#axis of symmetry

[math-journal2]

<— Unit 27: Part 3 —>

Trick

F + V —> Eq

F + e —> Eq

C, V, F —> Eq

Eq —> V, F, e

Non-Standard —> Standard

Page 76

[math-journal]

Parabolas

X

X

.

[funsizedcrow]

traditional art is fun until you have to draw something symmetrical

[sonic-adventure-3]

i shouldve been asleep 7 hours ago. i opened up blender just to quickly check out a couple things and then suddenly i was modelling jerry. weirdly higher poly than rig or squabble, super scuffed, but i am indeed able to model in blender. i need to go to beddddddd

[tenth-sentence]

Take the letter "A," flip it about a vertical axis passing through its apex, and it will provide you with a perfect replica of the original.

"The Fabric of the Cosmos" - Brian Greene

[fall24iksection]

ARCHITECTURAL DESIGN - ORDERING PRINCIPLES

consider these principles "fundamental ideas" that serve as the foundation for a system. these principles can structure your design and bring order to the lay-out of a building.

AXIS

SYMMETRY

HIERARCHY

TRANSFORMATION

DATUM

RHYTHM

PATTERN

REPETITION

[unravelingwires]

Paraboloidal

“You know,” Lakshmi mused. “I really hate math.”

Sam had finally figured out how to make alcohol on the ship. This may or may not have been a good thing, but Campbell hadn’t banned it, so the rest of them were taking advantage.

“You’re a physicist,” Lucian said incredulously.

“Yeah, but physics is just physics.” Lakshmi waved her bottle in emphasis. Ally, slumped into her side, snorted. “I get it when you have to calculate the strength of gravity or whatever, I just hate it when someone says ‘this pringle’s a parabola, actually,” and you have to nod along like that makes sense.”

“Pringles are actually hyperbolic paraboloids,” Sam corrected, the only sign of his inebriation a slight hesitation before “paraboloids.”

“That shit!” Lakshmi gestured. “That’s exactly what I’m talking about.”

“Think it’s better than your tachyon negative-mass bullshit,” Lucian muttered.

Lakshmi straightened. They all braced for an argument, but she just said “fuck you” before bursting into laughter. Shae rolled their eyes.

[spencerslover-blog]

did you know that jellyfish are radially symmetrical? they are symmetrical because of a central axis that runs through the length of their body. They have an upper and lower part, but no left or right sides. They are different from other types of animals such as reptiles, fishes, birds and arthropods, which exhibit bilateral symmetry. I love them

[art-of-mathematics]

I know I have drawn this shape so often already, but the process of drawing it is so soothing.

And for that, I have drawn a kind of step-by-step guide how to draw that shape in the top of this drawing:

(from left to right: ) [sorry in advance if I make it sound more complicated than it actually is. If you want to draw it, I would advice you to focus more on these illustrations rather than on my gibberish-text.]

1. draw a 2-dimensional Cartesian plane - or, in other words: just draw a cross like depicted

1.1. mark 2 points on the y-axis/vertical line with same distance to the coordinate origin, then mark 2 points on the x-axis/horizontal line with the same distance to the coordinate origin. (The markings on the y-axis need to be farther away from the origin than the markings of the x-axis)

2. connect the 4 marked points like depicted above. This is a function plot of a tractrix. (it has two mirror symmetry axes. )

3. draw an ellipse and connect the two markings on the x-axis. This becomes a kind of "belt" for the pseudosphere (4th picture)

4. part the ellipse into whatever-amount-you-want of partings (like you would cut a cake) and slightly mark these.

5. now imagine you cut that shape horizontally on the outer surface. (In the 5th picture I depicted that with red-ish pen across the pseudosphere. ) -

6. then the cut shape needs to be "(shape) shifted". For that we use a set of marked points we did in step 4). Furtherly, we "cut" the ellipse open, and push one end of it to the top, and the other end to the bottom. (depicted in picture 6 )

7. Then we connect the rest to get that shape:

[literaryvein-reblogs]

Some Greek Art Vocabulary

for your next poem/story

Alabastron - A small vase for olive oil, often scented.

