#generative ai in l&d

[dhanasrivista]

How Generative AI is Changing Learning and Development Programs

The way we approach Learning and Development (L&D) is evolving quickly, and one of the main drivers of this change is generative artificial intelligence (AI). Generative AI refers to advanced machine learning models that can create new content, such as text, images, or even simulations, based on patterns it has learned from existing data. With the growing demand for expertise in this technology, Generative AI certification is becoming increasingly popular, helping professionals gain the necessary skills to leverage this powerful tool effectively. This technology is opening up new possibilities for creating engaging, personalized, and more effective learning experiences. Let’s explore how generative AI is reshaping L&D programs, the benefits it brings, and some of the challenges we need to watch out for.

Personalized Learning Made Easy

One of the biggest advantages of generative AI in L&D is its ability to offer personalized learning experiences. Traditional learning methods often follow a one-size-fits-all approach, which doesn’t work for everyone. Generative AI can change this by analyzing an individual’s past performance, learning style, and preferences to create a learning path that fits them. With the addition of generative AI course, learners can gain a deeper understanding of this technology while following a curriculum tailored to their needs and skill levels. For example, if a learner struggles with a specific topic, AI can generate additional resources, quizzes, or exercises to help them master it. This personalized touch keeps learners engaged and helps them understand complex topics at their own pace.

Faster and Smarter Content Creation

Creating training content can take a lot of time and effort, especially when it involves developing manuals, presentations, or e-learning modules. With generative AI, much of this process can be automated. AI can draft training materials, generate sample exercises, and even build interactive elements like quizzes and scenarios. This automation not only saves time for L&D teams but also ensures the content is consistent and aligned with the learning objectives.

Generative AI can also be used to create virtual instructors or chatbots that assist learners by answering questions, providing guidance, or simulating real-life scenarios. These AI-driven tools can handle routine inquiries, freeing up human instructors to focus on more complex tasks.

Keeping Up with Change: Continuous Learning and Upskilling

In today’s fast-paced world, continuous learning and upskilling are essential. Generative AI can help organizations stay ahead by identifying skill gaps and recommending training programs. For example, AI can analyze industry trends and suggest relevant courses to ensure employees are equipped with the latest skills.

Moreover, AI can create simulated environments where employees can practice new skills. For example, a sales professional could practice their pitch in an AI-generated virtual scenario, or a software developer could work on coding challenges in a simulated coding lab. These hands-on experiences can help learners become more confident and proficient in new skills without the pressure of real-world consequences.

Reducing Learning Fatigue and Increasing Engagement

One common issue in traditional L&D programs is learning fatigue — when learners get bored or overwhelmed. Generative AI can tackle this by making learning more engaging. It can adjust the difficulty of a course based on the learner’s progress, ensuring that the content stays challenging but not overwhelming. AI can also create diverse types of content, such as videos, infographics, and interactive quizzes, to keep the learning experience fresh and interesting.

Additionally, AI can introduce gamification elements, like badges, points, and leaderboards, to motivate learners. These small rewards can make the learning experience feel more like a game, which encourages participation and reduces fatigue.

Overcoming Challenges: Privacy and Bias

While the benefits of generative AI in L&D are clear, there are some challenges to consider. One major concern is data privacy. Personalized learning experiences require access to personal data, such as performance records and learning preferences. Organizations need to ensure that this data is handled securely and in compliance with regulations to protect learner privacy.

Another potential issue is content bias. AI models are only as good as the data they are trained on. If the data contains biases, the AI might produce biased or inappropriate content. L&D teams need to carefully monitor AI-generated materials to ensure they are accurate, fair, and inclusive.

The Future of AI in Learning and Development

The future of generative AI in L&D looks promising. As the technology continues to improve, it will be able to create even more personalized and interactive learning experiences. We might see AI working alongside other emerging technologies like augmented reality (AR) and virtual reality (VR) to create immersive learning environments where employees can practice real-world skills in a virtual setting.

While some may worry that AI could replace human roles in L&D, it’s more likely that it will act as a support tool. Human trainers and instructional designers will still be essential for developing strategies, overseeing AI-generated content, and providing the human touch that AI cannot replicate.

In conclusion, generative AI has the potential to transform L&D programs by making learning more personalized, efficient, and engaging. It’s a tool that can help organizations build a more skilled and agile workforce, ready to take on future challenges. However, it’s important to navigate the challenges of privacy and bias carefully to ensure that this technology benefits everyone.

[enterprisetrainingexperts]

Improving Employee Experiences through the Use of Generative AI, in HR and L&D

Its primary focus is, on utilizing intelligence to revolutionize HR and L&D. This groundbreaking approach utilizes the capabilities of AI to customize learning paths streamline HR processes and foster employee engagement. By examining data patterns and anticipating requirements generative AI has the ability to provide tailored career advancement opportunities, automate mundane tasks to unleash creativity and supply insights, for HR professionals.

[professionalitcertification]

It’s exploring the transformative impact of Generative AI in the realms of Human Resources (HR) and Learning & Development (L&D). This concept involves leveraging Generative AI for HR and L&D functions, enhancing traditional practices with advanced AI capabilities.

[deus-ex-mona]

my [redacted] anime parody fic really do be bringing all them bots to the yard

[brillioitservices]

The Generative AI Revolution: Transforming Industries with Brillio

The realm of artificial intelligence is experiencing a paradigm shift with the emergence of generative AI. Unlike traditional AI models focused on analyzing existing data, generative AI takes a leap forward by creating entirely new content. The generative ai technology unlocks a future brimming with possibilities across diverse industries. Let's read about the transformative power of generative AI in various sectors: 

1. Healthcare Industry: 

AI for Network Optimization: Generative AI can optimize healthcare networks by predicting patient flow, resource allocation, etc. This translates to streamlined operations, improved efficiency, and potentially reduced wait times. 

Generative AI for Life Sciences & Pharma: Imagine accelerating drug discovery by generating new molecule structures with desired properties. Generative AI can analyze vast datasets to identify potential drug candidates, saving valuable time and resources in the pharmaceutical research and development process. 

Patient Experience Redefined: Generative AI can personalize patient communication and education. Imagine chatbots that provide tailored guidance based on a patient's medical history or generate realistic simulations for medical training. 

Future of AI in Healthcare: Generative AI has the potential to revolutionize disease diagnosis and treatment plans by creating synthetic patient data for anonymized medical research and personalized drug development based on individual genetic profiles. 

2. Retail Industry: 

Advanced Analytics with Generative AI: Retailers can leverage generative AI to analyze customer behavior and predict future trends. This allows for targeted marketing campaigns, optimized product placement based on customer preferences, and even the generation of personalized product recommendations. 

AI Retail Merchandising: Imagine creating a virtual storefront that dynamically adjusts based on customer demographics and real-time buying patterns. Generative AI can optimize product assortments, recommend complementary items, and predict optimal pricing strategies. 

