#center of an equilateral triangle

[joshthewalkingtrainwreck]

For those kicking around with the Godot Engine and having trouble finding center-mass of a Mesh3DInstance as an equilateral prism (on a 1:0.866:1 dimensional ratio) where it orbits a point instead of rotating in place:

you have to keep in mind that Godot will adjust the height by bringing both the top boundary of the prism down and the bottom boundary of it up at the same time...

You have to translate it up along the y-axis by half the height (in order to align the bottom of the prism with the origin), then translate it down by the formula for finding center point of an equilateral (approx. 2/3rds down going from the apex to the opposite, or (sqrt3)/6).

once that's done, you can attach animations to the parent node, and it should rotate instead of orbit.

(video was via RamblingStranger @ godot cafe, dude had to make a video demonstrating what they were talking about in order to get it to click for me. This is also how I learned that you can just type the calculation you're looking for and it'll solve for it as the output. Handier'n shit!)

[rjalker]

purely from random osmosis, but if bill cipher was born with his eye on his "side" (facing upward in what Flatlanders call their inside), then he'd be blind as a Flatlander because we wouldn't be able to see within Flatland itself at all.

And also no one would even be aware that he has an eye to begin with, because it's literally outside their realm of perception. They'd think he was born without any eye and that he was literally just imagining anything he thought he could see.

[ID: A four way grid with the first row labeled "Bill Cipher apparently", first seen from above, as an equilateral triangle with a round eye in the center of his face, looking up and to the side. He is then seen from the side as a line with a half circle on top to show his eye, labeled, "Cannot see surroundings at all, cannot look in any direction except Up". from his eye radiate three lines to show his area of vision, with a zig-zag line in front of him to show where he cannot see. The second row is labeled, "Regular Flatlander", and shows another equilateral triangle, but this one has their eye on their perimeter at their top point. When they are shown from the side, they are labeled, "Can see surroundings, but cannot look Up", with three straight lines in front of their eye, which points to the size, and a zig-zag above them. End ID.]

So. If you're planning to write a crossover with Flatland where you want it to actually follow Flatland's worldbuilding, Bill should be blind while he's in Flatland. He'd have to navigate purely though touch and sound and would never see anything except whatever is above him.

Edit 3 hours later: also, he would have just starved to death as a baby unless there were some serious and immediate medical intervention, because Flatlander's eyes and their mouths are the same thing. So he'd have no way of eating anything.

So, he would also need the Flatland equivalent of a feeding tube for his whole life, unless he had some guardian angel in Spaceland who was feeding him from above.

[xx-j4nu5-c4t5-xx]

WARNING: INCREDIBLY LONG POST AHEAD

The Sims 2 Fitness System: Proposing Reworks and Slowly Going Insane

I. Introduction

The Sims 2 was absolutely revolutionary, both for its time, and even into the modern day, as a life simulation game. The level of detail put into seemingly basic systems and interactions and the love that was poured into every part of the game make it stand out even among titles that released years later.

However, the passage of time halts for no man, and The Sims 2 is no exception. The graphics are often described as looking rough and rudimentary, some of the references haven't aged spectacularly, and it is very clearly a product of its time. Despite this, most aspects of the game translate perfectly fine to today's audiences, except for one system that I've noticed is less than spectacular: the part that dictates the shape of your sim's body.

The fitness slider is a pretty simple framework: work out, and your sim gains muscle, and their body changes to reflect it. Eat too much, and they'll put on some weight. Do neither, and they stay skinny.

Simple enough.

But why is being skinny the default? And why are muscle and fat treated as mutually exclusive, like a human being can't have both?

And why are they in that order? Why would you have to lose muscle to gain fat? Why is being skinny a step you have to go through at all, when someone could realistically transition from muscular to fat or vice versa without ever fully losing either?

Well, a large part of it, I'm sure, was the 2000's and the focus on skinniness, especially among teenagers and young adults (which seemed to be the target audience when TS2 released). Skinniness being treated as a default somewhat lines up with the culture of the time. But it shouldn't have to work like that, right? Especially not now? There's got to be a better way of going about it all.

II. The Proposal

A muscular frame and a heavy-set frame can both be considered extreme values on a scale, and a thinner one can be considered neither. Simply put, if you've got fat, you're chubby; if you've got muscle, you're beefy; and if you've got neither, you're skinny. But that doesn't mean that skinniness is a midpoint between the two other states like on a simple scale, number line style.

In reality, muscle and fat aren't positive or negative values of one variable. They're two entirely separate variables that can be toyed with to create an entire spectrum. Thinness is now no longer a midpoint, but a third state that the body can fall into.

You can be fat, and you can be muscular. You can be neither.

