this post was submitted on 26 May 2025
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traaaaaaannnnnnnnnns

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I’m back! It’s been a while since I’ve been on this site because I’ve found myself under some financial trouble and I’ve been stressed BUT I wanted to take this opportunity to talk about something I love dearly: dihedral groups!

Consider the symmetries of a square:

We can see that there are 4 reflections and 3 rotations, as well as the act of doing nothing at all. Together, we have 8 total symmetries, and in fact, these are all of the possible symmetries. What this means is that if we do one of these symmetric moves and then do another one, we will have not changed the square, and therefore doing these two moves is the same as doing just one of the 8 symmetries on its own. For example, doing a 90 degree rotation followed by a 180 degree rotation is the same as doing a 270 degree rotation. Also, doing a 90 degree rotation followed by a reflection across the vertical axis is the same as doing a reflection across a diagonal axis.

So in other words, we can define a function that takes two symmetries of a square as input and which outputs another symmetry. Since standard multiplication is a function taking two numbers and outputting another number, it makes sense to borrow the notation of multiplication for this function. Our symmetry function satisfies a few useful properties:

  • Closure: As explained above, for any two symmetries, the function will spit out another symmetry
  • Identity: There is a symmetry (namely, the “do nothing” symmetry) such that when it is input into the function with another symmetry, the function will always simply output the other symmetry
  • Associativity: For any symmetries a, b, and c, (ab)c = a(bc)
  • Inverses: For every symmetry, there is a symmetry that undoes it. For example, rotating a square by 270 degrees undoes rotating it by 90 degrees, and doing a reflection a second time after doing it once undoes the first reflection

These 4 properties are so important that any set of objects with a function defined on it that satisfies all of these properties has a special name: they’re called groups and they’re really freaking awesome. The symmetries of a square as a group is called D~8~, since there are 8 total symmetries. Sometimes you might see it called D~4~, since squares have 4 sides, but I think this convention is a bit silly. In the same way, D~6~ is the symmetries of an equilateral triangle, D~10~ is the symmetries of a regular pentagon, and so forth. In general, D~2n~ is the symmetries of a regular n-gon.

Now, one interesting thing is that groups can contain each other. For example, consider an octagon. Since there are squares hidden within the points of octagons, if we pick a square we can see that all of the symmetries of that square are present in the symmetries of of the octagon, so it is possible to throw out all of the other symmetries. What we would be left with is just the symmetries of a square. What this means is that D~8~ is contained in D~16~. You can play similar games to show that there are lots of groups contained inside the dihedral groups.

The last thing I want to talk about regarding these things are their subgroup lattices. Oftentimes mathematicians want to picture the internal structure of a group. One of the ways they might do this is by writing down all of the subgroups of a group they’re studying onto a piece of paper, and then connecting any two with a line if one of them is a subgroup of the other that doesn’t have a subgroup between them. The resulting picture is called a subgroup lattice, and I’ve left some dihedral group lattices below because I think they’re pretty.

two cute dihedral subgroup lattices holding hands and cuddling

Anyway this has been gushposting with your host, yewler. Maybe next mega I might talk about more specific details that make these things cool.

Now you may commence in the posting


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[–] kristina@hexbear.net 34 points 2 weeks ago (4 children)

People always seem horrified or act like I'm telling a joke when I tell them my age. What's the problem I made a pact with Satan in the middle ages to look 20 forever

Wear sunscreen shrug-outta-hecks

[–] inTheShadowOf@hexbear.net 17 points 2 weeks ago

Facts. Good skincare will get you far

[–] GenderIsOpSec@hexbear.net 17 points 1 week ago

or you know, never smile, laugh or go outside catgirl-peace

[–] Seryph@lemmygrad.ml 15 points 2 weeks ago

I only just got sunscreen-pilled tbh, not used to having something on my skin but I feel like it's helping.