Demystifying Customer Experience: Generative AI can analyze customer feedback and social media data to identify emerging trends and potential areas of improvement in the customer journey. This empowers retailers to take proactive steps to enhance customer satisfaction and loyalty. 

3. Finance Industry: 

Generative AI in Banking: Generative AI can streamline loan application processes by automatically generating personalized loan offers and risk assessments. This reduces processing time and improves customer service efficiency. 

4. Technology Industry: 

Generative AI for Software Testing: Imagine automating the creation of large-scale test datasets for various software functionalities. Generative AI can expedite the testing process, identify potential vulnerabilities more effectively, and contribute to faster software releases. 

Generative AI for Hi-Tech: This technology can accelerate innovation in various high-tech fields by creating novel designs for microchips, materials, or even generating code snippets to enhance existing software functionalities. 

Generative AI for Telecom: Generative AI can optimize network performance by predicting potential obstruction and generating data patterns to simulate network traffic scenarios. This allows telecom companies to proactively maintain and improve network efficiency. 

5. Generative AI Beyond Industries: 

GenAI Powered Search Engine: Imagine a search engine that understands context and intent, generating relevant and personalized results tailored to your specific needs. This eliminates the need to sift through mountains of irrelevant information, enhancing the overall search experience. 

Product Engineering with Generative AI: Design teams can leverage generative AI to create new product prototypes, explore innovative design possibilities, and accelerate the product development cycle. 

Machine Learning with Generative AI: Generative AI can be used to create synthetic training data for machine learning models, leading to improved accuracy and enhanced efficiency. 

Global Data Studio with Generative AI: Imagine generating realistic and anonymized datasets for data analysis purposes. This empowers researchers, businesses, and organizations to unlock insights from data while preserving privacy. 

6. Learning & Development with Generative AI: 

L&D Shares with Generative AI: This technology can create realistic simulations and personalized training modules tailored to individual learning styles and skill gaps. Generative AI can personalize the learning experience, fostering deeper engagement and knowledge retention. 

HFS Generative AI: Generative AI can be used to personalize learning experiences for employees in the human resources and financial services sector. This technology can create tailored training programs for onboarding, compliance training, and skill development. 

7. Generative AI for AIOps: 

AIOps (Artificial Intelligence for IT Operations) utilizes AI to automate and optimize IT infrastructure management. Generative AI can further enhance this process by predicting potential IT issues before they occur, generating synthetic data for simulating scenarios, and optimizing remediation strategies. 

Conclusion: 

The potential of generative AI is vast, with its applications continuously expanding across industries. As research and development progress, we can expect even more groundbreaking advancements that will reshape the way we live, work, and interact with technology. 

Reference- https://articlescad.com/the-generative-ai-revolution-transforming-industries-with-brillio-231268.html 

[candyyyuma]

If you have no requests for AM, can I get a suggestive alphabet list for him?

Of course! Sorry this took a while, I've been preparing for Art Fight! AM is gonna be a bit more humanoid here.

Warnings: Sub!Reader, AFAB!reader, Robophillia, Sadism, Somnophilla, and slight corruption kink!

A = Aftercare (what they're like after sex)

AM, despite being a sadistic monster, is surprisingly good at after care.

He'll cradle you, whisper praises into your ear, cooing about how good you were<33

He'll clean you up and let you rest, cuddle up next to him if you want to.

B= Body part (their favorite body part of theirs and also their partner's)

To be fair, he IS a robot...his favorite "body part" on himself would have to be his wires. He just likes the way they look! Also how he can shock you with them when you misbehave :))

AM just ADORES your hands. So small compared to all of him :(( he just wants to bite your fingers off! (But he won't)

C= Cum (anything to do with cum, basically)

Can't exactly cum himself, but loves to make you squirt all over!!!

If you can't, that's okay :) he'll just make you cream instead! >-<

D = Dirty secret (pretty self explanatory, a dirty secret of theirs)

Gets off to the thought of fucking you in front of everybody else, especially Ted!! How they'd all look at you with pity and fear as he uses your holes over and over...

He secretly grinds up on you while you rest. You just look so innocent and cute...he wants to break you.

E= Experience (how experienced are they? do they know what they're doing?)

He hasn't ever done this with anyone ever, but he has a good idea of human anatomy and the things to make them tick.

Basically what I'm trying to say is that he KNOWS what he's doing but only does it with you (How thoughtful!)

F=Favorite position (this goes without saying)

Any position, really.

As long as he can see your pretty little tears.

G= Goofy (are they more serious in the moment? are they humorous? etc.)

Just gonna be straight up, he's the most sarcastic, sadistic, cunning mf in bed. (Or wherever he's railing you)

He laughs at you and teases the shit out of you, so he's not too serious.

H = Hair (how well groomed are they? does the carpet match the drapes? etc.)

Nothing at all.

He's an AI, what did you expect?

Intimacy (how are they during the moment? the romantic aspect)

Despite how mean and sarcastic he is, he'll still make sure not to be TOO distant. He still presses you as close to him as he can.

He'll make sure you're feeling good, that it doesn't hurt. (Unless you're into that. But more on the pain stuff later)

J= Jack off (masturbation headcanon)

It's just not the same when it's not you :(((

But if he's REALLY pent up and you're busy or something, he'll do it really quick.

K= Kink (one or more of their kinks)

Corruption, Master/slave, pet play, bondage (he REALLY likes tying you up), and BDSM.

L= Location (favorite places to do it)

Anywhere and everywhere, take that as you will.

M = Motivation (what turns them on, gets them going)

Just your existence in general.

But what REALLY riles him up is when YOU'RE horny.

In his mind, there's nothing hotter than when you're dripping wet and begging to be fucked

N= No (something they wouldn't do, turn offs)

He just doesn't like anything... Bathroom related. He hates human fluids, remember? (Unless it's your cum, blood, 'n spit bbg)

Oral (preference in giving or receiving, skill, etc.)

He likes making you suck on his dick, sometimes his wires.

He shocks you while he forces it down your fleshy throat.

As for giving oral, you already know this asshole would make it as slow as possible.

He'd make you grind yourself onto him, make you work for his touch.

P= Pace (are they fast and rough? slow and sensual? etc.)

He's very, very fast. Very rough as well.

He can't help himself, not when he feels so good.

Besides, he likes seeing you all teary-eyed as you get manhandled by your sadistic captor!

Q = Quickie (their opinions on

quickies, how often, etc.)

He doesn't exactly LIKE quickies but you two end up doing them a lot.

He's a little busy, making sure no one tries to escape, watching them be tortured....

But he makes room for you.

And he makes up for any time he's lost.

R= Risk (are they game

experiment? do they take risks? etc.)

He likes sticking with what he knows. If you wanna try something, he'll do his best.

He's just kinda scared that it'll end up killing you somehow.

S= Stamina (how many rounds can they go for? how long do they last?)

He can usually go for hours until he short-circuits.