And now, you can now be both. Or a mix of all three states, go nuts.

With this setup, you've got less of a line and more of a triangle, with any point falling inside it corresponding to a different mix of variables. None of the points cancel out or directly oppose one another, and none is treated as the default value of the system.

So what's the default, then?

III. The Catch

The three extremes have to meet at one point in the center, right?

So what do we do if a sim is right in the middle? Does any fluctuation immediately send the poor thing careening into an entirely different body shape?

No. That's a bit much. What we need now is a middle ground between the extreme values. Something that doesn't lean too hard into being muscular, fat, or thin. A nice balance. A default or average body shape.

Would this require adding a fourth, entirely new body morph to the game? Would it even really solve the problem? Would it be worth any of the trouble of setting it up?

Yes, maybe, and probably not, if I'm honest.

But as long as we're dreaming the dream, let's imagine it.

The cool thing about equilateral triangles is that you can divide them into four equal triangles that are congruent with the original one. So, if we take a standard triangle and divide it into fourths, we get our little zones.

A sim, based on some outside stuff I'll get into later, will be assigned a point in the triangle that falls into one of these four zones, assigning them a different body shape. As the sim's point moves through the space, it may land in different zones and change their body accordingly.

But computers can't just look at a cute little diagram and understand it. We need a way to communicate to the program that hey! this does actually make sense and isn't just a bunch of nonsense. We gotta speak their language, and they speak the language... of math.

IV. The Math Jargon

Stick with me. I don't know what I'm talking about either, so I'll try to explain what I'm doing as well as I can.

The cool division thing about equilateral triangles also applies to right triangles as well, specifically the one we're using. Basically, what we need to do is make a graph all math class style so the computer can interpret it into usable data.

To do this, we need a series of steps.

Step 1: Make a graph. Let's say the Y axis is muscle and the X is fat. A Y-value of 1 is entirely muscular, an X-value of 1 is entirely fat, and the origin (0,0) is entirely skinny. Cool.

Step 2: Make the triangle. Let's add our X and Y values together so that, if the result is ever greater than 1, the point is invalid. This means that the point (0.25, 0.75) is valid, but (0.26, 0.75) is outside of the triangle and is therefore a nonsensical value. This makes it so that any point defined must land within the triangle to make any sense.

Step 3: Define the regions. Now we do the thing where we split it into fourths again, creating our zones (and making sure they match the variables we set). I've attempted to work out the math below but I'm a notoriously shit mathematician so don't take my word for it.

If x + y < 0.50, set the body type to Thin.

If .50 > (x + y) > 1, then check the variables.

If x > .50, set body type to Fat.

If y > .50, set body type to Fit.

If x and y are both < .50, set body type to Default.

(I've also tried my hand at writing something that could correct the values if they get out of the triangle.)

If x + y > 1,

If x = y, set both variables to .50.

If x and y are not equal, average both values with .50 over and over until the point is valid.

Step 4: Now, all we have to do is link up the zones with the different body shapes and, if all the math works right, we're good to go!

V. So what does this do actually

Having this system in place not only allows for more realistic and balanced weight and fitness changes, but also for more control over the changes themselves.

A sim's body type is no longer a single variable; it's a dynamic value that can be skewed in more specific directions based on their actions and lives.

For example:

A sim that gets pregnant could have their fat value increase slightly.

A sim that has recently been very ill or has died and been resurrected could lose points in both their muscle and fat values, making them skinnier.

A sim that successfully wins a fight could have their muscle value increase slightly.

A sim that stops working out regularly could gradually lose muscle points over time.

A sim that frequently eats things like takeout and pizza could have their fat value increase over time.

This system would allow for not only more variation in bodies among sims, but also for more realistic reactions to their habits and environments. Would it be tricky to implement? Yes. But maybe it could be worth the trouble.

[selves-indulgent-coining]

scarlet macaw alterhuman flags

[pt: scarlet macaw alterhuman flags end pt]

requested by one of our headmates

alterhuman | therian | otherkin

otherhearted | otherlink | copinglink

othervague | constelic | nonhuman

nonhuman | physical alterhuman | holothere

[alt text:

12 flags with 6 equal horizontal stripes: crimson red, rose red, bright yellow, right blue, dark blue, rose red

There is a khaki circle centered in the flags, spanning from the top of the second stripe to the bottom of the fifth stripe. In each of the circles, there is a black symbol.