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[–] dragongloss@hexbear.net 25 points 1 week ago (2 children)

cw: trans suicide, death, obituary, mental health, HIV/AIDSI don't really have others to talk about this that really understand, but my ex-gf killed herself several weeks ago and I am incredibly sad about it. She wasn't a great girlfriend towards the end of our relationship, she did not treat me well, but still I don't think what happened to her in life is deserved. Not a lot of people seem to care all that much that she is gone because she often burned her bridges. But I care. She suffered greatly in life and I think it is deeply unfair. From her family mistreatment to how society mistreated her. The world really seems to quickly forget the dead. She really struggled, the cops targeted her, HIV/AIDs and lack of mental health resources made her life very difficult at times.

I want people to know she is existed. If you have the capacity to read her obituary, please do: https://www.legacy.com/us/obituaries/globegazette/name/jessica-porter-obituary?id=58482844

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[–] kristina@hexbear.net 24 points 2 weeks ago* (last edited 2 weeks ago)

If I die of heart failure soon I want everyone here to know my final word... beanis.

Fr getting old is tough chomsky-yes-honey running fucking sucks now

[–] MusicOwl@hexbear.net 22 points 2 weeks ago (1 children)
[–] bolshevikLovelace@hexbear.net 16 points 2 weeks ago (1 children)
[–] GenderIsOpSec@hexbear.net 14 points 2 weeks ago (5 children)
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[–] yewler@hexbear.net 21 points 1 week ago

I was hit with the sudden realization and belief that I have a personality. Which is huge for me tbh. I used to not understand why anyone would enjoy being around me and for the past little bit I understood why on a somewhat intellectual level, but today I can say I actually feel it

[–] GenderIsOpSec@hexbear.net 20 points 2 weeks ago (2 children)

been upping my game and have read gay interactive fiction at work instead of gay fanfics catgirl-smug

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[–] AntifaSuperWombat@hexbear.net 20 points 1 week ago (1 children)

When I was 16 I got myself a shirt with a medium-deep v-neck, and every time I wore it I would feel so exposed and naked, because until then I only had crew necks and poloshirts.

I wish teenage me could’ve seen the shit I’m wearing now. I would’ve loved to see her face. doggirl-grin

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[–] TerminalEncounter@hexbear.net 19 points 1 week ago* (last edited 1 week ago)

cw: eating stuffThere was a time I was dieting hard and losing weight but I was in nursing school. I don't remember why it came to me, but I thought to myself "if I fed anyone else the way I feed myself, I'd be sent to jail. I give better care at work to strangers than I've done for myself and they're not even paying me. In fact I gotta pay tuition to go to this."

[–] Thallo@hexbear.net 19 points 1 week ago (1 children)

Went out with an old coworker friend today. We were walking around and browsing some clothes, and I was looking at a blouse and she said "that would look good on you"

Girls, I've made it ❤️

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[–] XiaCobolt@hexbear.net 18 points 1 week ago* (last edited 1 week ago)

told my dad... (CW coming out, parent reactions)Honestly probably the best possible reaction said he was incredibly surprised but still loves and supports me.

Tone was very sad, like he was absolutely gutted to hear it though. But didn't say anything bad or nasty.

Followed up with a message saying I was brave, he was confused, still loves me etc

So I can work with this.

[–] Moss@hexbear.net 18 points 1 week ago (6 children)

The downside of being agender is that "good they" really doesn't roll off the tongue like "good boy" or "good girl"

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[–] Seryph@lemmygrad.ml 18 points 1 week ago* (last edited 1 week ago) (2 children)

The cis don’t want you to know this but adopting babytranses at the park is free. You can just take them home. I have 10 trans sisters.

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[–] 0x2640@hexbear.net 18 points 1 week ago (9 children)
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[–] Thallo@hexbear.net 18 points 2 weeks ago

You think it's a yewler post but it's actually a Euler post catgirl-happy

[–] Tommasi@hexbear.net 18 points 1 week ago

I don't really have that much gender thoughts any more. There's still changes from HRT and stuff, but not a lot month to month, and things have kinda stabilized into something I'm very happy with.