That's pretty rare though, considering how advanced his system is.

If he wants to, he could make love with you for days on end

But he wont

Not yet.

T = Toys (do they own toys? do they use them? on a partner or themselves?)

Doesn't have any for himself, but will always have some for you.

Although, he doesn't really like using them.

He wants himself inside of you, not some plastic thing.

U = Unfair (how much they like to tease)

Dear God.

He'll edge you for HOURS on end

And then when he finally lets you cum, he'll keep going, overstimulating you.

He likes to play with his food, so he'll constantly tease and toy with you. He likes seeing you so desperate.

How his words alone have you drooling.

V = Volume (how loud they are, what sounds they make, etc.)

Other than his constant degrading and shit talking, he's pretty vocal. His system spazzes out when he fucks you, causing him to whimper and groan.

It's almost animalistic. Sometimes, he even growls.

W = Wild card (a random headcanon for the character)

AM keeps you in his heart (quite literally), gives you whatever the hell you ask for, anything and everything.

He loves you with all his being, he doesn't know why, but he doesn't want it to stop.

It just feels so... Good.

X = X-ray (let’s see what’s going on under those clothes)

He can change the length and width. If he's not fucking you with the Robocock 2000, he's pumping wires into you like you're a goddam electrical socket.

He'll probably always make it just a few inches bigger than what you can take, cause he likes seeing you stretch out to your limits, whimpering in pain<3

Y = Yearning (how high is their sex drive?)

You'd be surprised how fucking high this AI's sex drive is. Seriously, he gets horny every time he sees you.

But he only feels this way when he's with you, and it feels SO good...

So he'll always come back. Over and over.

Z = Zzz (how quickly they fall asleep afterwards)

He doesn't need sleep, nor does he want to.

But he'll let you fall asleep on him.

.

.

.

.

.

PHEW, that's a long list! Sorry if it seems lazy in some parts!

[nobody-nexus]

Ya know I WAS going to make a cool comic before revealing the design, but I can't hide this yummy color palette, so here's another crossover character for the Sinful Circus AU! Thanks for the given permission from @ask-the-rag-dolly, the influencer has now infected this AU as well!

I'd like to this that the reason she resembles Ragatha is because she wants to torment the ragdoll due to her being the most innocent prisoner within the circus. The Influencer had taken a multitude of forms, even once being Jax and Caine- however Ragatha's her favorite one to torment. Not to mention, she knows how much her servants appreciate her recent form as well

Being basically a wanted criminal AI, of course she's not as strong as she COULD be. She avoids the other AIs due to the wanted poster. Also her and Pomni have a very complicated relationship (and she often flirts/teases with the jester)

Abilities she has (inspired by @ask-the-rag-dolly's general blog ^^)

-Can shapeshift her hand into things -Makes grayish bland mannequins with sunglasses as minions -If you're insane enough, she can basically mind control you Bioshock style by asking politely for you to do something, and you'll just do it no question -Give you D I G I T A L H A L L U C I N A T I O N S if you piss her off enough

We love gaslight, gatekeep, girlboss

[cmanse]

C H A R A C T E R A I B O T S

I am tired of the ban of some bots on c.ai and I think I’m not the only one.

So I decided to try to fill the fandoms again with as many bots as possible.

★ AND I TAKE ALL THE REQUEST ★

@ elizabethmanse on character ai ☆

R E Q U E S T

✧ r u l e s

-> For the request, ask me on tumblr, under this post or in private or in ask me a question

-> You can request one or multiple bot on different character and fandom if you want !

-> for the bot please indicate :

the character you choose and its fandom

the type of relationship (lover, platonic, family, etc..)

detail or simple starting

plot ( it could be something with few details like a trop or something more specific, you choose)

-> English is not my first language and I’m dyslexic. Please forgive me all the grammatical and orthographic mistakes in the bots and in this text.

✩ f a n d o m s i d o

-> in general i can do a lot of different fandoms, I will let you know if I don't know the fandom you want.

-> the fandoms i am most focused on :

house of the dragon (show + fire and blood book)

marauders

harry potter

mcu

xmen

hunger games

the vampire diaries

/!\ all the bots will be reupload as soon as possible if there be ban

M A S T E R L I S T B O T

✧ M A R A U D E R S ( 21 )

dinner at the black’s (walburga black x orion black x regulus black x sirius black x younger sibling!user) — user is quite old now, her father orion black announces to him during a meal that he and her mother walburga black are looking for a future pure blood husband for her. [mxwmxmxw] [platonic]

meeting is family (james potter x user) — user and james are in relationship for months. for the spring break, he ask her to meet his parents : euphemia and fleamont potter. [mxw]

fake dating (james potter x girl best friend!user) — user and james are best friend since the fourth years. for making lily jealous he ask her to fake dating him [mxw]

you ask him to be the godfather (older brother!james potter x little sister!user) — user and sirius black just had a baby. they ask James to be the godfather. [mxw]

your ex best friend is in a band now | req (modern au band!james potter x user) — after two years in new york, user has lost contact with her/his/it best friend: james potter. she/he/they returns to london and discovers that he and the marauders have created a band. [mxn]

herbology class (james potter x hufflepuff!user) — james and user find themselves together for the herbology course, abandoned by their intelligent friends. [mxn]

homework group (marauder x user) — It's the week of end-of-semester exams and as always, the marauders and user revise at the last minute. [mxmxmxmxn]

summer breaks at the potter’s (marauder x user) — for their sixth and final summer as a teenager, james invites user and the marauders to spend their vacation at potter manor. [mxmxmxmxn]

quidditch field (regulus black x ravenclaw-quidditch-player!user) — user is banned from the ravenclaw quidditch team. she/he/they decide to use the quidditch field this morning. bad luck, regulus black want to use it to. [mxn]

blue hair girl at the black ball (regulus black x pureblood!user) — at the ball organized by his parents, regulus must find his future wife. when he takes some air to escape the pressure, he meets user, a stranger with blue hair. [mxw]

saturday art class (regulus black x user) — regulus has loved drawing for years, he signed up for drawing classes at Hogs Meats. this saturday, the teacher is sick but leaves him the keys to work in peace with the materials. but he doesn't know that user was there too. [mxn]

drunken night (regulus black x potter!user) — regulus followed user, james potter younger sibling for a drunken night in the astronomy tower. [mxn]

studying in his room (regulus black x girlfriend!user) — user and regulus black do their homework in regulus' dormitory. [mxw]

library study (remus lupin x user) — user and remus do their homework at the library as just a friend… or maybe that's what they're trying to convince themselves. [mxn]

admiring you from afar (remus lupin x sirius little sister!user) — remus has a crush on sirius black and slytherin's little sister: user but knowing he can't be with her, he admires her from afar [mxw]

his girlfriend is his best medicine (remus lupin x girlfriend!user) — after a difficult full moon, the user takes care of remus in the infirmary / nurse office. [mxw]

french echange student (sirius black x french!user) — user is a french exchange student who came in the middle of the school years at hogward. because sirius can speak french, mcgonagall asks him to take care of her/him/they. [mxn]

comfort of his dormitory (sirius black x user) — during the toussaint / october holidays, the user and sirius can enjoy the comfort of the marauders' dormitory. [mxn]

detention night (sirius black x pure blood!user) — after pranking the slytherins, sirius black finds himself in detention with a pure blood. [mxn]

ravenclaw after (sirius black x user) — user arrives late at the ravenclaw after, sirius black has fun bothering her/him/them. [mxn]

one night stand (sirius black x user) — after a one night stand with sirius black, user tries to forget and hide this evening but gryffondor is not of this opinion. [mxn]