Amphora - A two-handled terracotta storage jar used by the ancient Greeks to hold or measure oil, wine, or milk.

Calyx - The external, cup-shaped, leafy part of a flower.

Calyx-krater - A krater with handles in the cupped shape of a calyx.

Epitaph - A funerary inscription.

Krater - A large pottery vessel with a mouth broad enough to allow a jug to be dipped into it; used for mixing wine with water in ancient Greece.

Negative space - The area around the decorative subject on a work of art; the external or outside area that defines the subject.

Palmette - An ornament of radiating petals on a calyx-shaped or budlike base; along with the sphinx, palmettes often top Greek grave markers.

Positive space - The area on a work of art where the subject is represented; the internal area.

Registers - In art, horizontal bands of images that often appear in vertical series on walls, vases, and so forth.

Relief - A sculpted surface in which the decorations stand out, in varying degrees of depth; reliefs are meant to be viewed frontally, not in the round.

Sphinx - A fabled creature that is half human and half animal; in Greek art and legend the sphinx has the head and torso of a woman.

Stele - An upright slab of stone usually inscribed and sometimes decorated with designs or figures that are painted or carved in relief; used by the Greeks as grave markers or for displaying public notices.

Symmetry - The duplication of an image on either side of a real or imaginary central axis.

Terracotta - Clay that has been fired at a relatively low temperature, brownish-red or buff in color.

Source ⚜ More: Word Lists

[math-journal2]

<— Unit 16 — Unit 17: Parabolas — Unit 18 —>

Unit 17: Parabola

Part 1 —>

Basics

Misc

Domain & Range

Min & Max & x-intercepts

Graph —> Vertex Form

*new point, not new porn. Too lazy to change it.

Quadratic —> Graph

Page 45

[astrolovecosmos]

Aries - Libra Axis: Tells a story about taking action vs. indecision, inaction, and procrastination. Tells a story about selfishness but also giving to the detriment of self, lack of boundaries, assertion, charm, persuasion, force, peace and war, leadership and cooperation, independence vs. partnerships, passion, romance, self-awareness vs. shallowness and detachment, insensitivity vs. tact, cheating and deception, winning and losing, honesty and bravery. Tells a story about lovers and fighters.

Taurus - Scorpio Axis: Tells a story about control, power, jealousy, resentment, stubbornness, indulgence and sensuality, comfort and thrill, safety and danger, possessive behavior, materialism, emotional strength and influence, inner security or contentment and inner empowerment and passion, willpower, revenge, grudges, manipulation, obsession, seduction, self-destruction, transformation and rebuilding. Tells a story about self-mastery and self-esteem.

Gemini - Sagittarius Axis: Tells a story about communication, learning, knowledge, teaching, exploration of mind, body, and the world, trickery, con artists, betrayal, support, lies and truth, versatility, duality, variety, curiosity, superficiality vs. depth, philosophy, morals, logic, spontaneity and fickleness, symmetry vs. asymmetry, restlessness, carelessness, freedom, exaggeration vs. factual, movement, cunning wit and intellect as well as wisdom, optimism vs. skepticism, dissembling, analyzing, deception, schemes, gossip, boasting, charm vs. tactlessness, and promises. Tells a story about storytelling - lessons and adaptation.

Cancer - Capricorn Axis: Tells a story about protection, self-preservation, endurance, practicality, emotions and rationality, defense vs. offense, vulnerability, attachment, clinging vs. self-reliance, sentiment, nostalgia, home and family, ambition, purpose, clans, tribes, societies, private world vs. external/outer world, moods, cycles, authority, parents/mothers and fathers, caution, responsibility, duty, patience, compassion vs. cruelty, intuition, shrewdness, strategy, contentment vs. dissatisfaction, security vs. insecurity. Tells a story about needs and being uninhibited, as well as control and discipline.

