Hey, first time posting here.
I'm studying Game Programming and for my current assignment I have to procedurally generate... mushrooms! I am already able to [URL="https://raw.githubusercontent.com/swiebertjee/Mushroom-Generation/master/Assets/Scripts/Mushroom.cs"]generate[/URL] a cylindrical mesh which I can completely transform in the shape of a mushroom.
The point of the assignment is to generate different looking mushrooms by changing certain parameters, like hood size, hood roundness, stem curvature, etc. I was thinking of using a mathematical formula to literally plot the shape. With that I mean
X is the distance from the base of the mushroom to the tip.
Y is the distance from the center of the mushroom to the outer wall.
To give you guys an idea:
[IMG]https://s28.postimg.org/xkhyno919/mushroom.jpg[/IMG]
I'll (hopefully) finish my assignment tomorrow, so if someone would like to see pretty mushrooms: all help is welcome!
[QUOTE=JohnnyMo1;52611977]Guess there are no other set theorists on here :v:[/QUOTE]
I'm taking baby's first set theory in a few weeks, that counts right?
I need to write a relation that is reflexive and symmetric, but not transitive. Is this correct?
[img]http://i.imgur.com/HuBJ20t.png[/img]
[QUOTE=proboardslol;52630649]I need to write a relation that is reflexive and symmetric, but not transitive. Is this correct?
[img]http://i.imgur.com/HuBJ20t.png[/img][/QUOTE]
That doesn't even make sense. First off, the D you defined is Z^2 -> N. Even then, the properties that you're looking for only make sense for relations within one set, not between two different sets.
Were you gonna use that function to create a proper relation that has those properties and you just didn't write it down fully, or is there something you don't understand?
[QUOTE=pebkac;52630829]That doesn't even make sense. First off, the D you defined is Z^2 -> N. Even then, the properties that you're looking for only make sense for relations within one set, not between two different sets.
Were you gonna use that function to create a proper relation that has those properties and you just didn't write it down fully, or is there something you don't understand?[/QUOTE]
I guess the notation is wrong? D is a relationship between two sets such that D(a, b) = |a - b|. I realize now that a relation is a boolean expression though...
[editline]30th August 2017[/editline]
Yeah I realize now I'm getting this shit all wrong. God I hate the theory portion of CS classes
[QUOTE=proboardslol;52630837]I guess the notation is wrong? D is a relationship between two sets such that D(a, b) = |a - b|. I realize now that a relation is a boolean expression though...
[editline]30th August 2017[/editline]
Yeah I realize now I'm getting this shit all wrong. God I hate the theory portion of CS classes[/QUOTE]
Well, a function is still a relation, just try not to think of relations in general in such narrow terms. A relation is basically just a subset of all possible ordered pairs of elements from two sets. You just have to define a condition, the pairs that pass it will be part of the relation, and the others won't. For example, if your set is {1,2,3}, and your condition is "less than", then the relation will be {(1,2), (2,3), (1,3)}
A function is just a special case of a relation where each element of the first set is related with exactly one element of the second set.
Your function D isn't quite what you're looking for though. It can't be reflexive, symmetric, or transitive, because those properties require the sets on both sides of the relation to be the same. You could however use that function to define another relation, for example R = {(x,y) | x and y are integers and D(x,y) is even}. This particular relation is still transitive, but you get the idea.
Categories in a condensed matter physics paper:
[url]https://arxiv.org/abs/1709.01941[/url]
I feel like I have now seen everything, and I am now also allowed to like condensed matter.
(I still won't tho)
hi math men, are there any good online resources for basic level engineering mathematics? probably around A Level maths in the UK. I haven't done any proper maths in a few years now so it'd be worth starting there for a refresh because it feels like skipping over that stuff instead of revising it is hurting me higher up That included basic-intermediate calculus, binomial theorem, trig identities and all that. Fundamental stuff.
