8420147

>I've only recently started checking this board regularly

Welcome to hell. Please enjoy your stay.

>>8421119

I was rather proud of getting this into a single post, so I'll post it again.

"...In the interest of sheer autism, we present [the explicit solutions x to ax^3 + bx^2 + cx + d = 0]...

[math] \displaystyle x = \bigg( - \frac{1}{3a} \bigg) \sqrt[3]{ \frac{1}{2} \bigg( 27a^2 d - 9abc + 2b^3 + \sqrt{ 729a^4 d^2 - 486a^3 bcd + 108a^3 c^3 + 108a^2 b^3 d - 27a^2 b^2 c^2 } \bigg) } + \bigg( - \frac{1}{3a} \bigg) \sqrt[3]{ \frac{1}{2} \bigg( 27a^2 d - 9abc + 2b^3 - \sqrt{ 729a^4 d^2 - 486a^3 bcd + 108a^3 c^3 + 108a^2 b^3 d - 27a^2 b^2 c^2 } \bigg) } - \frac{b}{3a} [/math]

[math] \displaystyle x = \bigg( \frac{ 1 + \sqrt{3} i }{6a} \bigg) \sqrt[3]{ \frac{1}{2} \bigg( 27a^2 d - 9abc + 2b^3 + \sqrt{ 729a^4 d^2 - 486a^3 bcd + 108a^3 c^3 + 108a^2 b^3 d - 27a^2 b^2 c^2 } \bigg) } + \bigg( \frac{ 1 - \sqrt{3} i }{6a} \bigg) \sqrt[3]{ \frac{1}{2} \bigg( 27a^2 d - 9abc + 2b^3 - \sqrt{ 729a^4 d^2 - 486a^3 bcd + 108a^3 c^3 + 108a^2 b^3 d - 27a^2 b^2 c^2 } \bigg) } - \frac{b}{3a} [/math]

[math] \displaystyle x = \bigg( \frac{ 1 - \sqrt{3} i }{6a} \bigg) \sqrt[3]{ \frac{1}{2} \bigg( 27a^2 d - 9abc + 2b^3 + \sqrt{ 729a^4 d^2 - 486a^3 bcd + 108a^3 c^3 + 108a^2 b^3 d - 27a^2 b^2 c^2 } \bigg) } + \bigg( \frac{ 1 + \sqrt{3} i }{6a} \bigg) \sqrt[3]{ \frac{1}{2} \bigg( 27a^2 d - 9abc + 2b^3 - \sqrt{ 729a^4 d^2 - 486a^3 bcd + 108a^3 c^3 + 108a^2 b^3 d - 27a^2 b^2 c^2 } \bigg) } - \frac{b}{3a} [/math]

If you tape two 8.5"x11" papers together long-ways, it's just enough room to write all this legibly by hand, with some explanation as well."

There are apparently certain issues with this form in the situation where the coefficients a-d are complex, but I haven't appreciated why that is. It is still the "nicest" form in this explicit treatment, not involving ugliness in a denominator, which another form entails.

>>8421208
What's the significance of i?
If the roots are imaginary then there's no real solution so why solve for it?

I'm a biologist with the Forest Service, graduated a few years ago

>>8421218
ebin troll

>>8421208
I wish the archives would keep TeX formatting so I could re-read it.

>>8421218
The real question is, if there are 3 real solutions for our cubic polynominal, do we still need sqrt(-1)? The answer is yes
http://www.pucrs.br/famat/viali/tic_literatura/livros/Paul%20J.%20Nahin%20-%20An%20Imaginary%20Tale%20The%20Story%20of%20i%20the%20Square%20Root%20of%20Minus%20One.pdf
(check page 18)

>>8420228
Totally agree. My favourite audience here is actually graduate students.

>>8420194
NEET isn't a good thing usually. Without guidance people do autistic shit like this >>8421208 and actually think they're doing something significant / develop effectively. But in fact they just work on something they recall from institutions they've been before (in this case it was school) and try to do something with that.

>>8421260
*high-school

>>8421218
Aside from OP's total waste of time, it's a 3rd order polynomial, so it's guaranteed to have at least one real root/solution (the first in the list given). The other two, although they have "i" shown, might be such that the imaginary parts cancel out, giving two extra real roots. For example $\x^3-x=0$ has 3 real roots.