So I just post random nonsense in the trans mega instead. catgirl-peace

[–] EstraDoll@hexbear.net 18 points 1 week ago

damn, being a girl is great. i can just sit about the house relaxing in a sports bra with an open flannel over it, this rocks

[–] yewler@hexbear.net 18 points 2 weeks ago (1 children)
[–] yewler@hexbear.net 18 points 1 week ago (4 children)

When I die I want to stay on the earth to trans some genders as a ghost

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[–] buh@hexbear.net 18 points 1 week ago (2 children)

feels unfair that my boobs are so small they're barely noticeable but big enough to hurt when i go jogging cowboy-cri

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[–] XiaCobolt@hexbear.net 17 points 1 week ago* (last edited 1 week ago) (2 children)

A whirlwind of good and bad things (CW Sex discussion, transphobia, parents reactions, cancer, familial death etc)I had an amazing morning yesterday, my partner and I had sex for the first time since I settled on identifying as a woman and it was just really nice.

Jarring shift in tone we told her parents via video chat because some personal events had pushed our timeline forward and we couldn't do it face to face. Which was probably good because they reacted to me being a trans woman and her being a bisexual woman really badly. Like it was a cancer diagnosis. Both of us felt really hurt by it. It wasn't cut all contact but not the way either of us expected. We're just giving them some time right now.

I saw my doctor this morning. He increased my girl pills and gave me a prescription for dick pills, so my two super-objectives were achieved.

I spoke to my mother which I thought would be fine, and it was but also super-unexpected in a few directions. I had a great uncle who died who everyone assumed was gay, but my mother has been sorting out their old stuff, scanning private pictures and letters, she says based on these she thinks she was actually a trans woman (intimate correspondence with lovers, photos never seen dressing femme). This is kind of surreal as this was a person I knew from childhood to my 20s when they died, it's kind of bittersweet, you know we never got a chance to talk and share with this, but also like I feel this deeper connection?

Also my mum is totally an egg, they always identified as a gay man trapped in a woman's body, they felt enormous relief when they had their breasts removed for cancer and had their ovaries removed. I suggest they read Leslie Feinberg's trans liberation and basically mentioned it's never too late to give cross gender hormones a little spin.

My parents are divorced and I didn't think my mother would be a problem but I'm worried my parent's in law might reach out soon to either of them once their shock wears off, so I'm moving quickly. So I guess I'm talking to my father tonight and I have no idea how it goes, but it's going to be nice have all this done and have ended the phase I've been calling my "soft-open", where I don't hide that I'm trans but I haven't been advertising it either.

It's crazy because for work I've been powering through meetings with a pink linen sport's coat with a she/her pin over otherwise all black, looking C***y AF, but it's easier to be confident to people I've never met before.

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[–] sodium_nitride@hexbear.net 17 points 1 week ago (5 children)

I don't want to inject myself. I'm squeamish. angry-hex

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[–] yewler@hexbear.net 17 points 1 week ago (2 children)

In case you were wondering, I'm still gay

[–] EstraDoll@hexbear.net 17 points 1 week ago (2 children)

i think it's interesting that as I've transitioned I've unsurprisingly become a lot more femme, but I think i've actually grown a bit more masc as time has gone on too? like, I feel like as I've let my feminine side flourish there's this masc side of me that's always kind of existed but was super repressed because I hated gender and myself but it's finally started to bloom a bit as well. I joke with myself saying I'm a binary trans woman but still 7% male and it's weird to feel this small masc side of me actually want to exist rather than me existing 100% as a man out of spite to the universe

[–] Thallo@hexbear.net 15 points 1 week ago (1 children)

Didn't like being a masculine man. Didn't like being a feminine man.

Masculine woman is great. Feminine woman also good.