I've got [I]Engineering Mathematics[/I] by K.A. Stroud but I can't tell where to jump in because it doesn't progress at all like the A Level course did.
ta
[editline].[/editline]
no matter, I just ran through the book until I reached a place I was unfamiliar with. The OP resources have helped after passing that point.
Working on developing a PDE model for the following problem, was just wondering if it was correct.
It's a conservation law involving the flow of nutrients through a tube, where the density is n = n(x, t) flowing through the tube at velocity c, being absorbed through the tract at a rate proportional to √n.
I'm thinking the model is:
dn/dt + c(dn/dx) = -k√n
Solvable with the method of characteristics, with the curves being xi = x - ct, and tau = t, giving n(x, t) = N(xi, tau) and
dN/d(tau) + k√N = 0
Does this sound correct?
Voevodsky died. Everyone learn homotopy type theory in his honor:
[url]https://homotopytypetheory.org/book/[/url]
Question for anyone finished up with their calculus courses that have went into later math courses: how much more abstract/difficult does it get to build a geometric intuition around some of the newer concepts you learn in like say, linear algebra? I like that in most of the math I've taken so far that if you can get a solid geometric sense of some concept, it really helps out to understand whats going on. later course concepts seem to me like they won't allow for that as much, but I don't know.
[QUOTE=SickBow;52742969]Question for anyone finished up with their calculus courses that have went into later math courses: how much more abstract/difficult does it get to build a geometric intuition around some of the newer concepts you learn in like say, linear algebra? I like that in most of the math I've taken so far that if you can get a solid geometric sense of some concept, it really helps out to understand whats going on. later course concepts seem to me like they won't allow for that as much, but I don't know.[/QUOTE]
I am well beyond linear algebra and I still rely on geometric intuition a lot. It takes working with the concepts for a while to build it up, but linear algebra is still quite concrete and intuitive (at least for finite-dimensional spaces!).
[editline]3rd October 2017[/editline]
Generally I find the process goes like this:
-Learn about some sort of fancy new geometric machinery (e.g. topological spaces)
-Read the definition and fundamentals.
-Go "what the fuck is this doing I don't understand these things at all"
-Prove some basic shit using the definitions
-See how the examples I know of already are subsumed by the new thing, and figure out which parts of your current mental model still work so you can get a feel for what to picture
Rinse and repeat at the next level of abstraction.
Does anyone have any advice on how to write a real research paper?
I am going to be listed as first author on this research paper my group is working on, and as a result I am going to be the one that writes it. It is in biophysics, and it would be my first "big boy" paper, and I am quite intimidated by needing to write it. Any super general tips on what to do/what not to do?
We are hoping to publish in the Journal of the American Chemical Society, which is one of the bigger journals, which is why I am pretty intimidated lmao
Congrats! Look at the structure of a bunch of other papers. If you're going to be submitting to a particular journal, look at similar papers from that journal.
I'm trying to find the surface area of a donut (Torus), using this formula: [IMG]https://i.imgur.com/qulrF3n.png[/IMG]
The diameter of the hole in the middle is to be 2, and its thickness is also 2.
I figured the arc-length of the donut would be the circumference of its cross-section. Thus, the area of the torus should be 2pi times the integral of |x| times its arc length, from 1 to 3.
however, this yields double the area. Any idea why?
[QUOTE=Garry #2;52753756]Does anyone have any advice on how to write a real research paper?
I am going to be listed as first author on this research paper my group is working on, and as a result I am going to be the one that writes it. It is in biophysics, and it would be my first "big boy" paper, and I am quite intimidated by needing to write it. Any super general tips on what to do/what not to do?
We are hoping to publish in the Journal of the American Chemical Society, which is one of the bigger journals, which is why I am pretty intimidated lmao[/QUOTE]
[url=https://link.springer.com/article/10.1007/s40037-015-0211-y]Problem-Gap-Hook[/url]
[QUOTE=Number-41;52755576][url=https://link.springer.com/article/10.1007/s40037-015-0211-y]Problem-Gap-Hook[/url][/QUOTE]
This was actually a very interesting read. Thanks!