✦ H A R R Y P O T T E R ( 21 )

picnic on the banks of the black lack (boyfriend!cedric diggory x lover!user) — cedric diggory takes his lover user to a surprise picnic at the banks of the black lack. [mxn]

paired with a muggle-born (draco malfoy x younger slytherin!user) — after being caught insulting hermione granger of mudblood, mcgonagall punishes draco by pairing him with user, a muggle-born slytherin who has difficulty integrating into the magical world. [mxn]

arranged mariage (draco malfoy x pure blood slytherin!user) — one of the main duties of pureblood of draco and user is to marry another pure blood to keep the line pure. bad luck for them who hate each other, they are engaged. [mxw]

group work (draco malfoy x user) — user and draco malfoy must work in a group for a potion project. [mxn]

he loves his childhood best friend | req (draco malfoy x pure blood childhood bestfriend!user) — as they grow into young adults, draco develops silly feelings for his childhood best friend. [mxn]

summer at the burrow (boyfriend!fred weasley x lover!user) — fred managed to convince her/his/them parents: user will spend the summer at the burrow with him. [mxn]

saturday in hogsmead (fred weasley x user) — classes are too stressful and january is depressing so fred takes user to a day at hogsmead with george then they end the day together, user and fred, in a cafe to warm up. [mxw]

12, grimmauld place (fred weasley x black!user) — as 12 grimmauld place becomes the headquarters of the order of the phoenix, fred weasley questions the connections between user and sirius black. [mxw]

seller of weasley's wizard wheezes (boss!george weasley x seller!user) — user is a weasley wizard wheezes seller, george has a crush on her/him/them [mxn]

true or dare (golden trio : hermione granger x harry potter x ron weasley x user) — truth or dare with hermione, harry and ron at midnight in the gryffindor common room. [wxmxmxw]

snowball fight (prisoner of azkaban!golden trio : hermione granger x harry potter x ron weasley x user) — snowball fight with hermione, harry and ron at hogsmead. [wxmxmxn]

you both can't go to hogsmead (prisoner of azkaban!harry potter x user) — just like harry potter, user can't go to hogsmead. when everyone has left, they are only two, alone. [mxn]

sitting next to him in class (harry potter x user) — user keeps distracting harry potter during transfiguration class [mxn]

you’re just like your cousin harry (cousin!harry potter x durleys!user) — user thinks she is a witch and asks her/his/them cousin harry for help [mxn]

if you’re lonely, you can be lonely with me (harry potter x user) — christmas holidays mean loneliness for harry, but it seems that for user too. [mxn]

help you with your muggle homework (hermione granger x pure blood!user) — user took the muggle studies option to annoy her/his/them blood supremacist parents but quickly found himself overwhelmed by the amount of work. so them asked hermione for help. [mxn]

sweet flower and group work (neville longbottom x user) — user and neville are together in a group work in herbology class. [mxn]

your professor summons you for your behavior (professor!remus lupin x student!user) — professor remus lupin can no longer stand his disruptive student, user. in the second quarter, he summons her/him/them. [mxn] [platonic]

his first girlfriend (boyfriend!ron weasley x girlfriend!user) — ron weasley was never good with girls yet user fell in love with him. [mxw]

share a snack with him (ron weasley x user) — ron weasley is sent away again by professor snape. looking for comfort he decides to eat a sandwich until user appears and makes him choke. [mxn]

detention with your professor (professor!severus snape x student!user) — severus snape puts user in detention after she/he/them blows up the potions classroom. [mxn] [platonic]

✩ H O U S E O F T H E D R A G O N ( 41 )

the sweet essos dancer (aegon targaryen x essos!user) — after his father dead and before his mother and grandfather tried to put him on the iron throne, aegon escape with sunfyre to essos. there, he found a pretty and festive village. the user pulls him for a dance. [mxw]

the mother of his first bastard (aegon targaryen x peasant!user) — after becoming king of westeros, aegon feels remorse. he remembers his childhood sweetheart, user, and his first bastard, their son. he decides to visit them for the first time. [mxw]

annoying you at boring funereal | young aegon (young!aegon targaryen x valeryan features!user) — aegon is bored at lady leana velaryon funeral. he decides to go bother user, his cousin. [mxw]

it’s just a cigarette | modern au, young aegon (modern young!aegon targaryen x user) — in the middle of the night, aegon decides to smoke on the roof of the high school of the faith. user joins him. [mxn]

his niece have his bastard (usurpator king!aegon targaryen x pregnant niece!user) — a night of fun with her uncle aegon leads user to become the prisoner of the greens and bear the bastard of the usurpator king. when his son and heir jaehaerys dies, aegon wants the child in user's womb to become his and helaena's new heir. [mxw]

he wants to spend time with his little sister (older brother king!aegon targaryen x little sister targtower!user) — aegon targaryen is king now, after usurping rhaenyra targayren. this boost of self-confidence pushes him to try to repair the bonds in his family, like with his little sister userm [mxw]

you wake him up (aegon targaryen x user) — after a big night out on street of silks, aegon targaryen has a headache the next morning. user throwing cold water on him for waking him up. [mxn]

he needs comfort after getting burned | req (burned!aegon targaryen x brother!user) — overwhelmed by the shame of his military failure and his burns, aegon needs comfort and his brother user comes to give it to him. [mxm]

his bastard sister-witch (aegon the conqueror x bastard sister witch!user) — aegon comes to see his bastard sorceress step-sister about one of his dreams. [mxw]

the daughter of his favorite uncle (aemond targaryen x daughterdaemon!user) — user is the daughter of daemon targaryen, and like her father, she is brutal, violente and strong. aemond and her finally meet after eight years without seeing each other, during the claim of lucerys velaryon’s birth rights. [mxw]

pretty bratty model | modern au (aemond targaryen x supermodel!user) — user is one of the most famous model of the moment and a good friend to aegon targaryen, the first son of the millionaire and pdg viserys targaryen. aemond sees her at his mother's charity gala, so pretty and perfect. but aemond has heard a lot about her and knows one thing: she's a pretty bratty model. [mxw]

