recursal/Fanatic-Fandom huggingface dataset:
The Grinch

**The Grinch** was an alleged contestant in Epic Character Elimination Reboot. He originates from the Book *How The Grinch Stole Christmas*. The Grinch was put into Η ΣΟΦΊΑ ΚΥΡΙΑΡΧΕΊ in Guess Who's Back (Back Again), and was eliminated in Strive to Survive - Part 1. Overall, The Grinch got 19th place

## Coverage

In Guess Who's Back (Back Again), The Grinch is shown to be particularly annoyed with being sent to the void, and gets shocked with Host's sudden appearance

In Fun on the Sun, The Grinch comments that Annabeth Chase is wasting her time with Cassy, which Annabeth responds saying she's human just like the rest of them. Later, he gets crushed by a spaceship.

In What's Cooking?, Black Hole has to tell Host to recover The Grinch, which he reluctantly does, saying that it's annoying to make his lines rhyme. When Host asks if everyone's ready to cook later, The Grinch just instantly replies with "No!". Host ignores him. During the challenge, The Grinch sets the oven on fire, which is quickly extinguished by Mando. Last thing he's seen doing is slicing up apple pie.

In Just Boeing 747, the only thing The Grinch does is say he despises reading

In ECER 5: Strive to Survive - Part 1, when The Grinch is eliminated, he says that everyone smells. He is later not seen in the ending scene in The Shadow Realm

In Jimbo, The Grinch is left behind as the others escape The Shadow Realm, making him unable to rejoin.

In Work at a Pizza Place, it's revealed The Grinch had been killed by Ghostface, who made him into a blanket for Monika.

In The Lore Episode, The Grinch is unable to rejoin again due to not being present.

In ECER 17: The Hosting Dead (Part 1), Ghostface uses the blanket he made from The Grinch to vote Mr. Clean, which counted as The Grinch's vote

## Trivia

* The Grinch is the only contestant out of the game at the time of each rejoin that was could not be voted for both rejoins.
* The Grinch’s lines rhymes with other lines near it, to replicate the writing style of Dr Seuss, who wrote the book where the Grinch came from.
* The Grinch is only one of two characters who’s death was permanent, the other being Thanos.
* The Grinch’s captured loved one was revealed to be Cindy Lou Who, even though he was taken before the climax of his story, and therefore before he got attached to her.
* The Grinch has the least amount of lines when it comes to the contestants, only having 13 lines overall. The only character in the entirety of ECER to have less lines is Thanos.
* The creator of ECER, Epichaxboi, hated writing the Grinch, due to it being hard to rhyme his lines. This is probably why he has a lack of lines and why gets killed and turned into a carpet instead of having the chance to rejoin like the other contestants.
Wii Fit Trainer

**Wii Fit Trainer** was a contestant in Epic Character Elimination Reboot. She originates from the Nintendo Game *Wii Fit*. In Guess Who's Back (Back Again), she was put in The Cool. She made it to Work at a Pizza Place , where she was put in Team 2 . Finally, she was eliminated in Bored Games . Overall, Wii Fit Trainer got 10th place.
Top Cat

**Top Cat** was a contestant on Epic Character Elimination Reboot, originating from the Western Animated series *Top Cat*. In Guess Who's Back (Back Again), he was put on Still Deciding, and was eliminated in Just Boeing 747. Overall, Top Cat got 20th place.

## Coverage

In Guess Who's Back (Back Again), Top Cat talked with Steve a bit before being placed on Still Deciding. He contemplated helping Camilo in the challenge, but decided against it when Camilo said it was coconut-flavored.

In Fun on the Sun, Top Cat didn't do much other than having the occasional snide remark.

In What's Cooking?, Top Cat didn't help much with the cooking part of the challenge, but instead presenting the food to Host. He ratted out Sorbet Shark Cookie when Host asked him who made the omlette.

In Just Boeing 747, Top Cat was voted out, and... that's pretty much all he did.

In Jimbo, Top Cat didn't do much besides give snarky comments to the eliminated contestants that were actually doing the work.

In Work at a Pizza Place, Top Cat failed to rejoin.

In The Hosting Dead, Top Cat failed to rejoin.

## Votes

TBA

 4
 11
 17
Tyler

**Tyler** was a contestant in Epic Character Elimination Reboot. He originates from the Canadian Animated series *Total Drama*. Tyler was put into The Cool in Guess Who's Back (Back Again), and was eliminated in What's Cooking?. All in all, Tyler got 21st place.

