Elliptic Geometry Puns

How/Why can you construct a model of the hyperbolic plane within the elliptic plane?

https://preview.redd.it/ikghnsn19yv61.jpg?width=2703&format=pjpg&auto=webp&s=6dc4d20d2c27679babb5a8f313536770a11e9801

Gaming in Elliptic Geometry
Laszlo Szirmay-Kalos and Milán Magdics
Eurographics 2021 Short Paper

An interesting way to explore curved spaces is to play games governed by the rules of non-Euclidean geometries. However, modeling tools and game engines are developed with Euclidean geometry in mind. This paper addresses the problem of porting a game from Euclidean to elliptic geometry. We consider primarily the geometric calculations and the transformation pipeline.

EG digilib
PDF in EG digilib

Reading about the trapdoor nature of discrete logs, I understand why trying to find

G^y mod p = x

Is hard, give a base G, discrete log y modulus a large prime p and group element x where x is in Zp*

However, I’m having trouble marrying that concept of generalised discrete logs with the geometric description of ECC.

In ECC we know that the private key is a large integer and the public key is a point on the curve reached by scalar multiplication of the generator point G with the private key integer.

How does that marry with the discrete log hardness. It seems the hardness in ECC is defined by the fact that knowledge of which private integer was used requires trial and error scalar multiplication with guesses until the public point is obtained.

Is the public point analogous to the element x in the first DLP equation I described?

Thank you

Sorry if this is basic.

I tried asking this last week and didn't have any luck, so I'm going to try again.

I know there is a category of elliptic curves, whose objects are elliptic curves over some fixed field K and whose morphisms are isogenies between curves (a function which is both a morphism when considering the curve as a group and also a morphism when considering it as a variety). I've looked for more information on the category itself but haven't found much.

Does this category have things like products, coproducts, exponents, initial/terminal objects, quotients, pullbacks, pushouts, any notable subcategories or supercategories, or endofunctors? And any other interesting property that one might ask if a category has.

I'm an algebraist at heart and I feel knowing the answers to these questions would help my understanding of curves a ton. Thanks!

So today, M'ithra the Hound from Tindalos will be behaving according to elliptical geometry. The surface of a sphere follows elliptic geometry. Today, what is being broken is the Pythagorean theorem- namely, in elliptic space, the interior angles of a triange do not add to a sum of 180 degrees. We are actually operating on elliptical geometry, at a large enough scale. But in our immediate geometry, we perceive a Euclidean existence. M'ithra is kind of limited today in that he can only bend through space. No straight linear movements for him. He's interacting on a different curve, with different intersections, than the sphere of our world's surface. Imagine, if you will, a distorted football that is overlapped with Planet Earth. M'ithra must move along the surface of the foot ball. This means he has a cone of terrestrial interaction. Weirdly enough, he can appear to plunge into the earth at certain latitudes, while at other latitudes he can only interact at high altitudes. Once again, in this instance, M'ithra does not have any parallel lines.

What are some other implications that you can deduct about M'ithra today? What does he look like?

I can't ever seem to get anywhere and walking on the sidewalk is so difficult!

I really want to like algebraic geometry. I’ve read through 1-4 hartshorne and seen various applications to intersection theory (divisors and such), dimension counting on curves (RR), and know that ag is useful in arithmetic problems (etale cohom/Weil conjectures/etc).

However, it feels like there are vast chasms of new terminology / objects / methods between every new application. Often times it feels like I’m spending >50% of my time just learning a language, and the applications seem relatively scant in comparison.

I know that this is not true — i know there’s lots of active research in ag and that it’s central to mathematics, but I don’t know why yet.

TLDR With that being said, what excites you about algebraic geometry? Is there a better way to approach it (application centric)?

Hi! I am currently having my second course on Algebraic Topology and it seems that the further we delve into the topic, the more algebraic it gets. I actually quite enjoy Algebra, so I have no problem with it, but I've been wondering, what would you say is the actual algebra/topology ratio that the branch has?

I am recently reading "Elliptic Curves, Modular Forms, and Their L-functions" and stumbled upon Will Sawin's work and found out that some of his research topics revolves around analytic number theory, algebraic geometry, and étale cohomology (which I think is a word that is rarely seen in analytic NT world).

I know that people use complex analysis in analytic number theory, and that there's the analytic approach to algebraic geometry (I think Griffiths and Harris's "Principles of Algebraic Geometry" is such an example). I was wondering that were you aware of any applications of analytic number theroy to algebraic/arithmetic geometry (elliptic curves included), and vice versa?