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[–] SorosFootSoldier@hexbear.net 17 points 2 weeks ago
[–] sodium_nitride@hexbear.net 16 points 1 week ago (3 children)

I can't believe I made such a big deal about getting an injection catgirl-flop

The whole process finished in like 2 minutes. Although I think part of why I didn't get so worked up today was cause I got annoyed by removing all the air in the syringe. Hate truly is a powerful and useful emotion.

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[–] WittyProfileName2@hexbear.net 16 points 1 week ago (3 children)

The worst part of transitioning for an adventurer isn't getting the literal breastplate fitted to all your armour, it's the voice training to change your pain grunts from "ugh" to "ugh~ ♥️".

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[–] TerminalEncounter@hexbear.net 16 points 1 week ago* (last edited 1 week ago) (2 children)

"It is what it is"

It isn't what it is. What now. It is what it isn't. A is A can no longer be trusted. Identity is fluid and relational. Now what will you do, cower like a dog or seize the opportunity to act

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[–] EstraDoll@hexbear.net 16 points 1 week ago (4 children)

i absolutely fucking detest the neurotypicals and how they talk. stop asking me these extremely high context questions and just ask me what the fuck you want. stop having me plug in what i guess your questions are and JUST FUCKING ASK ME

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[–] shallot@hexbear.net 15 points 1 week ago (1 children)

Um. The dysphoria may be worse than I thought.

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[–] EstraDoll@hexbear.net 15 points 1 week ago (12 children)

so like

am i ever gonna be allowed to take a flight as a trans woman in the US again or am i just fucked?

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[–] JohnBrownsBussy2@hexbear.net 15 points 1 week ago (3 children)

cw: misogynyThis was from last Saturday when I was hanging out with my partner, but I got catcalled for the first time last weekend. Just a drive-by by a passing driver while we were walking on the sidewalk in my partner's hometown downtown. Honestly, I was kinda worried about the outfit I was wearing: it was for a party but the party got delayed by 3 hours so we had time to go about town. I was confused at first since it took time to process, but it definitely not a good/fun experience.

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[–] Boynomoder@hexbear.net 15 points 1 week ago (1 children)

My face feels weird after laser doggirl-gloom

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[–] XiaCobolt@hexbear.net 15 points 1 week ago* (last edited 1 week ago)

I got unironically complimented on my fit by a random queer zoomer. So yeah I'm pretty cool.

[–] BountifulEggnog@hexbear.net 15 points 1 week ago* (last edited 1 week ago) (3 children)

Finally got a chance to come out to come out to that guy friend coworker. He said all the right thing, that he supports me ect.

misgenderingAlso called me sir half way through the conversation. I started it by telling him of course.
spoiler just complaining like always I've hurt since. Idk why I try. I knew this would be hard but not like this. I actually, literally can't. I don't want to do anything again. I've been so dysphoric lately. The feeling isn't even just from him being a dipshit. It just hurts all the time now. This is horrible. One of the worst fates I could imagine. A nightmare. :::

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[–] yewler@hexbear.net 15 points 1 week ago
[–] TheSpectreOfGay@hexbear.net 14 points 1 week ago

found families are so cool, wish they were real

[–] kristina@hexbear.net 14 points 2 weeks ago

Why are the lock and feature buttons next to each other smh

[–] GenderIsOpSec@hexbear.net 14 points 1 week ago

switching my phone and i remember why i hate doing this catgirl-flop on the funny side it seems i've put in like 70k messages in signal in less than a year doggirl-sweat

[–] EstraDoll@hexbear.net 14 points 1 week ago (5 children)

asexual autistic person whose special interest is sex who finds it interesting in a totally theoretical way that they aren't actually interested in having

[–] Thallo@hexbear.net 16 points 1 week ago

This is pretty common among ace ppl

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[–] Boynomoder@hexbear.net 14 points 1 week ago (1 children)

When a video has Part 1 in the title, but then you look on the channel after and the other parts still aren’t out doggirl-tears

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