Leo - Aquarius Axis: Tells a story about leadership, charisma, confidence, individuality, self-expression, creativity, innovation, the power of one vs. the power of the many, attention, compulsion, pride, ego, play and discovery, experimentation and rebellion, drama, curiosity, socialization, influence, dignity, generosity, benevolence and/or common good, chaos, destruction, passion vs. dispassion, humanity, divinity, fellowship, organized groups, separation or standing apart, control or tyranny, strangeness and what's rejected vs. what's accepted or even celebrated. Tells a story about the king/queen/politician and anarchist/rebellion/revolutionist.

Virgo - Pisces Axis: Tells a story about the spirit and body, healing, helping others, service, caring for others, listening to your body or your intuition, purity vs. corruption, compassion, sensitivity, impressions, flexibility, logic, imagination, being receptive, mysticism, confusion, illusions, clarity, distillation, categorizing, researching, analyzing - a thorough search for facts/truth. Tells a story about sacrifice, empathy, saving others, discernment, efficiency and productivity vs. procrastination and rest, modesty, free and flowing energy vs. precise and predictable energy, perfectionism vs. admiring flaws, realism or skepticism vs. idealism, details vs. big picture. Tells a story about the dreamer and the worker, the ability to make our dreams come true.

[bestanimal]

Round 1 - Phylum Echinodermata

(Sources - 1, 2, 3, 4)

Echinodermata is a phylum of animals which are bilaterally symmetrical as larvae but radially symmetrical as adults. It includes starfish, brittle stars, sea urchins, sand dollars, sea cucumbers, and sea lilies.

Echinodermata is the largest marine-only phylum, and echinoderms can be found at every ocean depth from the intertidal zone to the abyssal zone. They make up a large portion of life in the deep sea. They are diverse, with some being sessile (lacking self-locomotion) while others are motile (able to move independently). Many are restricted to crawling slowly across the sea floor, while some can swim through the water column. They have a skeleton beneath their outer layer of skin, which is composed of calcite-based plates called ossicles. This would be heavy if it was solid, so it is instead porous. The ossicles may be fused together or articulated, and may have external projections such as warts or spikes. Echinoderms are often brightly-colored, and some of their pigment cells may even be light-sensitive, causing many echinoderms to change appearance completely as night falls. Their diet varies, with some species being predators, some being filter-feeders, some being herbivores, some only eating algae, and some being detritivores. Some injest food through a mouth and expell waste through an anus, while others can only expell waste back through their mouth. The ventral side of many echinoderms is covered in tube feet, each of which typically end in a suction cup pad. They primarily use their tube feet for movement, though some sea urchins will also “walk” with their spines.

Almost all species have males and females, though some are hermaphroditic and at least one reproduces by parthenogenesis. Eggs and sperm are released into open water, where they are fertilized externally. Some species may aggregate during reproductive season to increase the likelihood of fertilization. A small handful of species have internal fertilization. Some echinoderms, especially in colder areas, brood and carry their eggs until they hatch. Echinoderm larvae are usually planktonic, swim via cilia, and have bilateral symmetry. During metamorphosis, the left side of their body grows at the expense of the right side, which is eventually absorbed, ending with the body arranged in five parts around a central axis. Some species reproduce asexually. They do this by splitting in two, like a cell, and generating a new body half from the old one. Some larvae may also reproduce by budding.

The first echinoderms appeared in the Early Cambrian.

Propaganda under the cut:

Echinoderms are able to regenerate tissue, limbs, organs, and sometimes full bodies from a remaining portion of limb. Starfish and brittle stars may detach an arm as a defense mechanism, swimming away while a predator is distracted by the wiggling limb. Some sea cucumbers, on the other hand, take this to the extreme by expelling their cuvierian tubules (respiratory tubes) to entangle potential predators. Sometimes this is also accompanied by a discharge of toxic holothurin. It can take 1.5 - 5 weeks for the tubules to regenerate, depending on species.

The hard endoskeletons of dead echinoderms are geologicallly important, contributing to limestone formations.

Echinoderms sequester about 0.1 gigatonnes of carbon dioxide per year as calcium carbonate, making them important contributors in the global carbon cycle.