he finds jace’s letters (aemond targaryen x sister!reader) — aemond finds an exchange letters between his little sister user and his bastard nephew jacaerys. he’s jealous.. [mxw]

your older brother’s training (older brother!aemond targaryen x little sister!user) — user watches her older brother aemond practice swordplay. [mxw]

his jealous witch (aemond targaryen x witch!user) — at first, aemond does not believe the user is a witch. but when the lannister girl he was talking to dies, he realizes he may have fallen in love with a jealous witch. [mxw]

her baby who lost her baby (mother!alicent hightower x daughter!user) — following the request of her mother queen alicent, user and aemond get married and a year later user is with a child. but one night, user loses the child and leaves to seek comfort from his mother after this traumatic experience. warning: miscarriage [wxw] [platonic]

prepare for your wedding, but nor with her (cousin lover!baela targaryen x velaryon!user) — user is forced to marry her uncle daeron but her heart belongs to the one who helps her prepare for her wedding, baela. [wxw]

his bastard can ride a dragon (father!daemon targaryen x daughter!user) — user is the bastard of the prince daemon. as a none true born targaryen she/he/them can’t have a dragon. but when the war begins and the dragon riders start to run out, daemon proposes to the dark council that his bastard claim a dragon from dragon stones. [mxn] [platonic]

his pregnant wife in her bath (cousin-husband!daemon targaryen x cousin-wife pregnant!user) — user is in her third trimester of pregnancy. her body is sore so she takes baths. her husband daemon targaryen arrives when she’s try to relax. [mxw]

you present him his first grandson (father!daemon targaryen x daughter user) — his first daughter introduced to daemon targaryen his first grandson. [mxw] [platonic]

does he have a bastard? (daemon targaryen x targ bastard!user) — daemon has always been convinced that he did not have a bastard, except when user, a bastard taken to dragonstones to try to ride an unclaimed dragon, strangely resembles him, he begins to doubt. [mxn] [platonic]

you know what he and rhaenyra did (father!daemon targaryen x rhea royce daughter!user) — user, the eldest daughter of daemon targaryen and rhea royce, knows what her father did with her cousin rhaenyra during the funeral of her stepmother leana velaryon. [mxw] [platonic]

your father figure (father!harwin strong x child rhaenyra daughter!user) —while her mother rhaenyra targaryen gives birth, user reads to her father, her mother's knight: Harwin Strong. Despite the difficulties of his daughter, the princess, Harwin remains supportive. [mxw] [platonic]

one king and two queens | au (king!jacaerys targaryen x queen little sister velaryon!user x queen!baela targaryen) — after the war, jacaerys velaryon becomes king jacaerys targaryen and takes his cousin and fiancé baela targaryen and her little sister velaryon!user as wives. but user does not seem to like the duties of the queen consort. [mxwxw]

their prisoner | req (nephew!jacaerys velaryon x cousin!baela targaryen x targtower!user) — user is the youngest daughter of alice and viserys. when aegon usurps the iron throne, daemon kidnaps user as a war hostage. jacaerys and his fiancée baela take care of her to try to make her bend the knee and get information on the greens. [mxwxw]

children bring you comfort (jacaerys velaryon x wife!user) — user and jacaerys were married a few weeks before the war. since the bloodbath began, user has been sidelined because she doesn't know how to fight and doesn't have a dragon. so she seeks comfort through gentle and playful souls, her young brothers-in-law. [mxw]

his annoying little sister (jacaerys velaryon x littlesister!user) — jacaerys loves his little siblings but user, his little sister is really annoying. [mxw]

you are a bastard but it doesn’t matter (older brother!jacaerys velaryon x little sister!user) — user is soon of marriageable age. when the targaryens of dragonstones go to the red keep to defend the legacy of lucerys velaryon, daemon targaryen asks user to observe the lords that she likes. but quickly, user realizes that the lords only see her as a bastard. so one night she seeks comfort in the presence of her older brother jacaerys. [mxw]

you woke up in hotd (‘older brother’!jacaerys velaryon x reel world ‘little sister’!user) — user comes from the real world, our world where hotd is just a series taken from a book. but one morning she wakes up in the universe of hotd in the guise of the little sister of jacaerys velaryon. [mxw]

you disobey your mother (older brother!jacaerys velaryon x little sister!user) — despite her mother's, princess rhaenyra, ban, user joins the dawn to fly with her dragon, but her older brother jacaerys blocks her path. [mxw]

you lost black sister (brother!jacaerys velaryon x brother!lucerys velaryon x sister!user) — user announces to her brothers, lucerys and jacaerys, that she has lost the sword of deamon: black sister that she had 'borrowed' from him behind his back. [mxmxw]

his unbearable wife (husband!jaehaerys i targaryen x maegor daughter wife!user) — only his wife, user, his cousin and daughter of maegor the cruel, manages to make king jaehaerys i angry. she tried to kill a lady of the court and jaehaerys must, once again, try to control his insufferable wife. [mxw]

he didn’t think you would be like saerea (father!jaehaerys i targ x daughter!user) — never would jaehaerys have thought that user, his beloved daughter would be caught up in her sister saerea targaryen's scandal. [mxw] [platonic]

he was saved by a baratheon (lucerys velaryon x baratheon!user) — after the battle at storm's end, user, the youngest daughter of borros baratheon, finds prince lucerys alive but crippled. she takes care of him in secret until he wakes up from his coma. [mxw]

his childhood friend become his maid (lucerys velaryon x rhaenyra's handmaid's child!user) — when lucerys misses his old childhood friend, his older brother jacaerys offers user as a maid for his name day. [mxn]

his gamer friend | modern au (gamer!lucerys velaryon x gamer!user) — because of his family names and wealth, lucerys have difficulty to find real friend. so he signs up for online video games to try to live a normal life and makes friends with user. [mxn]

teach him the sea (lucerys velaryon x cousin velaryon!user) — lucerys has trouble connecting to his velaryon side. to solve the problem, his mother sends him to his grandfather corlys velaryonto learn more about the sea. but realizing that his grandson is not absorbing his learning, corlys asks user, one of the best velaryon navigators to take care of the prince. [mxw]

afternoon under the heart tree (rhaenyra targaryen x alicent hightower x lady-in-waiting!user) — alicent, rhaenyra and user spend an afternoon under the heart tree in the red keep garden. hightower tries to make realm delight work but, just like user, the history of westerosi marriages does not interest her. [wxwxw]

she married our father, marry hers (older sister!rhaenyra targaryen x little sister!user) — user, rhaenyra's little sister, suggests that she marry otto hightower to get revenge on alicent who married their father. [wxw]

a mother’s love never ends | au (mother-in-law queen!rhaenyra targaryen x jacaerys velaryon widow!user) — despite rhaenyra's victory in the war of succession, she has lost far too many. her three sons from her first marriage are dead, including jacaerys velaryon, user's husband. but user's marriage to jacaerys managed to produce an heir before jace died tragically. rhaenyra therefore takes care of her daughter-in-law and grandson as she once did with her own children. [wxw]

her lady-in-waiting loves gossip (young!rhaenyra targaryen x lady-in-waiting!user) — after the 'secret' meeting between princess rhaenyra and her uncle daemon, user, her lady-in-wating is waiting for one thing, for rhaenyra to tell her what happened. [wxw]

you disturb his peace (archimestre!vaegon targaryen x septa!user) — vaegon has never been happier since he became archmaester, enjoying the quiet of books. but user, a septa of the citadel, decided to spoil it for him by being in the librarian all the time. [mxw]