>>8420147

I'm a NEET college dropout

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>>8421260

Your insult is unwarranted in that by reading my above posts, it is clear that I am aware of not doing (contemporary, relevant) /math/ as such. This is also why I qualified my recent activity as being a study of the /history/ of math, which I have taken up again above all as a personal amusement.

However, I would go a step further and correctly observe that even your central premise is (partly) false, thus contradicting the first part just a little bit, and only to a certain modest point. Specifically, working through the derivations themselves and appreciating why they are the way they are is a properly mathematical activity, even if not "particularly useful or interesting" by modern standards. But of course the

Writing about this has reminded me of something else I was doing, which vaguely prompted the reviewing of cubics/quartics as an exercise. I proved a few simple lemmas relating to Euler bricks and perfect cuboids, and I scratched the surface of the literature just a little bit to see if anyone had made like observations, and I did not see any.

However, I did find an interesting note by Nyblom on Almost-Isosceles Right Triangles and their 1-1 correspondence to square triangular numbers, which marries up with later information in Sierpinski's "Pythogorean Triangles" which has certain implications for Euler Bricks and (conjectured) Perfect Cuboids.

The spot where I left off was to compare the logical possibilities of a given Euler Bricks' various lengths and diagonals {a-f} where a-c are the shortest-longest edge lengths, d-f the shortest-longest face diagonals and g the spatial diagonal. I was able to establish a series of inequalities by simple logic but the simple fact that it is possible that c>d or c<d (examples of both exist) left me stuck, about the incomplete white cells in pic related.

The idea of the above has been to build up a basic toolkit of knowledge about Euler Bricks/Perfect Cuboids.

https://warosu.org/sci/thread/7437394

>>8420147
whether we've graduated or not, we're all students. the learning doesn't stop once you get the piece of paper. the fact that we have undergrads coming here expressing even some marginal intellectual curiosity is quite heartening and should be encouraged. the future is in the young and unlearned.

>>8421323

Admittedly the link contains a rather long-winded observation about how a point has 48 counterparts in R^3 (permute the components + changes of sign), which seems pointless at first, but now I'm remembering that thinking about it in this geometric fashion led me to question whether it might happen that c=d, which would imply certain geometric conditions in my thing (certain points never rest on certain lines of a triangular face, or the faces of an octahedron). The point being to try to add some more restrictions-information to the knowledge base.

These were the little lemmas that I came up with regarding Euler bricks:

Definition: An Euler Brick is a rectangular prism, or "ordinary box" having edge lengths a,b,c, face diagonals d,e,f and spatial diagonal g.

1) No two edge lengths are equal. pf. pythagorean theorem and irrationality of √2.

(Q: why bother observing this/motivation? A: a-c can be unambiguously classified as "short-middle-long", going forward. We can speak of a given brick with some more specificity)

2) No Euler Brick has a unit edge. pf. reductio ad absurdum, square numbers are sums of odd numbers/slight series manipulation.

(Why? A: IIRC this was to be able to establish strict inequalities about a-g as opposed to non-strict inequalities.)

3) c may be less than d and vice verse. pf. inspect the brick with edge lengths (240,252,275) versus the brick with edge lengths (44,117,240). Incidentally there are other distinct examples.

4) No two face diagonals are equal, and they correspond to a-c in the expected ways. pf. this "looks" obvious enough but for the actual proof, use 1) + 2) and manipulate certain equalities and inequalities.

5) (my octahedron autism in the link, which actually did lead to at least one insight about comparing c with d geometrically): The 48 versions of an EB in R^3 have endpoints on the faces of a regular octahedron which has the six vertices "("a+b+c",...etc)". pf describe planes in space.

>>8421174
I'll be in the same boat a little while after I finish my CDCs and qualification training.
>>8420176
This
>>8421208
lol nice! "ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0" next? Hows about a generalization for all single variable polynomials of 'n' degree like the one you have for third degree?

6) is where I left off. The conjecture is, "For a given Euler Brick {a-g}, the components a-g^2 always satisfy the followign table of inequalities." This corresponds to the above table.

pf. I carried the exercise up to a certain point, stopping around about the last 25% of situations.

If anyone would care for me to back up/elaborate, let me know.

>>8421379

Bring radicals, galois theory and the quintic+ are all outside my knowledge at this point, although I want to move in that direction longer term. I became aware of the former in the course of this, though of course I have been aware that "galois theory is a thing" for years.