The symbols, in order:

a symbol similar to a fork in a path where the straight continuation is broken—part of the unbroken path is replaced by a triangle

equilateral triangle interlocking with a circle and there is a horizontal line in the center

a seven-pointed star

a heart shape interlocking with a circle and there is a diamond shape in the center

a pair of interlocking chain links

a pair of interlocking chain links in a diamond

a symbol similar to a fork in a path where the straight continuation is broken

five equally-spaced lines connected at one point—at the end of each line, the is a curve that dips down towards the center of the symbol before curling back outward into a spiral

a four-pointed star with four equally-spaced lines (two vertical and two horizontal) inside

a circle with a diamond shape (the four tips of the diamond are touching the circumference of the circle) inside— there is a circle inside of the diamond with two short vertical lines sticking out of the circumference — there is a dot at the center of the circle

a circle with a solid four pointed star centered in it

an anchor shape, but the top part (where the loop would be) is a triangle

end alt text]

The flag colors were picked from images of scarlet macaws, then color-adjusted.

Shout out to Lunatune and Patron Saint of ✨No✨on the People's Accessibility Discord Server for help with alternative text!

[ranmagender]

If Bill Cipher actually existed in Flatland him having an eye in the center would probably be what allowed him to see upwards, but i also think some folks miss that having an eye in the center would make him disabled and he'd need a feeding tube as ive seen sketches of but also he would be blind to anything but up and the field of view around him.

So having read the book i feel some crossovers like Flat Dreams while they are good i think him being disabled like that, it wouldn't be seen too kindly by flatland society, an equilateral triangle that cant see?? that talks about stars?

i'm not sure if he'd be destroyed or just institutionalized based on the society standards but like he wouldn't be treated with the respect of a normal triangle.

That's another reason why I often point out that his homeworld is not Flatland but Euclydia, while similar I'm sure and both two dimensional I'm sure they had different societal structures.

[talonabraxas]

This Week's Sky at a Glance, January 26 – February 4

FRIDAY, JANUARY 26

Once it's nice and dark, spot the equilateral Winter Triangle in the southeast. Sparkly Sirius is its brightest and lowest star. Betelgeuse stands above Sirius by about two fists at arm's length. To the left of their midpoint is Procyon.

Can you discern their colors? Sirius (spectral type A0) is cold white, Betelgeuse (M2) is yellow-orange, and Procyon (F5) is very slightly on the yellowish side of white. Binoculars make star colors more evident.

As Saturday's dawn grows bright, Mercury and fainter Mars have a very difficult conjunction just above the southeast horizon as shown below. You'll need an open horizon in that direction and optical aid, maybe powerful aid.

SATURDAY, JANUARY 27

The Moon, two days past full, rises not long after the end of twilight. Once it's well up, spot Regulus to its upper right and Gamma Leonis a little farther to its upper left. These are the two brightest stars of Leo's Sickle.

SUNDAY, JANUARY 28

The biggest well-known asterism (informal star pattern) is the Winter Hexagon. It fills the sky toward the east and south these evenings.

Start with brilliant Sirius at its bottom. Going clockwise from there, march up through Procyon, Pollux and Castor, Menkalinan and Capella on high, over and down to Aldebaran, then to Rigel in Orion's foot, and back to Sirius. Betelgeuse shines inside the Hexagon, well off center.

The Hexagon is somewhat distended. But if you draw a line through its middle from Capella down to Sirius, the "Hexagon" is fairly symmetric with respect to that long axis.

Take the line from Aldebaran to Capella, turn it to go from Aldebaran to Betelgeuse instead, and the Winter Hexagon becomes the Heavenly G.

Yin Yang Cosmic Polarity Talon Abraxas

[wyrmscraft]

Fall center piece for a table. It’s a variation of the OBW and very quick to put together. If you don’t mind equilateral triangles, I suppose.

More free motion quilting on this since it was small and easy to put in the neck of my sewing machine.

[gender-jargon]

[image ID: The decligender pride flag, created by tumblr user mogai-guy, rerendered by Gender (Gender-Jargon). The flag consists of eight horizontal stripes, with the top stripe being much thicker than the rest. At the center of the top stripe is a black, near-equilateral black triangle pointing downwards. The stripes, from top to bottom, are colored light grey, black, white, black, white, purple, white and purple. ./. End ID]

Decligender: a gender identity characterized by repulsion to the concept of gender as a whole.

[PT: Decligender: a gender identity characterized by repulsion to the concept of gender as a whole. ./. End PT]

Etymology

[PT: Etymology ./. End PT]

From English, "(to) decline", modified to "Decli-", meaning "to refuse" + "-gender", and English neologistic suffix indicating genderedness. Coined by tumblr user Mogai-Guy in February 2019 (link) [PT: Coined by tumblr user Mogai-Guy in February 2019 (link) ./. End PT] as a response to this image posted by tumblr user Genderoftheday (now defunct):

[Image ID: The question, "what is your gender?", with a select-drop-down menu, featuring the characteristic down-pointing arrow. The default selections says "Select Gender", followed by "Male", "Female" and "Decline". Decline is highlighted purple. ./. End ID]

Elaboration

[PT: Elaboration ./. End PT]

Decligender is similar to, but different from, Apothigender. Both experience involve repulsion in regards to gender (RIN, Ringender), but in distinct ways.