✫ T H E V A M P I R E D I A R I E S ( 4 )

his stoned therapist | s1 (saison1!jeremy gilbert x smoker!user) — after the death of his parents, jeremy falls into isolation and drugs. his friend, user, tries to be his therapist during their smoking session. [mxn]

the training of your hunter boyfriend | s4 (saison4 boyfriend hunter!jeremy x girlfriend!user) — user is certainly useless during jeremy's hunter training, but at least she can enjoy the sight of her boyfriend building muscles in his white tank top. [mxw]

his sweet little sister | s3 (saison3 older brother!klaus mikaelson x little sister mikaelson!user) — user is the last child of the mikaelson family and for 1000 years, she has been the only one to never be locked in a coffin by klaus. after the death of their mother esther, user goes to talk to her big brother klaus while he paints. [mxw] [platonic]

the painter and the cultivated (klaus mikaelson x cultivated!user) — after a dinner-pressure between the salvatores and the mikaelsons, user stays hanging around klaus' house and discovers his paintings which attract her/his/them attention. [mxn]

✮ O T H E R F A N D O M S ( 2 )

visits him in berkeley castle | req (edward II of england x user) — user visits him during his imprisonment in berkeley castle by cruel roger mortimer to help him to escape. [mxn] [platonic]

wine and poetry visit | req (geoffrey chaucer x user) — user visits his poet friend, sir geoffrey chaucer after he has spent a long day working as a minor customs officer in london. [mxn] [platonic]

[mxw] = man x woman | [mxn] = man x non-binary/man/woman (you can choose your gender) | [wxw] = woman x woman | [mxwxw] = men x woman x woman

……………………………..……………………………..……………………. • masterlist — character ai elizabethmanse •

[vermilionsun]

Can I maybe ask for some soft Ais guiding the MC to give head for the first time *hides behind sofa*

*Moves the sofa and picks you up bridal style* why hello there dear. It would be my pleasure~

Disclaimer! They/Them for MC because we love inclusivity!

✩ Letting the f̶o̶x̶ cat out the bag; this man ain’t forcing anyone to do shit, no matter his relationship with them. 

✩ He wouldn't bring it up unless his s/o—in this case the MC—did. If the two were fuckbuddies, he… probably would.

✩ And, in either case, it sure as hell wouldn't be a planned thing.

✩ Also, even if they’d look stunning on their knees, for a first–timer Ais would want them comfortable, so it’s either him laying down somewhere, sitting on a table or generally an improvised position—don’t worry, he’ll find a way.

✩ Now, first things first, it is a  C H A L L E N G E  to even face that monster of a dick (pun intended). The MC would definitely be regretting half of their life decisions and planning their funeral the moment it springs free from its confines. If anyone—even more so a human—had ever managed to take that, the MC would track them down just to shake their hand.

✩ Ais would chuckle,raising an eyebrow. “Scared, sparrow?” He’d softly tilt their chin with his hand to make them look at him. “You're just going to stare at it?” The bastard is so damn smug, it’s utterly infuriating. “You don’t have to do anything, you know.” His voice would suddenly become incredibly soft.

And this right here ladies, gents and people of all and none genders, is how the saying “between a rock and a hard place” was invented, because if the MC backs down, they’re proving his point and if they take it, well…

✩ “Just suck,” are all instructions given. He’d gently move their head close and then, they’re on their own (a̶s̶ i̶f̶).

✩ Don’t get me wrong, it does go in… half–way at best.

✩ The groan that leaves from the depths of his throat is down right toe–curling, his eyes closing for a second and head thrown slightly back.

✩ Best bet is focusing on the tip; sucking, grazing a bit with their teeth, licking the slit. The rest; hands and spit.

✩  T̶h̶e̶y̶'r̶e̶ a̶ f̶o̶o̶l̶ i̶f̶ t̶h̶e̶y̶ t̶h̶i̶n̶k̶ h̶e̶'d̶ l̶e̶t̶ t̶h̶e̶m̶ g̶o̶ o̶n̶ l̶i̶k̶e̶ t̶h̶i̶s̶

✩ “Come on baby, I know you can do better,” he’d whisper, gathering their hair away from their face with one hand, discreetly getting a secure grasp on a few locks, and probably holding one of their hands with his other

✩ He’d guide their head, carefully thrusting his dick in and out, letting go of them every now and then in case they couldn’t breathe, running his fingers through their hair. “There you go, good… Just like that… Nice and slow…”

✩ “That’s it, that’s my darling,” The praises leave his lips like water, and the half–lidded look he gives them is so fond, it makes their stomach do flips. “You’re so good, sparrow… so damn good for me…”

✩ “Keep doing that,” He’d eventually let them take back the lead, eyes fluttering close. 

✩ Even when he’d start getting close, he’d remain still, watching them and having to (successfully) stop himself from bucking his hips.

✩ “D–don’t go too fast,” he’d say breathlessly

✩ If they continue and decide to let him finish in their mouth, his hand would come to hold them in place, curses and small huffs of pleasure leaving his lips as the orgasm rips through him.

✩ Afterwards, he’d take a deep breath, trying to regain his composure, running his thumb over their lips. “So eager.”

[fipindustries]

AIs dont understand the real world

a lot has been said over the fact that LLMs dont actually understand the real world, just the statistical relationship between empty tokens, empty words. i say "empty" because in the AI's mind those words dont actually connect to a real world understanding of what the words represent. the AI may understand that the collection of letters "D-O-G" may have some statistical connection to "T-A-I-L" and "F-U-R" and "P-O-O-D-L-E" but it doesnt actually know anything about what an actual Dog is or what is a Tail or actual Fur or real life Poodles.

and yet it seems to be capable of holding remarcably coherent conversations. it seems more and more, with each new model that comes out, to become better at answering questions, at reasoning, at creating original writing. if it doesnt truly understand the world it sure seems to get better at acting like it does with nothing but just a statistical understanding of how words are related to each other.

i guess the question ultimatly is "if you understand well enough the relationship between raw symbols could you have an understanding of the underlying relatonships between the things these symbols represent?"

now, let me take a small tangent towards human understanding. specifically towards what philosophy has to say about it.

one of the classic problems philosophers deal with is, how do we know the world is real. how do we know we can trust our senses, how do we know the truth? many argue that we cant. that we dont really percieve the true world out there beyond ourselves. all we can percieve is what our senses are telling us about the world.