Sea stars are heavily muscled, and are able to go from soft to rigid in order to pull open the shells of their mollusc prey.

Sea urchins are among the main herbivores in reefs and there is usually a fine balance between the urchins and the kelp and other algae on which they graze. In the past, mass mortalities of sea urchins have led to algae blooms.

Some sea cucumbers have webbed swimming structures that allow them to swim freely through the water column. Pelagothuria natatrix (seen below) is the only truly pelagic echinoderm known so far.

(source)

Echinoderms seem to have an innate internal clock. Even at the depths of the ocean where no light penetrates, they are still able to synchronize their reproductive activity.

We don’t know much about Sea Pigs (Scotoplanes globosa) (seen in gif) other than that they’re poisonous sea cucumbers that feed on detritus at the sea floor. But we do know that they are often seen clutching young king crabs (Neolithodes diomedea) and carrying them around. One possible theory is that these crabs latch onto S. globosa to gain access to nutrients and movement, and sheltering beneath the poisonous sea pig allows them to hide from predators. As sea pigs are sometimes plagued with parasites that bore holes into their bodies, the crabs may also help the sea pigs by keeping them clean of parasites. For now, all possibilities are just hypotheses, but we can stil Awww at the globby pink sea cucumbers cuddling their little pet crabs.

Along with Hemichordata, they are the closest relatives of Chordata (aka our phylum!)

Some sea urchins pick up rocks, shells, and other debris and carry them around to shade themselves from the sun. Some people who keep them as pets have come up with creative ways to allow them to do this without dismantling the architecture:

(source)

Silly hats aside, these seemingly simple animals are using tools.

[renardiererin]

satoru gojo with his six-inch fingers stuffed deep inside of you, other hand shoving fingers down your throat while his mouth worked at your neck. suguru geto, on the other hand, had his mouth roughly attached to your plush thighs, working firm deep purple teeth marks up your body.

“look at our cute girl, satoru. she’s shaking so much for us already.”

“she’s just so good for us, suguru. think she can take some more?”

the two didn’t give you a chance to respond before both of them had shoved their respective middle and ring fingers into you, stretching you out nice and wide.

“please i can’t— i can’t fit— too big, too much”

“oh don’t be stupid, dollface, you can handle whatever we give you. i say, we work one more orgasm out of her like this and then we make her take our cocks. what d’ya think about that, satoru?”

“i think it may be the only good idea you’ve ever had.”

gojo slapped a cheshire cat grin on his face and pressed a light kiss to your clitoris, sucking and biting on the soft nub while his and his best friends fingers worked at all the right little spots and corners inside of you.

“feel good, baby?” he asked

“yes, ‘toru, yes it feels so good”

he elicited a small, deep chuckle against your bud, the slight vibration causing you to lose your restraint. back arching, hands gripping the sheets beside your hips so hard your knuckles turned white, whimpers, whines, and cries leaving your lips without any self control, seeing nothing but white and stars.

“what a good fucking girl she is, did you see that suguru?”

“i saw. i think she’s ready for more, don’t you?”

“nononono, please please i can’t— it hurts i can’t take it i can’t take more please”

“but don’t you want us to stuff you full? paint your pretty insides all white?” geto poured his eyes into yours, shimmering with lust and mischief.

“okay. i can handle it. i’ll make it work, fill me up, please.”

“oh now look at that, sugu, she’s so needy. i say we’ve prepped her enough, don’t you think?”

“oh absolutely. she doesn’t need anything more. she’s a big girl, after all. she can take it.”

their dicks lined up against one another, ramming into you almost immediately without easing in. screams and cries falling from your lips at the sudden stretch and piercing pain, but thrusting your hips to get them deeper nonetheless. all of it had you seeing entire galaxies in under five minutes: the pair stretching you out on their ridiculously huge dicks, satoru’s fingers working at your clit while suguru had one of your tits stuffing his mouth full and the other being fondled rather aggressively as he pulled and squeezed and pinched and prodded at your sensitive nipples. satoru’s mouth moving back to one side of your neck while suguru’s took the other side, suguru’s hands now cupping your ass as he squeezed and spread and manhandled the fat, satoru’s got one hand on your tits and one on your clit, suguru lifting your thigh up to spread you open even further, pressing the top of your thigh to your chest. it’s truly a perfect combination if you wanna get your brains fucked out and your guts rearranged.