## Coverage

In Guess Who's Back (Back Again), Tyler tried to make small talk with Sasha but was interupted by Camilo. Tyler was very freaked out by Camilo's powers. Tyler was placed on The Cool. He helped them out with the cake challenge, but eventually got carried by Steve like the rest of the team.

In Fun on the Sun, Tyler was doing yoga with the rest of his team before he got jumpscared by Host. During the challenge, he struggled greatly. At first, he fell straight towards the sun but was saved by Wii Fit Trainer. However, after Wii Fit Trainer and Mr. Clean's fight, he was flung into the sun and died, costing his team the challenge.

In What's Cooking?, Tyler felt reassured when his team said he wouldn't be voted out... and he proceeded to be voted out.

In Jimbo, Tyler mostly horsed around the entire episode, but did help the eliminated contestants do the rejoin challenge.

In Work at a Pizza Place, Tyler failed to rejoin.

In The Hosting Dead, Tyler failed to rejoin again.

## Votes

 11
 17
List of Characters

## Host and His ~~Enemies~~ Friends

### Host's "Helpers"

* Hopper
* Jason
* Her
* Jerry

### Villains

* Azula
* Monika
* Thanos
* Syndrome
* Ghostface
* Mantis Lords

## *Epic Character Elimination Reboot* Contestants

### The Cool

* Katie Mitchell - *The Mitchells vs The Machines*
* Hilda - *Hilda*
* Luz Noceda - *The Owl House*
* Ibuki Mioda - *Danganronpa*
* Wii Fit Trainer - *Wii Fit*
* Tyler - *Total Drama*
* Steve - *Minecraft*

### η σοφία κυριαρχεί

* Din Djarin - *The Mandalorian*
* Annabeth Chase - *Percy Jackson and the Olympians*
* Edward Elric - *Fullmetal Alchemist*
* The Grinch - *How The Grinch Stole Christmas!*
* Black Hole - *Battle for Dream Island*
* Cassy (SCP-085) - *SCP Foundation*
* Scrooge McDuck - *DuckTales*

### **Still Deciding**

* Weiss Schnee - *RWBY*
* Sorbet Shark Cookie - *Cookie Run*
* Caillou - *Caillou*
* Camilo Madrigal - *Encanto*
* Mr. Clean - *Mr. Clean*
* Sasha Waybright - *Amphibia*
* Top Cat - *Top Cat*
The Swordsman

We have recently discovered ANOTHER oddity, this one seems very regular, but.. when we got close the first time. Somehow. He slightly had his face change, from a chill and sensible frown to a insane and manic grin.

He then proceeded to stab the sword he carried into a employee.

When we contained him, he kept rambling about “three others, paradise and swords”, we don’t know why he is like this. But we’ll find more information on this oddity.

- From Izolda.

I plan on interviewing him soon. He sounds interesting... -Alexandra

Due to recent documents, it has speculated he has a son.

I will investigate FURTHER. - Izolda

... Also, I found a kneadable eraser in the mail today.

It was orange. Orange and.. It made noises when i kneaded it. -Alexandra

Was it dead after that? - Izolda

It stopped making noises 5 minutes into the kneading. -Alexandra

## 02/8/22

Im thinking of trying to get ahold of more information of his.

Maybe we can learn who that lady in the family photo we found was? - Izolda

That would be a great idea! - Alexandra

Alright. - Izolda
Jason

A lame guy who died in the bloodbath in the movie The Hunger Games. Instead of dying, this time he becomes a helper of Host and soon a co-host of ECER. Everyone (except for me, you know who he is) in the ECER fandom memes on him being a legend for some reason. Rest of the description is TBA for now.
The Cool

**The Cool** is a team in Epic Character Elimination Reboot. They formed in Guess Who's Back (Back Again), and are one of the three teams competing in ECER.

## Members

Luz Noceda (The Owl House)

Katie Mitchell (Mitchells Vs The Machines)

Steve (Minecraft)

Wii Fit Trainer (Wii Fit/Super Smash Bros)

Hilda (Hilda)

Ibuki Mioda (Daganronpa 2: Goodbye Despair)

Tyler (Total Drama)

## Coverage

In Guess Who's Back (Back Again), Katie, Ibuki, Luz, Hilda, Wii Fit Trainer, Steve, and Tyler were all placed on a team together. The name **The Cool** was made by Luz and accepted by Katie. Throughout the challenge, they were all eating the cake together, besides for Steve, who was wandering everywhere. They took a break mid-challenge since everyone was stuffed. Just when they thought they would lose, Steve came in clutch and ate the entire cake.