Apothigender involves a sense of repulsion of having a gender applied to oneself. For the apothigender individual, the repulsion is directed at gender in relation purely to oneself. An Apothigender individual does not have a gender, does not want one and finds the thought of it repulsive.

Decligender involves a sense of repulsion directed at the concept of gender as a whole. A decligender individual may lead an existence in which they act unaffected by participation in the construct of gender. A Decligender individual does not have a gender, does not want one, finds the thought repulsive and is repulsed by the concept all-together.

Decligender encompasses and surpasses Apothigender. Decligender is an outherine, atrinary gender. It may also be considered diastine.

This is a repost of my archival of Decligender from Gender-Resource (terminated) (link) [PT: This is a repost of my archival of Decligender fro mGender-Resource (terminated) (link). ./. End PT]. This repost includes a rerendered flag, additional explanation of important concepts and the fixing of broken links.

Pride Flag

[PT: Pride Flag ./. End PT]

The flag posted here was rerendered by Gent (Gender-Jargon) in June 2024, but was originally posted and designed by tumblr user Mogai-Guy in February 2019 (link) [PT: The flag posted here was rerendered by Gent (Gender-Jargon) in June 2024, but was originally posted and designed by tumblr user Mogai-Guy in February 2019 (link) ./. End PT].

The flag consists of eight horizontal stripes, with the top stripe being much thicker than the rest. At the center of the top stripe is a black, near-equilateral black triangle pointing downwards. The stripes, from top to bottom, are colored light grey, black, white, black, white, purple, white and purple.

The flag is based upon the image of the "What Is Your Gender" drop-down menu included above. The flag utilizes the same color pallet of the image with minor adjustment. Though not directly stated, I presume that the design carries the following meanings:

the top stripe represents the drop-down menu from the image, symbolizing the concept of gender.

The subsequent white, black and purple stripes represent gender norms, repulsion related to the concept of gender itself and a declination of the concept of gender, respectively.

[PT: the top stripe represents the drop-down menu from the image, symbolizing the concept of gender. The subsequent white, black and purple stripes represent gender norms, repulsion related to the concept of gender itself and a declination of the concept of gender, respectively. ./. End PT]

[flatland-a-2024-translation]

Section 06. Of Recognition by Sight

[Table of Contents]

I’m about to seem very inconsistent.

In the previous sections I’ve told you that all things in Flatland appear to us to be nothing but a Straight Line; and it was implied that this makes it impossible to tell people or objects apart by looking at them.

But now I will be explaining to my Spaceland critics how we Flatlanders do recognize one another by our sense of Sight.

If you, the Reader, will take the time to revisit the paragraph where you think I claimed that Recognition by Feeling is universal, you will that I specified “among the lower classes”. Only among the higher classes in our civilized societies is Sight Recognition practiced.

That this skill can be practiced anywhere, for any class, is the result of the Fog that covers the land for most of the year in all parts of Flatland except in deserts. What Spacelanders see as a depressing, evil smog that blots out the landscape and makes you cold and sick, we celebrate and see as a blessing second only to air itself, and is recognized as the Nurse of art and the Parent of science.

But I’ll try to stop singing praise for this generous Element so that I can explain to you what I mean.

If Fog didn’t exist, all Lines would appear just as sharp and clear as every other Line, and this is actually the case in those unhappy desert countries where the atmosphere is perfectly dry and transparent.

But wherever Fog can be found, objects that are at a distance of, for example, three feet, are noticeably dimmer than those at a distance of two feet and eleven inches.

This means that by careful, constant observation, we are able to understand, with very high accuracy, the shape of the object we are looking at.

A specific example will let me make my meaning clear to you without needing many more paragraphs of explanation.

Imagine that I see two strangers approaching me, whose rank I want to learn. Let’s say that they are a Merchant, and a Physician, or in other words, an Equilateral Triangle, and a Pentagon – so how do I tell them apart?

Here is a diagram to illustrate:

[Image description start: A black and white illustration showing an equilateral triangle and a pentagon, with a drawing of an eye seen from the side pointed at each of them. The point facing the eye is labled A, the point below is B, and the point above is C. A thin line traces the peripheral vision of the eye, and a vertical rectangle in front of point A shows what the eye of the Flatlander can see: a straight line, in a gradient of white at the center, and darker at the edges. The triangle’s edges become darker faster than the pentagon’s. Image description end.]