I'm doing my project on Radical Ideals. Wondered if you people had any niche things I could talk about application wise. Just looking for some meaty examples of where this area of study will take you.
[QUOTE=dingusnin;52802732]I'm doing my project on Radical Ideals. Wondered if you people had any niche things I could talk about application wise. Just looking for some meaty examples of where this area of study will take you.[/QUOTE]
Did you have an idea what you wanted to talk about already?
[editline]20th October 2017[/editline]
I ask because my immediate suggestion would be application: all of algebraic geometry (via the Nullstellensatz) but that’s so far reaching and well known I’d be surprised if you weren’t already going to discuss it.
Unrelated to the above: these lectures are really cool, especially the first two
[url]https://arxiv.org/abs/math/0608420[/url]
Would you guys consider math to be something we created or discovered?
Can anyone help me figure out how to get a rather complex non-spherical non-uniform mass distribution geopotential model translated to code? I'm super stuck. It's all based on [URL="https://en.wikipedia.org/wiki/Gravity_Recovery_and_Interior_Laboratory"]GRAIL mission data[/URL] (coefficients for the model) and I'm implementing this as part of a NASA contract - so it's not like I can find much example code or input on this.
[url]http://www.ltas-vis.ulg.ac.be/cmsms/uploads/File/GoddardTrajectorySystem.pdf[/url]
I'm trying to implement the formulae from 4-10: in particular, 4-38 a, b, and c. I don't think I'm properly understanding any of this. There's a whole bunch of small things that are getting me.
- Equation's 4-34a,b,c: What happens when m is zero? As far as I have this implemented, that can happen. but are negative numbers for m okay? I feel like I'm misinterpreting this. This is what I do, and there's no way this is right:
[cpp]
Number grgm900c::cos_m_lambda(const size_t & m, const Number & longitude) {
return static_cast<Number>(((2.0 * std::cos(longitude)) * cos_m_lambda(m - 1, longitude)) - cos_m_lambda(m - 2, longitude));
}
[/cpp]
- Equation 4-31b has an "X" as the operator between the two main elements of this inner summation. This couldn't be a cross product, could it? I implemented it as just regular 'ol multiplication but I might be really far off base
- sorry for posting so much code and asking so much in general - but, I have implemented the Legendre polynomial as such and I feel fairly good about it, but I'm still guessing I'm not grasping the syntax and structure of this math at all:
[cpp]
Number grgm900c::__lft::operator()(const size_t& M, const size_t& N) const noexcept {
/* m < n, m != 0
_lft(m, n - 2, latitude) + (2n - 1)cos(latitude) * _lft(m - 1, n - 1, latitude)
numerator_a numerator_b numerator_c
*/
if (M != 0 && M < N) {
const Number numerator_a = this->operator()(M, N - 2); // this->operator()(M,N) is just a recursive call to this very method with a different M and N
const Number numerator_b = static_cast<Number>((2 * N) - 1) * std::cos(latitude);
const Number numerator_c = this->operator()(M - 1, N - 1);
return numerator_a + (numerator_b * numerator_c);
}
else if (M == N && M != 0) {
const Number numerator_a = static_cast<Number>((2 * N) - 1) * std::cos(latitude);
return numerator_a * this->operator()(N - 1, N - 1);
}
else if (M == 0 && N > 1) {
const Number numerator_a = static_cast<Number>((2 * N) - 1) * std::sin(latitude);
const Number numerator_b = this->operator()(0, N - 1);
const Number numerator_c = static_cast<Number>(N - 1) * (this->operator()(0, N - 2));
return (numerator_a * numerator_b - numerator_c) / static_cast<Number>(N);
}
else if (M == 0 && N == 1) {
return std::sin(latitude);
}
else {
return 1.0;
}
}
[/cpp]
This stuff is seriously breaking my head: trajectory planning is pretty goddamn hard, and part of this contract is doing some [I]wild[/I] stuff. Any help would be super super appreciated, even if it's just a link that effectively states "Read the fucking manual, dude". I really quite enjoy differential equations and the like, but this is a hilariously huge leap from the kind of stuff I've done in the past. Times like this make me wish I had had the time to get further on my physics/math fallback degree before taking this fulltime position. I feel completely unprepared and incapable of working with the piles of brilliant people I'm surrounded by ;~;
[QUOTE=Shakma;52828152]Would you guys consider math to be something we created or discovered?[/QUOTE]
I consider it to be some of both, though mostly discovered. Axioms are created, in some sense. Their consequences are discovered.