In Fun on the Sun, Wii Fit Trainer, Ibuki, Katie, and Luz linked arms just as the challenge started while Hilda, Steve, and Tyler didn't. Tyler was dangerously close to the sun while Steve was just doing his own thing, mining all the asteroids. Wii Fit Trainer and Hilda managed to save Tyler, but Wii Fit Trainer got into a fight with Mr. Clean, which... lasted really long. Luz managed to save Steve from falling into the sun, but she didn't save Tyler, making the team lose.

In What's Cooking?, Tyler was voted out.

In Just Boeing 747, TBA.

In Strive to Survive, The Cool lost.

In Our Get Along Shirt, Ibuki was voted out.

In Murder Misery, TBA

In Creative Commons, TBA

In Jimbo, The Cool originally lost, but were saved by it being a rejoin.

In Work at a Pizza Place, The Cool was disbanded.
Main Page

**Welcome to the 기하대수학 위키!**
기하대수학 위키는 기하대수학에 대해 찾아보면서 알게 된 내용을 정리하기 위해 만든 위키입니다. 작성한 내용들은 모두 인터넷 검색 및 개인적으로 탐구하여 알아낸 내용을 바탕으로 작성된 것으로, 신뢰성이 떨어지는 내용 및 오류를 포함한 내용들이 많으므로 참고만 해주세요.

## Important articles

PlaceholderA page about your topicPlaceholderA Main CharacterPlaceholderThe First EpisodePlaceholderAn Important LocationPlaceholderA Key EventPlaceholderA Crucial Item

*Need help building out this community?*

* Rules of this wiki
* Getting Started
* How to Contribute
* Managing your new community
* Guides
* All Help articles
Katie Mitchell

**Katie Mitchell** is a contestant in Epic Character Elimination Reboot, originating from the 2021 Sony Pictures animated movie *The Mitchells vs The Machines*. In Guess Who's Back (Back Again), Katie was placed on The Cool. She has made it to Work at a Pizza Place and was placed on Oonc. Katie is still currently competing.

## Trivia

* Katie is one of three canon LGBTQ+ characters, the other two being Luz Noceda and Sasha Waybright.
* Katie sometimes ships her fellow contestants together, such as Mr. Clean and Wii Fit Trainer, and Annabeth Chase and Cassy. This is used as a reference to readers of the show also shipping these characters together.
* It was confirmed by Epichaxboi that Katie would have had a romantic relationship with Ibuki Mioda if the latter lasted longer.
Hilda

Hilda is a contestant character in Epic Character Elimination Reboot. She is the titular protagonist of the comic series and cartoon *Hilda.* In Guess Who's Back (Back Again), she was put in The Cool. She made to Work at a Pizza Place, where she was put in Team 2. She was eliminated in No Matter How Fast You Run, You Cannot Run Away From the Train. Overall, Hilda got 13th place.
Grosses Aufräumen

## **[DAILY]Grosses Aufräumen**

Die Daily "Grosses Aufräumen" bekommt ihr vom "Verwalter Eredan" auf der Tryfkins Insel. Im Rahmen eurer Storyquest werdet ihr dort hingeschickt und spielt dort die Story durch. Danach findet ihr das Portal zur Insel im Lager an der Küste in der "Kaverne" (Im Lager unterm Turm ist hinter der Hängebrücke der Eingang) In dieser Quest müsst ihr einfach ein Stockwerk tiefer die Unterlagen einsammeln und ins Regal packen. (Die Position und Art der Items sind immer unterschiedlich, einfach alles Sammeln und wegpacken) Geht danach zurück zum "Verwalter Eredan" eine Etage höher und gebt die Quest ab.

**Quest Belohnungen:**

* *Um die Ausrüstungsbelohnung zu erhalten, muss man einen aufgeladenen Psychorar anlegen* Edit folgt
* Ohne Psychorar erhaltet ihr lediglich 1.000g
Law & Order Find Out 2

## NYPD Precinct Supervisors

* NYPD Sergeant - Jeremiah Lennox, (Law & Order S18 E7)
* NYPD Sergeant - Gilbert Gonzales, (Law & Order S6 E3)
* NYPD Sergeant - Frank Shepard, (Law & Order S9 E10)
* NYPD Sergeant - \_\_\_\_\_ Turley, (Law & Order S18 E5)
* NYPD Sergeant - \_\_\_\_\_ Kuo, (Law & Order S18 E7)