(I am aware that analytic number theory seems to use some results from algebraic geometry (bounds from Weil's conjectures) and there are some conjectures, like Manin's, that involves both of them.)

I'm wondering if there's some kind of Cliff's Notes or something, or, at least one, single, good book that would provide the background necessary to understand WTF is going on. I'd say assume a couple semesters of graduate-level abstract algebra, maybe some category theory, and miscellaneous/more specialized topics in group theory.

Sorry if this is OT, since asking for book recommendations is generally frowned on. But this is a specific, non-low effort request, so, I throw myself upon the mercy of the moderators to let this post stand. :P

Ross Coulthart has spoken at length about the reverse engineering cold war happening between the US, China, and Russia, going so far as to say his sources have told him that some scientists working on these US black programs have defected to China.

> "Now I'm not leaping to conclusions when they say they've been involved in a crash retrieval program. I'm not leaping to conclusions that's true. Because one thing you have to take into account as a journalist, and I've been on the receiving end of these before, is deliberate disinformation. A country like America might be at a strategic disadvantage, for example. It might know that, say hypothetically, the Russians have been able to develop some kind of breakthrough in anti-gravitics. Or maybe the Chinese. Maybe somebody who was working for the Americans might have defected to the Chinese. I'm told that they have. And maybe that anti-gravitics technology is now being worked on in the black by the Chinese, and maybe this behind the scenes great race going on of trying to develop this technology before anyone else...maybe that's the reason for the Dr. Salvatore Pais patents."

This AFP article on AOIMSG includes a reference to China’s hypersonic missile test in the last paragraph.

>Last year, the Pentagon released a still inexplicable video taken by navy pilots of objects moving at incredible speeds, spinning and mysteriously disappearing.

>China's July test of a globe-circling hypersonic vehicle that was able to launch a separate missile while traveling at more than five times the speed of sound alerted Washington that Beijing might have technologies the United States has yet to develop.

DefenseOne implies UAP tech is seen in the same light as Russian and Chinese space weapon technology.

>The establishment of the office is important; for years, reports by Navy pilots were dismissed and those aviators were reluctant to discuss the encounters. Bringing the office into the mainstream, where it will coordinate with ODNI and have high-level Joint Staff input, signals that amid new technologies being rapidly fielded by China and Russia, whatever it is that the pilots are seeing out there, the Pentagon want

I graduated with my Master’s in Mathematics last June, and I want something interesting to study in my free time. What are some suggestions for topics or fields to study?

For a bit of context, I specialized in stats and logical problem solving but took graduate coursework in complex geometry, matroid theory, galois theory, and ring theory. I feel like that's a solid primer to casually study a lot of different things, but can’t decide on one.

https://www.researchgate.net/publication/312032093_An_explanation_of_the_de_Vries_formula_for_the_Fine_Structure_Constant

>An explanation of the de Vries formula for the Fine Structure Constant
>
>January 2017
>
>Authors: Luke Kenneth Casson Leighton
>
>Rhombus Tech
>
>The de Vries formula, discovered in 2004, is undeniably accurate to current experimental and theoretical measurements (3.1e-10 to within CODATA 2014's value [1], currently 2.3e-10 relative uncertainty). Its Kolmogorov Complexity is extremely low, and it is as elegant as Euler's Identity formula. Having been discovered by a Silicon Design Engineer, no explanation is offered except for the hint that it is based on the well-recognised first approximation for g/2: 1 + α/2π. Purely taking the occurence of the fine structure constant in the electron: in light of G Poelz [2] and Dr Mills' [4] work, as well as the Ring Model [9] of the early 1900s, this paper offers a tentative explanation for α as being a careful dynamic balanced interrelationship between each radiated loop as emitted from whatever constitutes the "source" of the energy at the heart of the electron. Mills and the original Ring Model use the word "nonradiating" [6] [7] which is is believed to be absolutely critical.
>
>[...]
>
>4 Discussion
>
>The fine structure constant reoccurs in dozens of different places in nature, and is critical to our understanding of the universe, electronics and more. It's remained elusive for such a long time that only has the accuracy of the experimental and theoretical work carried out recently been so high that all other formulae with no sound theoretical background of the past century that also have that critical characteristic of low Kolmogorov Complexity fall away except for one [1]. In 2004 the CODATA values for α were simply not accurate enough, but now, in 2016, to within 7e-11 of the current relative uncertainty of 2014 CODATA [1]

I want to learn more about the geometry, astronomy, and arithmetic of the universe a brother from the grand lodge recommended a book on elliptic geometry but I want knowledge and a deeper understanding. I’m trying to be my lodges JW in the new year to get a deeper understanding of the degrees but I seek knowledge on all of it every part of the lectures, the double meanings that I’ve figured out just everything that I can learn. Please recommend some books that can help me out.