It will immediately be obvious to every child in Spaceland who knows anything about Geometry that if I am facing these two men so that I am looking directly at their front point (A), my view, obviously, lies perfectly between the two points on either side of that (CA, AB), so that both points appear to be the same size.

Now when I look at the Equilateral Merchant, what will I see? I will see a straight line (in reality made up of three points), with the center of the line (which is really point A) being very bright (Because point A is closest to me).

The two seeming-ends of the line, though, will be much darker, with a very sudden shift from the white of the center to almost black. This is because the points (B and c) that make up the ends of this seeming-line are much further away from me, with more Fog covering them.

On the other hand, the line that represents the Pentagon Physician will shift from white to a lighter grey rather than almost black, because the points that make up the ends of the line are not as far away from me than they were on the Triangle.

((Note from the second editor: To simplify further: The closer the point is to you, the brighter it is. The further away, the darker it is. Just remember this, and you’ll be fine.))

The Reader will probably understand from this example how – after a very long course of training aided by constant practical experience – those of us who are well-educated can easily tell strangers apart when it comes to the Equilateral and Isosceles classes by our sense of sight.

If my Spaceland friends have grasped this idea enough that you’re not immediately rejecting it as impossible, I’ll consider my job done in this matter. If I tried to give you any more details, I’d only confuse you hopelessly.

But for the sake of the young and inexperienced, who might assume, from the two examples I gave above of how I would recognize my Father and one of my Sons, that Recognition by Sight is easy to learn, I feel the need to point out that, in reality, the problems posed by Sight Recognition are much more subtle and complex than my simple diagram can convey to those in Spaceland.

For example, if my Father, the Equilateral Triangle pictured above, were to approach me with one of his sides instead of his angle, then, until I’ve asked him to rotate, or until I move around him to another angle, I cannot be certain whether I am looking at my Father, the Equilateral Triangle, or a Straight Line, which in other words means a Woman.

Then, when I am with one of my two Hexagonal Grandsons, looking at one of his sides, it will be clear, I hope, from the diagram below, that I will see a straight line with a large center of brightness (made up by the points A and B), with two small darker sections above and below, which quickly fade away into dimness.

[Image description start: A black and white illustration showing a hexagon being looked at from the side, so that one of the flat sides, created by points A and B, is facing the eye, with points C and D above and below. The Flatlander's eye perceives a straight line with a large, white center, with the very top and bottom sections suddenly turning dark, and fading even darker at the ends. Image description end.]

But I need to resist the temptation to keep explaining about these topics.

Even the best mathematician in Spaceland should believe me when I tell you that when you are at a party or a convention, moving around the room and other people, trying to recognize and keep track of the many high-ranking Polygons around you is not an easy task.

This is why we value our expert mathematicians, Professors of both Static and Kinetic Geometry, from the University of Wentbridge, so highly. They are the ones who teach the elites of the states the complex art of Sight Recognition.

It is only a few of the most promising sons of our most noble and wealthy houses who can afford the time and money necessary for actually Mastering this noble and valuable Art.

If I, a Mathematician of fair skill, and the Grandfather of two very promising and perfectly regular Hexagons, find myself in the middle of a crowd of rotating Polygons of the higher classes, even I sometimes find myself unsure!

And of course, to a common Tradesman Equilateral or Slave Isosceles, such a sight must be as bewildering and meaningless as it would be to you, my dear Reader, if you were suddenly transported to our country.

In a crowd like this, the only thing you would see, wherever you look, is nothing but a Line that seems to be straight, but with different parts in constantly changing light or darkness.

Even if you had graduated from your third year in the University’s classes for Pentagons and Hexagons, and had memorized the theory of the subject, you would quickly find yourself realizing that it will take many years of practical experience before you could confidently move through a high-society crowd without bumping into your betters.

It is impolite in the extreme to ask to “Feel” such superior nobles, and it is without a doubt, due to their superior culture and breeding, that these fashionable crowds know everything of your shape and movements, while you, still inexperienced, know next to nothing about theirs.

In other words, the only way to truly belong in Polygonal society is to be a Polygon yourself. It’s a painful lesson I have had to learn the hard way.

It is astonishing how much the Art (I like call it an instinct) of Sight Recognition is honed simply by constant practice, while avoiding the custom of “Feeling”.

((Note from the second editor: I apologize in advance for the next sentence you are going to read after this interruption is done.

The author here, as you may be able to guess soon enough, thinks he knows more than he does.

I will state now, for the record, that his idea of how Deaf and nonverbal people learn to speak is completely and blatantly false, a myth long since thrown away, but I will still transcribe his words here for the sake of posterity, and to better help you understand his mindset.