“pretty, can you tell me the vertex coordinates of the parabola f(x)=6x^2-9x+7 with an axis of symmetry of -8?” suguru finally got out, bringing you back to the whole reason for all of this. the fucking study group.

“start her off easy, sugu, cmon. what’s the rush? baby, can you tell me which function system f(x)=x^2 even is?”

“q-uadr..atic” you stammered out through whines and ragged breaths.

“that’s right, baby. i guess maybe she is ready for your questions, sugu. i’ll let you handle the rest of the questions. i’ll just focus on her pretty little cunt right here. so messy.”

“okay princess. you wanna cum?” geto spoke while pulling out and flipping you over the table rather than on top of it how you had been, ass up, back arched, tits pressed flat against the wood of the table, bent over all pretty just for them.

“then how about you fill out that worksheet for us, yeah? cmon, doll. get through 3 problems and i’ll let you cum. 5 and we’ll cum inside just for you.”

and just like that, both their dicks were shoved balls deep in your tight little pussy all over again, brain trying to operate properly enough to graph those fucking quadratic formulas.

[wifetomegatron]

perceptor wants to study you. afab!reader. nsfw! drabble. skirt mentioned.

Perceptor is a scientist. It is his job to learn. To observe. In many ways, when the situation calls for it, it is also his job to solve things. The most reliable questions to answer were equations, solid and truthful: numerical variables were tangible enough to pull apart and rebuild without straying too far from his reality. They only have one answer.

But you were different. A moving target that never stood still. Always changing and taking him by surprise. You were a blow to his ego. And that caught his attention. A beauty that had no source in his stout and unyielding world. The possibilities were endless.

He wants to drink you dry.

" Open your mouth."

His voice was barely short of a whisper. Do all humans have this ability to render sentient beings speechless, to rob the room of any sound? Maybe they are also capable of manipulating magnetic fields: of defying the laws of gravity to knock their opponents off their axis. That would be dangerous. It was a good thing that you didn't see him as a threat. Not when you were looking at his past your lashes, eyes coy — fingers drawing circles around his shoulders.

" My," You hummed, " How bold of you, Perceptor."

Have you always had this lilt to your voice? He searched his processor for a comparison — the water running down the creek back in your green organic planet, the lonely echo of bullets as they ricochet, the tentative hum of a spark as it reignites. None of them comes close. He feels sick. Dizzy. Maybe he needs to go and see Ratchet.

" Open your mouth, please."

He repeats himself. Voice surprisingly level, even though it felt like his vocalizer was going to snap. And that earned him a smile. He did nothing to warrant your laughter, and yet you indulged him like you always do. Tongue — pink and wet — peeking past the row of pearls you call teeth as you tilt your neck gently backward. His hand moved instinctively, dwarfing the back of your head for support. 

He pressed the pad of his thumb flat across the soft surface and felt the metal sink. Your eyes fluttered shut, legs, slightly parting to let him slot his body in between. He held you in place. Chest to chassis, the thin fabric of your shirt did nothing to hide the subtle race of your heart.

Sinew and muscle, humming, unlike anything he's ever heard. 

This is for science, Perceptor tells you, retracting his servos to pick up his PADD, mind bursting with a flurry of thoughts. He couldn't even remember what he wrote down. He will have to review it later. 

He runs a few more exams. Medical needs it. And yet he had offered himself to run them. He says it was also crucial for his research. 

What kind of research, Ratchet had asked him.

A personal one, he had replied.

No one stopped him, especially not when you were so eager to help.