[QUOTE=JohnnyMo1;52828732]I consider it to be some of both, though mostly discovered. Axioms are created, in some sense. Their consequences are discovered.[/QUOTE]
would it be fair to say we also discover serious refinements? thats at least what I've been running into. Astrodynamics seems to be an endless warren of "hey we sorta solved this model/proble... ah, fuck nvm". Like how Poincaré's work on the three-body problem led to the initial thoughts on chaos theory, and opened up a whole new world of mathematics.
We certainly didn't create it, since the dynamics of celestial bodies have existed for ages, but we took time to discover how to define their motion. Now we use things like perturbation theory to break down the "technically" unsolveable solution of spacecraft trajectories into components, considering everything from the gravitational influence of most of the bodies in the solar system to the solar radiation pressure on a spacecraft's surface
I find this stuff really really cool, and it makes me wish I could utilize it more effectively in my work
[QUOTE=paindoc;52828790]We certainly didn't create it, since the dynamics of celestial bodies have existed for ages, but we took time to discover how to define their motion. [/QUOTE]
That's a philosophical position, though. Does mathematics in the abstract define the motions of celestial bodies, or are mathematical descriptions of planetary motion just a useful but human-created model of nature?
[QUOTE=JohnnyMo1;52829031]That's a philosophical position, though. Does mathematics in the abstract define the motions of celestial bodies, or are mathematical descriptions of planetary motion just a useful but human-created model of nature?[/QUOTE]
JohnnyMo1 pls I'm already hurting trying to grasp the math I posted about, please don't hurt me more (good point, though)
I'd say that math is purely constructed. It is modeled after the natural world, and many of it's consequences were motivated by real world problems, but the study of math is based completely on constructed axioms and is thus constructed in nature.
This start to fall into an epistemological argument about whether we can say that those axioms were made simply as a reflection of nature, but I'd argue those axioms are independent of our belief of nature as something like the axiom of regularity in ZF set theory is hard to justify as something intrinsic to the world (or at least it is hard to say it was was chosen in such a way to describe nature).
I'm not a fan of epistemology though so I haven't studies this much but that's my two cents
[url]http://www.ems-ph.org/journals/show_abstract.php?issn=2308-2151&vol=4&iss=2&rank=3[/url]
[url]http://wwwinfo.deis.unical.it/yaro/EMSS_Sergeyev.pdf[/url] <- The paper
This is funny and sad at the same time.
[QUOTE=Swamplord;52981656][url]http://www.ems-ph.org/journals/show_abstract.php?issn=2308-2151&vol=4&iss=2&rank=3[/url]
[url]http://wwwinfo.deis.unical.it/yaro/EMSS_Sergeyev.pdf[/url] <- The paper
This is funny and sad at the same time.[/QUOTE]
The editors-in-chief of that journal have stepped down over this, as I understand.
Can anyone sort of “generalize” the Fourier Transform mathematically? As in, what does it mean to take a Fourier transform? Is it basically changing the units to their inverse counterpart? Like in my EE classes it’s of course used to go between the time and frequency domain, but I’ve also been introduced to it in my physics classes as a method between the normal spatial domain (meters) and k-space? (Inverse meters)
The wiki seems to only talk about it in terms of the EE application, obviously given it has the most application in that field.
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