#Chebyshev

[the-goodkhush]

i don’t think anyone’s gonna get this but slayyyy chebyshev inequality and markovs inequality slayyy ilysm my beloveds

[irockasingranite]

this work of art is hidden 430 pages deep into a dense numerical analysis textbook[1], and that is a crime.

[1] Boyd, J.P.: Chebyshev and Fourier Spectral Methods, 2nd ed. (2001)

[rlyehtaxidermist]

Adrien-Marie Legendre's contributions to mathematics are numerous but will forever be overshadowed by two really really funny facts about him:

First, Legendre's constant. This is the value B that describes the asymptotic behaviour of the prime-counting function π(x) (no relation to the better known constant π):

Legendre first estimated B as 1.08366 from empirical data, but about twenty years after he died, Chebyshev proved that if B exists, its value must be exactly 1. As nobody's going to call 1 a name as lengthy as "Legendre's constant", the name was stuck to Legendre's early approximation. Having a constant named after your empirical result that turned out to be wrong, but only obviously wrong if you can compute well into the hundreds of thousands of n, is obviously pretty embarrassing, especially since naming of constants is generally pretty prestigious.

The other funny fact is that we have exactly one known image of him, a caricature by Jules Boilly. That looks like this:

[mathsuggestions]

Fourier series expand functions in terms of Chebyshev polynomials rather than sine and cosine.

[max1461]

Reading about Chebyshev

His first name comes from the Greek Paphnutius (Παφνούτιος), which in turn takes its origin in the Coptic Paphnuty (Ⲡⲁⲫⲛⲟⲩϯ), meaning "that who belongs to God" or simply "the man of God".

According to Wiktionary:

From Demotic pꜣy-pꜣ-ntr (literally “the one of the god”). Equivalent to ⲡⲁ- (pa-, possessive masculine article) +‎ ⲫⲛⲟⲩϯ (phnouti, “God”)

Ancient Egyptian...

[taohun]

affirmations im winning. im good at statistics. i know the foundational matter of one part of my degree. i love you alive girl (chebyshev's inequality)

[petriquors]

FIVE MEALS PT. 4 | Junior Year MASTERPOST

“I feel like I need spicy nuggets to get through this,” Chikara says, somewhere between a laugh and a sigh. Textbooks, notebooks, calculators—all kind of academic paraphernalia is strewn across your dining room table, and the digital clock on your stove cheerily touts that it’s way past the point of a casual study session. Nope, this is the tenth circle of hell.

Happy finals season, indeed. You sigh and let your head fall forward until it thunks against Chebyshev's inequality. “I could totally use fries and a milkshake. Oh, and a quesadilla.”

“Gross,” he chuckles.

“I know. That’s how bad it is.”

A few moments pass and, though you’re genuinely trying your hardest to get through your ten-page study guide, your thoughts keep drifting to fries instead of the advanced statistics class you’re both required to take.

“Chikara.”

“Hm?”

“Can we go get fries?”

Now, he looks up. One of his eyebrows is raised, and he eyes you warily, as if he’s not sure you’re being serious. He glances at his phone. “It’s 1 A.M.”

“It’s an emergency.”

“No one’s open—”

Now determined to prove a point and get your fries, you hold up your hands and start counting on your fingers. “Sonic. Checkers. The diner on the boulevard. Taco Bell—”

“Taco Bell doesn’t have fries.”

“Wrong,” you laugh. “Nacho fries. Limited time only.”

The look he gives you is entirely incredulous, and you just smile sweetly in the face of his tired exasperation. And then he laughs, which makes you laugh, and it’s a sound that almost makes you forget that you’re exhausted, stressed, and counting the days until Christmas break.

“Okay,” he sighs, standing up by bracing his hands on his thighs like he’s ten years older than he actually is, or something. “Come on.”

“Where are we going?”

“The diner,” he says as if it’s obvious, because it is. Somehow, some way, the two of you always end up at the diner. Whether the moment is dire or triumphant, some of your best memories are set among vinyl booths and canola oil smell. “Where else am I going to find your weird laundry list of cravings at 1 A.M.?”

“It’s called a girl dinner,” you offer while you scramble to follow after him before he wanders off without you. He snorts, then pauses at the door while you shrug into your coat, back facing him.

You don’t see the way he’s looking at you. He thinks maybe, someday soon, he should tell you what he’s thinking and how it keeps him up at night. “This feels more like a girl cry-for-help.”

“Well, then.” You turn, looking haphazard in sweatpants and a big coat, and look right at him in a way that makes him wonder if you can see right through him. For that moment, he swears his heart stops. “Thanks for being my hero.”

🔖: @alienaiver @cup-of-fluff @mrs-kurooo @dira333 @uc1wa @baskin-robinhoods @chibishae34 @tetsuskei

[tangleworm]

NOMIA Devlog 3 -- Diagonals

(Been working on the mix of enemy generation, but I haven't done the art for many of them yet!)

There's lots of weird stuff that happens when your game is tile-based, like how to handle movement and knockback.

There's lots of ways to handle "distance" in a tile-based world. You could make it so that 1 unit of movement lets you step left, right, up, or down -- this is called rectilinear distance, or Manhattan distance. Fire Emblem does this. You could make it so that a unit of movement also lets you step diagonally -- this is called chessboard distance, or Chebyshev distance. Many D&D battlemaps do this.