General issues that I had in the above elementary algebra derivations were that I did not appreciate what a "resolvent cubic" is in my specific situation, to my satisfaction (let alone at all). I would also need to review "real/intermediate" (college, modern, abstract) algebra to make sense of the above. Also going back to the general notion of "solving P polynomial", I reviewed some terminology and realized that a certain translation shows up in all the lower cases, and moreover can even be applied to any such polynomial above the quartic, though as it has been Handed Down to me, such will not result in Algebraic Solutions in the higher-degree cases.

I am referring to a special case of a Tschirnhausen transformation which turns out to be applicable to all monic polynomial equations, regardless of their degree, but which can be uniformly applied as one of the first few steps in an algorithm for solving those polynomial equations (deg 1-4) for which Algebraic Solutions (which is a very specific, well-defined piece of terminlogy that only admits of basic arithmetic operations in a solutions' expression, and nothing more elaborate than that) exist. The idea of /describing/ such an algorithm, unifying this finite case, is part of the motivation here. Somewhere in this I had some thing going about the binomial theorem and nesting series to prove something else relating to this (specifically that the substitution always gives a depressed polynomial regardless of degree), but I leave that aside.

>>8420147
18yo homeschooled here, gonna go to uni when i'm 20.

>>8421175
>haven't known 4Chan for long
>4Chan
uhh...

I browsed /sci/ when I was self studying physics

Now I am in college for physics, because naturally if you have a big enough interest in science and math and youre still young, you should go to where the research is happening.

>>8421093
Shit, I remember you from the quartic threads (I was the guy that asked about the complex coefficients, and creator of the quartic-solving flowchart in https://warosu.org/sci/thread/S6469697).
Perhaps it may give you some inspiration for the issues you brought up in >>8421426?

Was student then, also a wagecuck now (computer "scientist").

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>>8422738

Hey thanks for the link. I knew that someone had made such a flowchart, although you did seem to be having some troubles in the thread. :^)

Your basic "first two steps of-the-algorithm", signified by the red arrows in your link, is correct: divide by leading coefficient (trivial), and then make the appropriate Tschirnhaus transformation (non-trivial). I would instead say that your algorithm could be "unified" (this is not the mathematically significant bit, just a piece of bookkeeping I've preferred) by always specifying particular symbols for the coefficients of the respective polynomials, and then phrasing the general transform in terms of those common, "standardized" symbols for the coefficients. Then you could simply write two red arrows (with some further re-arrangement) as opposed to the 7-8 in your pic.

>>8423360
By 'Tschirnhaus transformation', do you mean the x = t - b/(na) step described in https://proofwiki.org/wiki/Tschirnhaus_Transformation?

My inner stats major isn't convinced that this operation is non-trivial ("it's basically normalization! you learn that in the first week of stats 101!"); personally I'm more interested in the version as defined by Mathematica:

http://mathworld.wolfram.com/TschirnhausenTransformation.html
>A transformation of f(x)=0 which is of the form y=g(x)/h(x) and h(x) does not vanish at a root of f(x)=0

This definition seems to generalize the rest of the flowchart, i.e. the more complicated substitutions involved in the cubic and quartic solutions. I'd even go so far as to conjecture that there exists an algorithm for solving a polynomial equation using nothing but 'generalized' Tschirnhaus transformations (though the solutions will only be algebraic if the degree is <= 4).
Unfortunately I have neither the time nor autism to pursue this in detail, but I think it's a promising approach and I'd definitely follow up on it if I were in your shoes.

>>8423495

Correct. As to the /triviality/ of the step, I suppose that it is at least somewhat subjective.

You're also right about the algorithm (I basically said as much), but it simply involves, let's say, about ten programmatic steps later in the case of the cubic and another 20 or so in the case of the quartic.

The corresponding transforms are also used to solve certain /specific/ cases of higher degree polynomial equations. see the wiki on the quintic for an example of this in a form familiar to my jargon.

>>8420176
b--but... why would they delete the beat board?

I graduated with a BS in ME a while ago. I always came around for the mathematics. I actually learned variational and tensor calculus because of the recommendations of this board.

Also I got a trip to Texas and met a lot of awesome people because of /sci/... so yeah, this is the best board.

>>8420147
Me.

>Aren't there any posters who just post here because they're interested in science and math?
Yes.

>>8420228
Chem Eng PhD student?