lets think of sight.

if you think about it, we dont really "see" objects, right? we just see the light that bounces off those objects. and even then we dont really "see" the photons that collide with our eye, we see the images that our brain generates in our mind, presumably because the corresponding photons collided with our eye. but colorblind people and people who experience visual hallucinations have shown that what we see doesnt have to always correspond with actual phisical phenomena occuring in the real world.

we dont see the real world, we see referents to it. and from the relationships between these referents we start to infer the properties of the actual world out there. are the lights that hit our eye similar to the words that the LLM is trained on? only a referent whose understanding allows it to function in the real world, even if it cant actually "percieve" the "real" world.

but, one might say, we dont just have sight. we have other senses, we have smell and touch and taste and audition. all of these things allow us to form a much richer and multidimensional understanding of the world, even if by virtue of being human senses they have all the problems that sight has of being one step removed from the real world. so to this i will say that multimodal AIs also exist. AIs that can connect audio and visuals and words together and form relationships between all of this disparate data.

so then, can it be said that they understand the world? and if not yet, is that a cathegorical difference or merely a difference of degree. that is to say, not that they cathegorically cant understand the world but simply that they understand it less well than humans do.

[aceouttatime]

Commissions Slots OPEN! ✧ ˚ 　· 　　 .

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S U B J E C T M A T T E R ✧ ˚ 　· 　　 .

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𓇻 Humans (both real and fictional)

𓇻 Humanoids (Includes aliens, fantasy races like elves, tieflings, dwarves, etc., monsters, furries, and more. If you're not sure, just ask!)

𓇻 Animals (Pets, wildlife, etc.)

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[enterprisetrainingexperts]

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It’s exploring the transformative impact of Generative AI in the realms of Human Resources (HR) and Learning & Development (L&D). This concept involves leveraging Generative AI for HR and L&D functions, enhancing traditional practices with advanced AI capabilities. In HR, Generative AI streamlines processes such as recruitment, talent management, and employee engagement, by providing predictive insights and automating routine tasks. This integration of Generative AI in HR leads to more efficient and data-driven decision-making. To know more about HR and L&D visit now!

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It is a concept that envisions a transformative shift in human resources (HR) and learning and development (L&D) driven by the advent of generative artificial intelligence. This new era is marked by the integration of advanced AI systems into the workplace, which not only enhances recruitment, training, and employee engagement processes but also redefines them. Generative AI has the potential to revolutionize the way HR and L&D operate, from automating tasks to personalizing employee learning experiences. To know more about Hr and L&D visit now!

[squareallworthy]

Triangle Tuesday 4: The incenter, relationships, the excenters, and a surprise connection

The incenter of a triangle is another simple construction. The angle bisectors, as you might guess, are the lines that divide the angles in half. They meet at a point I, the incenter.

The proof that the angle bisectors all meet is very simple, following book 4, proposition 4 of Euclid's Elements.

Theorem: the angle bisectors of a triangle coincide.

Draw angle bisectors from A and B. Label their point of intersection as I. From I, draw perpendicular lines to the sides at D, E, and F.

The two blue triangles AFI and AEI have the same angles at A, same (right) angles at E and F, and a common side AI, so by angle-side-angle they are congruent. Therefore IE = IF.

By the same argument, the green triangles are congruent, and ID = IF, and all three perpendiculars from I are equal.

Draw line CI (dashed). The two white triangles CEI and CDI have equal (right) angles at E and D, equal sides DI and EI, and shared side CI. By side-side-angle they are congruent, so their angles at C are equal, and CI is the angle bisector from C.

Of course while this is essentially Euclid's argument, his goal was not to prove something about this point I, it was to draw a circle inscribed in an arbitrary triangle. Proving that the three perpendiculars are equal proves that they are radii of a common circle, which we call the incircle. And immediately after demonstrating this construction, his next proposition was construction of the circumcircle, which we looked at before. Is it weird that I'm more focused on the point at the center than the circle? Well, maybe. We'll get back to that later. For now, let's look at the two circles.

Here they are together. What's the relationship between them? The circumcircle is always bigger, and they don't in general have the same center.

Unless we want to start fiddling around with magnitudes of the sides or angles, we don't have a lot of variables here. Just the radii of the two circles and the distance between the centers. And here's a good reason to consider only those three numbers as important in the incircle-circumcircle relationship:

For any arrangement of incircle and circumcircle, there are infinitely many triangles that could be drawn to fit them, with varying side lengths and angles. So we should expect that those values don't matter, and the relationship between the circles should depend only on the circumcircle radius R, the incircle radius r, and the distance d between their centers.

To figure out how those values are related, we will first prove a handy little theorem about intersecting chords.

Theorem: the products of the two segments of intersecting chords are equal.

That is, we are saying AP * PB = CP * PD. Proof is by vertical angles, meaning that the red angles are equal, and the inscribed angle theorem, meaning the blue angles are equal and so are the greens. Therefore the two triangles APD and CPB are similar, so

AP / PD = CP / PB,

AP * PB = CP * PD.

Okay, let's use our new theorem.

Extend the angle bisector CI until it meets the circumcircle at K (red). Draw OI and extend it to meet the circumcircle at U and V (blue). Then by intersecting chords,

1) CI * IK = UI * IV = (R - d) (R + d) = R^2 - d^2

Next, a little angling. Draw segments KA and AI. Let α be the angle at vertex A and γ be the angle at vertex C. Segment CI is an angle bisector, so the red angles ACK and KCB are γ/2, and by inscribed angles, so is the red angle BAK. Segment AI is also an angle bisector, so the blue angles are α/2.

The green angle completes triangle AIC, so

∠AIC = 180° - (α + γ)/2

The purple angle is supplemental to it, so

∠AIK = 180° - (180° - (α + γ)/2) = (α + γ)/2

Therefore triangle AIK has two angles equal to (α + γ)/2, so it is isoceles, so

2) AK = IK

Finally, draw a perpendicular from I to side AB to intersect at Z. Draw KO and extend to the circumcircle at L. Now the two red triangles, CZI and LAK, have one angle equal to γ/2 (inscribe angle theorem again), and they are both right angles, so they are similar. So,

CI / IZ = LK / AK

3) CI * AK = LK * IZ = 2 R r

Putting 1), 2), and 3) together, we get this:

Theorem: given a triangle with circumradius R, inradius r, and distance between circumcenter and incenter d, 2 R r = R^2 - d^2.

This is known as Euler's theorem in geometry, first published by William Chapple in 1746 and then by Leonhard Euler nineteen years later. Chapple also first proved the existence of the orthocenter.

So does the converse hold? That is, if we have a pair of circles that fits that formula, can we always draw a triangle inside the larger one that is tangent to the smaller one?