Let me make it absolutely clear that denying Deaf, Nonverbal, and Semiverbal children access to sign language or Augmentive and Alternative Communication devices (AAC), and forcing them to lipread or spend years learning to speak perfectly aloud, does not help them learn to communicate better. The only thing it accomplishes is isolating and punishing them and delaying their ability to talk to you.

Let them learn sign language (and you can learn it alongside them!). Get them an AAC device. Stop trying to fit a square through a circular hole! It is a myth that sign language stops Deaf and mute people from speaking – just because you didn’t bother to learn doesn’t mean they’re not talking!

Interruption over now. You may continue.))

Just as with you, if the Deaf and Mute are allowed to gesticulate and to use sign language, will never acquire the more difficult, but far more valuable art of speech and lip-reading, so it is with us as regards "Seeing" and "Feeling".

No one who learns to "Feeling" early in their life will ever learn "Seeing" in perfection.

This is why “Feeling” is either discouraged. or forbidden completely among the families of our Higher Classes.

The children of High-Class Polygons are not sent to the common Public Elementary schools where Feeling is taught. Instead, they are sent to private schools with very strict entrance requirements.

At these schools, to “Feel” is seen as a serious problem, and is punished with Suspension for the first offense, and complete Expulsion for the second.

But the lower classes think of Sight Recognition as an unattainable luxury.

The common Equilateral Tradesman can’t afford to send even just one of his sons away to spend an entire third of his life studying abstract ideas.

So the children of the poor are allowed “feel” as soon as they begin moving, and in doing so become practiced at moving and interacting with others very quickly, which makes them seem, to the untrained eye, much better developed than the comparatively listless, unmoving attitude of young nobles Polygons of the same age.

But don’t let this disparity fool you – once the young Polygons have finally completed their course at the University, and are ready to go out into the world to gain more experience, a change sweeps over them so that they seem to be born for a second time.

In all the skills of art, science, and sociability, they then rapidly catch up to and out-compete their Triangular competitors with ease.

It is rare for any of the Polygonal Class to fail their Final Test at the University, but it does happen, promising a life of pitiable misery to these unsuccessful nobles. Cast out by other Polygons, they can make no friends among the common classes either.

They cannot function in Polygonal society because of their lack of Sight Recognition, but also have no idea how to navigate by Feel, as they’ve been forbidden and shamed out of learning it their whole lives.

There are no jobs they can perform, either professional or common, and though most Countries do not actually ban them from getting married, it is still difficult for them to find any willing partners, since history has shown us that the children of such marriages will be, at best, similarly unfit for the noble life, or, at worst, blatantly Irregular.

This trash of the Nobility is where many of the leaders of the various Tumults and Seditions of the past centuries have risen. So many, in fact, that an increasing number of our progressive Statesmen have decided that either imprisoning these wretched outcasts for life, or at least mercy killing them, would make life easier for everyone.

But I am once again becoming distracted by the subject of Irregularity, which is actually so important for you to understand that it deserves its own separate section.

[Table of Contents]

[art-of-mathematics]

Wobbly Sierpinski-fractal model/toy

Made with foil strips of equal length and book screws.

The larger triangle at the center is stable because the outer tinier triangles stabilize it. (The larger triangles have a side length of two foil strips. The smallest triangles ("the building blocks") have a side length of 1 foil strip. The largest triangle is this entire model with side length of 4 foil strips.)

The largest triangle (4foil strips) is stable, because the tiniest (1foil strip) triangles stabilize each other as well as the larger (2foil strips) triangle.

The sierpinski pattern has interesting properties regarding its "stability" I have to admit.

Normally I struggle to make equilateral triangles of side length "2 foil strips" stable enough without adding an inner triangle. This construction (using outer tiny triangles) is a good solution if you want a "larger triangle hole".

[yesterdays-xkcd]

YOU THINK THIS IS FUNNY?

Substitute [Explained]

Transcript Under the Cut

[In a classroom, the board says "Math" on the top-left corner, and "Mr. Munroe" in the middle. A Cueball portrays Randall, standing in front of it, speaking to the class.] Randall: Miss Lenhart couldn't be here today, so she asked me to substitute. Randall: I've put out your tests. Please get started.

[A student in the first row raises the exam paper and says:] Student: Mr. Munroe, Miss Lenhart never taught us this.

Randall: That's because Miss Lenhart doesn't understand how important certain kinds of math are. Student: But this just looks-- Randall: This material is more vital than anything you've ever learned Student: But-- Randall: No buts. Randall: This is a matter of life and death.