I decided to go with rectilinear distance for this game, since it's more intuitive when we consider distances in the real world. This means that going diagonally costs 2 points of movement -- an attack with a range of 2 will only be able to target the immediately adjacent diagonal tiles.

However, certain attacks can move the caster (lunging and retreating), the target (knockback and pull-in), or both. There are a number of ways we can make a "line" from one point to the next in rectilinear geometry. How do we handle non-orthogonal pushing and pulling?

I could think of three ways to handle it.

1. Don't

If we restrict any self/target-moving abilities to just the orthogonal tiles, we can sidestep the whole issue. This is simple to implement, and the player will always understand exactly how knockback will work, because it only happens when we can count exactly how many tiles everything will move.

The downside to this is that this cross-shaped target can get extremely annoying when you want to hit an enemy that's directly diagonal to you. Because movement costs an action point in this game, it can get annoying to have to spend that point to do a very minor positional adjustment to hit an enemy that already "feels" adjacent to you.

2. Kinda Do

If the target is at exactly 45 degrees, it only gets a little more complicated to understand, but it gets a lot less annoying at close ranges. Every diagonal tile needs 2 units of knockback.

The tricky part is handling the different corners an enemy can get knocked into. Because knockback does damage based on how much remaining knockback there is when the unit hits a wall, how do we handle when it hits a corner, but there's only 1 unit of knockback left? How do we handle them hitting a convex corner (e.g. being shoved into the corner of a building from the exterior) versus a concave corner (e.g. being shoved into the corner pocket of a pool table)? Can we make this intuitive for the player to understand?

3. Really Do

We can go all the way and let knockback abilities hit every tile a non-knockback ability can.

This is difficult for both the developer and the player, since there are many ways to form a line (i.e. the shortest distance between two points) when we're in rectilinear space. Should we snap the knockback to the closest direction? Should we push the enemy on a path that might not be what the player wanted? Should we let the player choose, and slow down the decision for every knockback card by an extra click? Even this diagram is complex to look at, and we haven't even gotten into handling convex corners versus corner pockets.

It didn't seem worth it for the tradeoffs.

In the end: I originally went for Don't, but after some consideration I'm partway through implementing Kinda Do, and I'm happy with this choice. It prevents knockback-related abilities from feeling underpowered due to needing to spend an action point on a minor positional adjustment before casting them, and most knockback abilities are close range anyway.

If anything, this shows how much thought must have went into the various tile-based worlds we've seen before.

[kolroguelike]

Week 3 (and 4) of Roguelike Dev

Made a big post about this, tried to save it, it didn't so I'll make this brief with lots of images:

It's grown up so much! It has color, it has personality, it has UI!! Let's talk about things that are added in and work and things that didn't work: -We can now progress through an endless number of levels

-We can now level up and gain xp endlessly, as well as use level ups to choose a stat to level

-There are multiple useable items and an inventory system. Items have a range of characteristics, though that range is small and simple right now

-Enemy and item spawns and quantity are determined by what floor you are on as well

-I added in a new enemy type who is supposed to be a nice in between the basic orc mob and the scary troll mob

-Enemy AI now will only attack in cardinal directions like the player

--This took a bit and required me to learn how to change the distance formula provided (Chebyshev) to a cardinal distance formula (Manhattan/Taxicab). This took several hours, but it's been working effortlessly now.

Things that didn't work:

-One thing specifically didn't work and it was making items have multiple functions, namely, making a firebomb item do both aoe damage and leave a burning status effect. This took a while and ultimately couldn't get it to work. Plan is to make a separate component to help this out and see if I can make enemies not just wander confusedly, but also take damage and panic when on fire.

[magical-bear-dubin]

Im sorry but when you say that i cant help to think on the great hungarian rhyme that was recited by numberphile

"I've said it before and i'll say it again

There is always a prime between N and 2N"

(In the original hungarian rhyme its actually Chebyshev that said it before)

ive said it before and will say it again but if you’re trans and a bit into your transition and suddenly become super vain, obsessed with your looks and think you’re fucking hot? GOOD. keep it up

[freyalise]

PAFNUTY CHEBYSHEV MENTIONED

[orwxllainthere]

I read and took notes on a whole textbook in a single day yesterday to prep for finals and now my brain is fried. Screw you, Chebyshev

[hackernewsrobot]

Chebyshev Polynomials in the 16th Century (2022)

https://arxiv.org/abs/2203.10955

[codingprolab]

MATH 4753 Laboratory 2 Introduction to R and Chapter 2 solved

In this lab you will learn the basics of R. This program is free and you are encouraged to obtain a copy for your Mac, PC or Linux machine. Install it and then download and install R studio (this is a nice front end to R and is also free). Objectives In this lab you will learn how to: 1. Use the empirical rule 2. Use the Chebyshev rule 3. Transform data to z values 4. Find outliers using z…

[tagitables]

16 September 2024, 14:54 PM

Hello, cosine vectors, as well as Euclidean, Manhattan, Mahalanobis, and Chebyshev metrics!

[minimal-effort-name]

I would like to sincerely apologize to Linear algebra, I simply was not familiar with your game.

Anyways, FUCK chebyshev polynomials, FUCK trigonometry, I'M PROVING THAT arccos(1/3)/π is irrational BY MATRIX DIAGONALIZATION.

I DONT CARE THAT ITS COMPLEX AND UGLY AS FUCK, WE TOUCHING THE STARS WITH A ROCKET MADE OF SCRAP IN HERE