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

Hi.

I've been searching for a simple guide to research topics in Mathematics, but couldn't find one.

So I was just hoping that maybe people here can tell us a little about the field they work in, what are some open questions in your field, how active that field is according to you, who are some of the leading researchers in your field, etc.

Thanks!

The nurse asked the rabbit, “what is your blood type?”

“I am probably a type O” said the rabbit.

The doctor says it terminal.

Alot of great jokes get posted here! However just because you have a joke, doesn't mean it's a dad joke.

THIS IS NOT ABOUT NSFW, THIS IS ABOUT LONG JOKES, BLONDE JOKES, SEXUAL JOKES, KNOCK KNOCK JOKES, POLITICAL JOKES, ETC BEING POSTED IN A DAD JOKE SUB

Try telling these sexual jokes that get posted here, to your kid and see how your spouse likes it.. if that goes well, Try telling one of your friends kid about your sex life being like Coca cola, first it was normal, than light and now zero , and see if the parents are OK with you telling their kid the "dad joke"

I'm not even referencing the NSFW, I'm saying Dad jokes are corny, and sometimes painful, not sexual

So check out r/jokes for all types of jokes

r/unclejokes for dirty jokes

r/3amjokes for real weird and alot of OC

r/cleandadjokes If your really sick of seeing not dad jokes in r/dadjokes

Punchline !

Edit: this is not a post about NSFW , This is about jokes, knock knock jokes, blonde jokes, political jokes etc being posted in a dad joke sub

Edit 2: don't touch the thermostat

Do your worst!

Throughout my studies in analysis, I’ve mostly focused on stochastic analysis and dynamical systems. However, I would like to learn more on what is (imo) one of the most central topics of analysis, PDE. I feel like I still barely know any PDE theory.

So far I know some Sobolev function theory which I gleaned from Evans and various lecture notes. I have also covered chapters 1, 2, 5 and 6 of Evans, as well as Le Dret’s Nonlinear Elliptic Partial Differential Equations, which focuses mainly on variational methods for nonlinear elliptic PDE, and have done some elliptic regularity theory - De Georgi-Nash-Moser theory and Schauder estimates.

As you can see, most of my background is in elliptic PDE. I would like to learn more about different kinds of PDE, most interesting to me right now seems to be dispersive PDE and geometric PDE. However there seems to not be too many resources in these areas. I know of Tao’s text for dispersive PDE, but its beyond my current ability in analysis to tackle. For geometric PDE I am only aware of Aubin’s books which seem good, but maybe a bit dry and unmotivated.

Which brings me to my first question - that is if anyone could recommend some accessible texts/lecture notes in these two areas.

My second, more broad question is how to go further than the standard texts. At least from what I’ve seen, it seems the textbooks don’t get you very far when it comes to PDE. In contrast to, say stochastic analysis, where I feel you can get really far just by reading standard texts. They easily go deep enough for you to reach the research frontier after reading several books. I have been able to get to the point of being able to understand most papers on the arXiv (save for really specialised areas like SPDE and stochastic geometry), and be able to ask and answer interesting questions on MathOverflow.

On the other hand, I feel the textbooks in PDE are far too general and don’t do nearly enough to prepare you for modern PDE theory. Maybe part of it is due to the nature of the subject, I am not sure.

Hope some of the seasoned PDE analysts can help out here. Thanks in advance!

How the hell am I suppose to know when it’s raining in Sweden?

Mathematical puns makes me number

We told her she can lean on us for support. Although, we are going to have to change her driver's license, her height is going down by a foot. I don't want to go too far out on a limb here but it better not be a hack job.

Ants don’t even have the concept fathers, let alone a good dad joke. Keep r/ants out of my r/dadjokes.

But no, seriously. I understand rule 7 is great to have intelligent discussion, but sometimes it feels like 1 in 10 posts here is someone getting upset about the jokes on this sub. Let the mods deal with it, they regulate the sub.

They were cooked in Greece.

I'm surprised it hasn't decade.

He lost May

Now that I listen to albums, I hardly ever leave the house.