He kissed you on the lips. Tentatively, once, twice. You sighed into his mouth. Lips soft. Too soft. He needed to know if you were just as delicate between your —

This is for science, Perceptor tells himself, already sinking onto his knees. You were a plethora of texture, so different from his biology. So far from the mundane. While he clings almost religiously to the dependable — facts, numbers, metal — the purest, rawest form of science is the unknown. He nudged your knees with his nose, wider, and you wordlessly complied. 

Every scientist is an explorer at heart. And what is more unfamiliar than the feel of your skin? 

Perceptor rubs up and down your thighs, feeling you shiver. His cooling fans clicked to life, reacting, responsive. And this pleased you. And you pleased him.

Prettiness is symmetry, all things in the right place. And yet you were an artifact of unknown beauty, with no origin, no source. All things have to start somewhere — stars were born out of gases, sparks out of a mass of positrons supercharged by energon. But where did you come from? So alien. So different.

If the Earth was your creator, then you must be molded out of clay, shaped by her gentle hands, not carved, for he was sure even under his touch you would break. That the slightest misplace of pressure would shatter and scatter you into pieces.

But humans were known to be resilient. He likes to call you generous instead. Ever so giving, ever so kind.

Today, you wore what you called a skirt. Isn't it pretty? He doesn't have much to say about its color other than that it was practical and worn with a purpose. An invitation.

You mewled in encouragement when he pressed a kiss square against the plush, wet slit of your cunt.

Perceptor is a scientist. It is his job to learn. To observe. In many ways, when the situation calls for it, it is also his job to solve things. And there is still so much he wants to learn from you. He wants to map every sensitive spot that made you gasp and writhe. He wants to chart every delicate twitch, every clench. And with your body arching atop his table — sweat dripping down your brow, you were his muse.

But make no mistake, this was a symbiotic relationship. You were also studying him, changing him. ( He was certain you've ruined him for anyone else.)

Perceptor knows he should have stayed as an objective observer, standing on the sideline. Yet you were a very seductive hypothesis, just waiting to be kissed to life. There was lubricant leaking down his chin as you reached your high, nails scratching the back of his helm. Objects cluttered off the table in the distance, yet he continues to drink.

You broke his idea of truth, and Perceptor lets you.

[eri-pl]

The sad thing about Elrond

(no, not everyone sailing or going brr on him, the other one)

From all the people who like Elrond, who claim to be friends, even to love him maybe, very few see him as himself. His parents (sailed, effectively sailed + parents extended edition: dead, ???), his brother (brr), his wife (sailed), his kids (brr, ?, ?). Maybe a few others.

Others look at him and see someone else's face. Or at least they see Elrond as a symbol of this or that. Never as himself.

He just tends to remind everyone of someone or another.

Many of the old Noldor see him as The Last Feanorian (minus the kinslaying problem), many elves see him as Luthien 2.0, many humans see him as the blend of all the elves they ever heard of (at least the good ones) and/or as a stand-in for their legendary ancestor king Elros, even Bilbo sees him as Mister Related To All The Stories Which I'm Gonna Sing Anyway. And there are probably many other things worrying is seen as.

(yes, Arwen has this problem too, but she's not in the Silm, and I mostly think about the Silm)

I suppose even Elwing sometimes looked at her kids and saw Earendil's face in them. That's what parents do, especially when missing the other parent. But it was only moments.

And then she was chased and jumped.

I'm sure M&M initially saw the twins, at least subconsciously, as a replacement Ambarussar, and as their redemption for what happened to Dior's sons. But I think they (at least Maglor) got over it and learned to actually see them, and this was one of the things that made "and love grew" possible.

And then one died and the other disappeared.

What's most sad in this is that I don't treat Elrond better. All the reasons I like him (at least the vast majority) aren't really about him. Realizing that may be the reason why I count him on my fave list lower than Finrod. He's still 3rd on the list anyway. But I wish he was there more as himself and less than the symmetry axis of the Silmarillion and all the associations I have to him.

Tbh he probably wouldn't be this high. I imagine Elrond is actually thie same kind of well-mannered, polite and kind as was one of my friends in high school and while it was fully a good thing, it also somehow made her hard to approach or to relax around. Which... Is even more sad, I guess.