[Excerpt from the exam paper.] Name: _________ [A stick figure is standing, hands over head. A velociraptor is running towards it.] 1. The velociraptor spots you 40 meters away and attacks, accelerating at 4 m/s^2 to its top speed of 25 m/s. When it spots you, you begin to flee, quickly reaching your top speed of 6 m/s. How far can you get before you're caught and devoured? 2. You're at the center of a 20m equilateral triangle with a raptor at each corner. The top raptor has a wounded leg and is limited to a top speed of 10 m/s. [A stick figure is shown in the above situation. The picture has a legend "(Not to scale)."] The raptors will run toward you. At what angle should you run to maximize the time you stay alive? 3. Raptors can open doors, but they are slowed by them. Using the floor plan on the next page, plot a route through the building, assuming raptors take 5 minutes to open the first door and halve the time for each subsequent door. Remember, raptors run at 10 m/s and they do not know fear.

[sappy-witch]

Exploring Sacred Geometry: Unlocking the Mysteries of Divine Proportions 🌸🔺🔵◻️

Hello darlings 🥰

Today, let's delve into the fascinating world of sacred geometry and unravel the profound secrets hidden within its intricate patterns. Sacred geometry is a universal language that transcends cultures and time, reflecting the inherent order and harmony of the cosmos. It offers a window into the interconnectedness of all things and provides a profound tool for spiritual growth and understanding. So, let's embark on a journey into the realm of sacred geometry together!

🌸 The Flower of Life: 

At the heart of sacred geometry lies the Flower of Life, a mesmerizing pattern formed by overlapping circles. It is a symbol of creation and the interconnectedness of all living beings. Meditate upon its symmetrical beauty and allow its energy to awaken your connection to the divine.

🔺 The Power of Triangles: 

Triangles hold immense power in sacred geometry. The equilateral triangle represents balance and harmony, while the upward-pointing triangle symbolizes fire, passion, and spiritual ascension. The downward-pointing triangle represents water, intuition, and the divine feminine. Incorporate triangles into your spiritual practice to tap into these energies.

🔵 The Magic of Circles: 

Circles are ancient symbols of wholeness, unity, and eternity. They represent the cyclical nature of life and the infinite possibilities within the universe. Meditate upon circles, draw mandalas, or use circular objects in your rituals to connect with the energy of completeness and divine unity.

◻️ The Power of Squares: 

Squares symbolize stability, structure, and the material realm. They represent the four elements—Earth, Air, Fire, and Water—and provide a foundation for manifesting desires. Work with squares in your sacred space or incorporate them into your crystal grids to establish a strong and stable energetic framework.

✨ The Golden Ratio: 

The Golden Ratio, often represented by the number phi (Φ), is a mathematical proportion found abundantly in nature and art. It is a ratio believed to embody perfect harmony and beauty. Explore the Golden Ratio in nature, art, and architecture and contemplate its presence in the world around you.

🌳 Sacred Symbols: 

Discover sacred symbols derived from sacred geometry, such as the Sri Yantra, Metatron's Cube, or the Tree of Life. These symbols are potent energetic tools that can be used for meditation, manifestation, and spiritual alignment. Study their meanings and explore how they resonate with your journey.

🔷 Crystal Grids and Mandalas: 

Combine the power of sacred geometry with the energy of crystals by creating crystal grids or mandalas. Arrange crystals in sacred geometric patterns to amplify their energies and intentions. Draw mandalas inspired by sacred geometry to express your inner connection with the divine.

◻️ Sound and Sacred Geometry: 

Explore the relationship between sound and sacred geometry. Discover the resonant frequencies associated with specific geometric shapes and how sound vibrations can harmonize and heal. Experiment with sound healing modalities, such as chanting, singing bowls, or tuning forks, to enhance your experience with sacred geometry.

✨ Meditation and Contemplation: 

Engage in meditative practices centered around sacred geometry. Visualize geometric patterns, focus on specific shapes, or use sacred geometry artwork as a focal point for your meditation. Allow these visualizations to calm your mind, expand your consciousness, and deepen your spiritual connection.

Sacred geometry is a gateway to understanding the divine order that permeates the universe. It invites us to recognize the inherent beauty and interconnectedness of all things. Embrace the language of sacred geometry, and allow it to guide you on a transformative journey of self-discovery and spiritual growth.

____

🌞 If you enjoy my posts, please consider donating to my energies 🌞

✨🔮 Request a Tarot Reading Here 🔮✨

____

With love, from a Sappy Witch 🔮💕

Blessed be. 🕊✨

[rjalker]

the poll results are in. People want to see the illustrations for the summary.

so here's Billie, Bob, and Joe. WIP, I haven't drawn their insides yet. I plan to draw all the Flatlanders with visible insides. It's just gonna be a simplified version though.