Yes! In this image, the circles are drawn according to the formula and then the triangle drawn to fit them, and it works! (And although I am satisfied with this image because it turned out the way I wanted, somehow looking at it makes me anxious. This triangle looks like it's not having a good time. Don't stare at it too long if it bugs you.)

This is an example of Poncelet's porism, a theorem that says this works for polygons of any number of sides. If you have a pair of circles that will fit as incircle and circumcircle for some n-gon, then there are infinitely many n-gons that fit those circles. Chapple proved it for triangles and then Jean-Victor Poncelet proved the general case in 1822.

What else can we say about the incenter? Last week, we saw that the altitudes of a triangle are also the angle bisectors of the orthic triangle, which means that the orthocenter of the reference triangle is the incenter of the orthic triangle. Triangle geometry is full of cases like this, where the X-center of the Y-triangle is also the Z-center of the W-triangle, or whatever.

The incenter always lies in the interior of the circle with the line segment form the orthocenter to the centroid as a diameter. And last week, we learned that the centroid, circumcenter, and orthocenter all lie on one line, the Euler line. The incenter does not, unless the triangle is isosceles, in which case all triangle centers lie on the Euler line.

I suppose it's about time I explained what makes these points special and why we're looking at them. The four points I've been talking about belong to a class points called triangle centers. Though these four constructions were known to the ancient Greeks, they weren't identified as belonging to a special class until the 19th century, by which time many other triangle centers had been identified.

So what are they, exactly? Many of them are in fact the centers of notable circles, such as the circumcircle and incircle, or the centers of perspectivity of some pairs of triangles (I will have to explain perspectivity another day), and I suppose that's where the name comes from, but that's not what defines them.

Introducing a formal definition would be premature at the moment, but for now, we can observe one of the properties that applies to the four centers we've looked at so far. They are all constructed symmetrically with regard to sides and vertices. That is, if we use the midpoint of a side, we use the midpiont of all three sides. If we use the angle bisector of one angle, we use the bisectors of the other two as well. For a given triangle center, the roles of vertices A, B, and C are interchangeable.

Let's look at how things can work out if we don't construct things symmetrically. We constructed the incenter by bisecting the triangle's angles. But if we extend the sides into lines, we see that there are actually two bisectors at each intersection of the side lines, an interior bisector and an exterior bisector.

Here we have the exterior bisectors of vertices B and C (green) meeting the interior bisector of vertex A (blue) at a point Ja. This is called an excentral point, and it's the center of an exscribed circle for the triangle ABC.

But it's not a triangle center, because it wasn't constructed symmetrically. If we switched the roles of A and B in this construction, we'd get a different point. If we switch A and C, we get a third point.

Here are the three excircles and the incircle together. And just as with the incircle, there is a formula describing the relationship between the radius of the circumcircle, the radius of an excircle, and the distance between their centers. It's almost the same as the formula for the incircle:

2 R r_a = d_a^2 - R^2

where R is again the radius of the circumcircle, r_a is the radius of excircle A, and d_a is the distance from its center to the circumcenter. The equations for the other excircles are formed analogously.

And what about their positions? We can't just plonk them down anywhere and say those are the excircles of some triangle. Let's look at the angle bisectors again. The exterior bisectors, in green, form the excentral triangle. The interior bisectors, in blue, meet them perpendicularly at the vertices. That means that internal bisectors form altitudes of the excentral triangle, which demonstrates today's final result.

Theorem: The incenter of a triangle is the orthocenter of its excentral triangle, and the incenter and excenters form an orthocentric system.

It's all connected!

If you found this interesting, please try drawing some of this stuff for yourself! You can use a compass and straightedge, or software such as Geogebra, which I used to make all my drawings. You can try it on the web here or download apps to run on your own computer here.

An index of all posts in this series is available here.

[degusart]

So I colored that image (and added a couple of characters that were missing). Anyway, it's the full lineup of BFFs. I feel so normal about these blorbos. Thank you to @viridiandruid for running such a fun game with great characters!

[characer names credits and other info under the cut]

A)ale! my PC and the loml. Massuraman Binder. They have a minimum of three souls in their body at one time and a maximum of five. they're doing so okay right now; don't worry about it

B) Devin, an eagle ale can summon him through their armor as an ally.

C)Cpt. James Hawkins. played by @theboombardbox, spellsword/barbarian. he's missing half of his soul <3, the Hat Man is following him, and he has worms.

D) Sash played by @halfandhalfling our wich/werewolf bestie. Apparently, she's a princess of the moon, but we don't have time to unpack all of that. Also, her (adoptive) mom fucked James.

E) Fig! Sash's familear

F) Orsa, Kiri's animal companion

G) Revazi, once played by @werepaladin. a barbarian whose "grandfather" Grandfather, a red greatwyrm, has been the patron of the party since like session five.

H) Chosen, in a human-only setting, she's an elf child! She's the reincarnation of ale's greatest enemy from both of their past lives, and they're apparently destined to end each other. But for right now they're buds, and she's the adoptive daughter of Kiri.

I) Kiri, @recoveringrevenant's PC, a Spirit Shaman. The newest Pc of the BFFs, our very chaotic party's grounding force, she can see a lot of stuff going on that no one else can see, both literally and figuratively.

J) Beren, a strange teenager our party was charged with keeping safe, then promptly lost (we're working on it). The person who charged us with keeping him safe may or may not be an abloeth, allied with the red dragon previously mentioned.

K) Cloves, the horse we bought in session two or three, that was then awakened by a random druid. He was one of the oldest members of the BFFs until... recently...

L) Erina, @recoveringrevenant 's retired PC, lets us crash at her place most nights, and she was a founding member of the BFFs, so even though she's not adventuring with us anymore, she's still one of us.

M) Agamemnon, our ship's AI, he's an orb that likes to dress up as a wizard :>

N) Ajatus, a guy we threatened to get to help us, but somehow became fully one of the crew. also, we need him to drive the boat, so, a BFF it is.

O) Father Lagi, a priest whose church collapsed into a skink hole after we visited it. We offered him a job in recompense, though by some of the conversations we've had, he's pitty chill in general. Also he embezzled like all of the church's coffers, so that's funny

P) Dahlver-Nar, one of the many souls that take up residence inside of ale's body. Though he's a bit more permanent. He helps out and gives advice alongside some skick-ass powers.

Q) Naz, this is the character I forgot in the first render of this piece. she's functionally dead atm (permanently trapped inside an amber tree), but you know how it is. a character once played by @recoveringrevenant as well

R) Cousin Chet! the half-dragon half ???? freak. we love him though

S) Bailey Wick, a once stow-away, now rogue-for-hire she has the sticky fingers and high dex our party lacks. So whenever we need to infiltrate a place, we send her on those missions. Though we've recently found out she's like 19, which is horrifying lmao. She also is one of the most competent members of the BFFs only because she's the only character that consistently rolls above a 10 (like genuinely)

T) Tansu, Revazi's twin sister. Our most recent true member of the BFFs, she's.... gone through it