Hey babe, are you Cohen-Macaulay? Cause despite your flaws you're gorgeous ❤

Hey dear, you're Gorgeous, you're singularities are so cute and Gorenstein

If you were an abelian variety, then your son is a very cute good reduction for you

Learn to be proper in your way of talking like an elliptic curve over an algebraicly closed field

You're curvier than the Gaussian distribution

Your face is uglier than the graph of van der Waerden function, you're so dense

You're so picky even more than the Picard function of an hyperelliptic curve

Crossing the road is as normal as a relative normal crossing divisor for the étale topology

Deeply, some mean and harsh people can be kind if you work on the étale topology

My girlfriend might be flat but she's faithful and represents love and kindness, she's a sheaf on the faithful flat locally of finite presentation (fppf) site of schemes

You chest is such a stack, it fits in the infinitly beautiful categories

Personnaly i'll make out with anyone who brings up algebraic geometry on our first date 🥰

I tried to install EGSnrc on my HP Windows 10 Laptop (Windows version 10.0.19043) using MinGW 7.3.0 and ran into 2 Failures:

Compiling C++ Library - Compilation Failed

Compiling dosxyznrc_win3264.F - Compilation Failed

The Log file shows both Failures contain many statements "No such file or directory".

I tried using MniGW 6.3.0 but had the same Failures.

I used Git to clone the EGSnrc repository.

Any help would be appreciated!!

Pertinent parts of the log file follows (I deleted many lines dealing with copying files).

--------------------------------------------------

GNU Fortran (x86_64-posix-seh-rev0, Built by MinGW-W64 project) 7.3.0

Using xml test file C:\EGSnrc\HEN_HOUSE\pieces\tests_win.xml

===> Checking for availability of system dependent functions

gfortran -c -o HasObject.obj HasObject.f

gfortran -fPIC -o DoesExe.exe DoesExe.f

gfortran -fPIC -o ExitFun.exe ExitFun.f

./ExitFun.exe 1

exit

Exit code is 1

Reference is 1

./ExitFun.exe 5

exit

Exit code is 5

Reference is 5

./ExitFun.exe 25

exit

Exit code is 25

Reference is 25

gcc -c -o egs_exit.obj egs_exit.c

egs_exit.c: In function 'my_exit':

egs_exit.c:7:4: warning: implicit declaration of function 'exit' [-Wimplicit-function-declaration]

exit(s);

^~~~

egs_exit.c:7:4: warning: incompatible implicit declaration of built-in function 'exit'

egs_exit.c:7:4: note: include '<stdlib.h>' or provide a declaration of 'exit'

gfortran -fPIC -o SystemFun.exe SystemFun.f

./SystemFun.exe 0

0

Exit code is 0

Reference is 0

output:0

reference:0

gfortran -fPIC -o SystemFun.exe SystemFun.f

./SystemFun.exe 1

1

Exit code is 0

Reference is 1

output:1

reference:1

gfortran -fPIC -o FlushFun.exe FlushFun.f

./FlushFun.exe 0

flush

Exit code is 0

Reference is 0

gfortran -fPIC -o DateAndTime.exe DateAndTime.f

gfortran -fPIC -o FDateFun.exe FDateFun.f

./FDateFun.exe 0

fdate

Exit code is 0

Reference is 0

gfortran -fPIC -o SecndsFun.exe SecndsFun.f

./SecndsFun.exe 0

secnds

Exit code is 0

Reference is 0

gfortran -fPIC -o DateFun.exe DateFun.f

C:\Users\AS\AppData\Local\Temp\ccGgPzGN.o:DateFun.f:(.text+0x20): undefined reference to `date_'

collect2.exe: error: ld returned 1 exit status

gfortran -fPIC -o DateFun.exe DateFun.f

C:\Users\AS\AppData\Local\Temp\ccqSEXcu.o:DateFun.f:(.text+0x20): undefined reference to `date__'

collect2.exe: error: ld

Two muffins are in an oven, one muffin looks at the other and says "is it just me, or is it hot in here?"

Then the other muffin says "AHH, TALKING MUFFIN!!!"

Don't you know a good pun is its own reword?

I know there is a category of elliptic curves, whose objects are elliptic curves over some fixed field K and whose morphisms are isogenies between curves (a function which is both a morphism when considering the curve as a group and also a morphism when considering it as a variety). I've looked for more information on the category itself but haven't found much.

Does this category have things like products, coproducts, exponents, initial/terminal objects, quotients, pullbacks, pushouts, any notable subcategories or supercategories, or endofunctors? And any other interesting property that one might ask if a category has.

I'm an algebraist at heart and I feel knowing the answers to these questions would help my understanding of curves a ton. Thanks!