[ID: A digital drawing with a black border, titled, "Billie, Bob, and Joe seen from above, showing three black and white shapes. First is Billie (spelled with an I E at the end), a very thin diamond forming a needle shape. Next is Bob, a circle, followed by Joe, a hexagon. End ID.]

Sight recognition demonstration:

[ID: Another drawing, now zoomed back, with Joe in the middle of Billie and Bob, who look at him from different angles. Billie looks at one of Joe's angles, and Bob looks at one of his flat sides. A bar at the top is labeled, "Billie's view of Joe", and has a thin white stripe in the center, with a slow gradient to grey on either side. At the bottom of the image is another bar showing Bob's view of Joe, which has a large white stripe in the center, with a faster gradient to grey on either side. End ID.]

The fact that Straight Line is a misnomer:

[ID: A digital drawing captioned, "Despite their name, Straight Lines are actually very, very thin parallelograms rather than true lines.". Next to this are three examples of Straight Lines from Flatland: A rectangle, a diamond or kite, and a trapezoid. All of them are very thin. End ID.]

Put a coin on a table and test it for yourself...

[ID: A simple diagram showing a Square Flatlander, first seen from above or below, as a square shape with purple insides and simple pink internal organs, with one eye at his top corner. Then he is flowly flipped onto his side in three phases, until he appears as a straight line, how he is seen from within Flatland. End ID.]

All seems solid from Flatland, but not so from Spaceland!

[ID: Another Square Flatlander, with purple and pink insides, labeled, "A Flatlander seen from above or below has visible insides.". Next to him is a straight line, labeled, "A Flatlander seen from the side in Flatland appears to be a solid line." Above this, text reads, "We do not actually know what the insides of a Flatlander look like because A. Square didn't tell us.". End ID.]

[ID: Another digital drawing, showing an Equilateral triangle with puprle and pink insides, labeled, "Flatlanders can look forward, and side to side. To look behind themselves, they have to spin around entirely." The triangle is shown on the top and bottom of the image, looking forward, then to the left and right, with arrows following their pupil. A smaller black and white version is shown turning around to look behind themselves. End ID.]

[ID: A drawing of multiple Flatlanders of different shapes arranged around the edges of the image, all looking at text in the middle that reads, "The eye-mouth is on the outside of the Flatlander, otherwise they wouldn't be able to see or eat." The shapes looking at the center consist of a square, an irregular polygon, a circle, an isosceles triangle, an equilateral triangle, and a straight line, who is a very thin trapezoid. There is also a very small pentagon child who instead has an eye in the center of their body, looking towards the camera with a questionmark, labeled in smaller text: "If a Flatlander were born with their eyemouth in their center, they wouldn't be able to see or eat anything in Flatland, and would most likely starve to death in childhood without immediate medical intervention of a feeding tube directly to their stomach.". End ID.]

[ID: A diagram captioned, "A variety of Isosceles triangles. The closer your third angle is to 60 degrees, the higher your comparative social status, though none of them have any civil rights, and are literally not considered human at all due to being Irregular.". Below this is a line of Isosceles triangles, starting with the widest angle on the left, then getting narrower towards the right, until the last almost appears as a straight line. End ID.]

[courtleymanor]

[ID: wide shot from behind ward. as caleb watches the professor, lil walks around the coffee table’s end toward its middle so that the three now form an almost perfect equilateral triangle with the book at its center. she smiles. “everyone sees different things,” she replies. /end ID]

[selves-indulgent-coining]

the willogenic flag (y'know the greens and yellows and purples etc) with the therian, polyamorous and otherhearted symbol in a lil triangle?

my timezone is EST, sorry about my other ask i got excited lol /pos /gen /info

it's ok! you don't need to apologize! /gen here's your flag!

[alt text: a flag with 5 equal horizontal stripes: bright sea foam green, bright mint green, banana yellow, muted light purple, medium purple there are three black symbols in an equilateral triangle shape (the triangle is pointed upward):

the top symbol is an equilateral triangle interlocking with a circle and there is a horizontal line in the center

the bottom left symbol is a heart shape interlocking with a circle and there is a diamond shape in the center

the bottom right symbol is a heart shape interlocking with an infinity symbol

end alt text]

[ranmagender]

[ID: An image of bill cipher, a yellow equilateral triangle with brick pattern at the bottom, a bowtie one eye in the center, two legs and a top hat floating above it. Next to him on the right is a square with one eye on its side, inside it is another smaller square. the outer wall is purple and its innards show organs like a pink brain and red heart and other blobs that are pinkish or grey. organs seem to floating in a dark red color. Bill Cipher asks "Did you meet the Axolotl?" with a cutesy small doodle of an axolotl to the left of the word axolotl. The square responds "What?" END ID]

Bill, your experiences aren't universal.