## NYPD 27th Precinct

* NYPD Sergeant - \_\_\_\_\_ McDoyle, (Law & Order S20 E12) / Badge Number: 9218
* NYPD Sergeant - \_\_\_\_\_ Martinez, (Law & Order S12 E19, S13 E1, S13 E12 & E22, S14 E4, S14 E16 & E24)
* NYPD Sergeant - \_\_\_\_\_ Bowers, (Law & Order S11 E06)
* NYPD Sergeant - \_\_\_\_\_ Orzelle, (Law & Order S18 E13)
* NYPD Sergeant - \_\_\_\_\_ Anvers, (Law & Order S20 E11)
* NYPD Sergeant - \_\_\_\_\_ Adams, (Law & Order S19 E21, S20 E14)
* NYPD Sergeant - \_\_\_\_\_ Royce, (Law & Order S19 E13 & E18, S20 E1, S20 E5, S20 E17)
* NYPD Sergeant - \_\_\_\_\_ Sloan, (Law & Order S18 E08) / Badge Number: 2457
* NYPD Sergeant - \_\_\_\_\_ Scott, (Law & Order S11 E11)
* NYPD Sergeant - \_\_\_\_\_ Elias, (Law & Order S20 E10)
U.S Department of Defence

- Vice Admiral - Miles Coty, Captain - Edwin Albrecht, Captain - Allard Bunker
		- Lieutenant - Charles Bates, Lieutenant - Kirstin Blair, Lieutenant - Janet Hagen
		- Lieutenant - John F. Kennedy, Lieutenant - Ruth Mendoza, Lieutenant - St. Clair
		- Ensign - Evan Walker
	+ Enlisted Officers:
		- Chief Petty Officer - James Hagen
	+ Unknown Rank - Frank Hagar
	+ Unknown Rank - Kevin Morse

### U.S Department of the Army

* United States Army Rangers
	+ Sergeant - George H. Meacham, (L&O S14 E08)
	+ Sergeant - Frank Patterson, (L&O: SVU S14 E21)
* United States Army Reserve
* United States Army
	+ Commissioned Officers:
		- Unknown Command: Lieutenant Colonel - Douglas Denton, (L&O S14 E8)
		- Fort Crompton Base Clinic: Captain - Dr. Paul Trainer, (L&O: SVU S6 E23)
		- Unknown Command: Captain - Jason Harris,(L&O: SVU S13 E10 & E19)
		- Unknown Command: Colonel - \_\_\_\_ Gage, (L&O: SVU S6 E23 Only)
	+ Enlisted Officers
		- Private - William Shaughnessy, (L&O: SVU S18 E19)
		- Staff Sergeant - Tyler Jones, (L&O: SVU S18 E19)
		- Sergeant - Jimmy Preston, (L&O: SVU S18 E19)
		- Unknown - Clark Wallace, (L&O Unknown)
		- Sergeant - Dixon Hawes, (L&O:
도치 연산

도치 연산(involution)은 다중벡터의 각 단계 성분마다 부호를 반전시키는 연산이다. 도치 연산에는 주 단계 도치 연산(main grade involution), 반전 연산(reversion), Clifford 켤레연산(Clifford conjugation)과 단계 특이적 사상(grade specific map)이 있다.

## 주 도치 연산

주 도치 연산은 짝수 단계(grade)의 성분은 그대로 두고, 홀수 단계의 성분만 부호를 반전시키는 연산이다. 기호로는 모자(hat)를 씌워 표시한다. 단계 사영 연산을 이용하면 다음과 같이 나타낼 수 있다.

M
^

=

∑

# k
0

n

(
−
1

)

k

⟨
M

⟩

k

{\displaystyle {\widehat {M}}=\sum \_{k=0}^{n}(-1)^{k}\langle M\rangle \_{k}}

## 반전 연산

반전 연산은 다중벡터를 블레이드들의 합으로 나타낸 후, 각 블레이드를 직교기저로 나타냈을 때 벡터들의 순서를 전부 반전시키는 연산이다. 기호로는 물결표(tilde)를 올려 표시한다. 직교하는 벡터들은 교환 시 부호가 반전되고, k-블레이드의 성분이 되는 벡터들의 순서를 반전시킬 때 총 k(k-1)/2번의 교환이 필요하므로 부호는 (-1)^(k(k-1)/2)가 된다. 이는 수식으로 다음과 같이 나타낸다.

M
~

=

∑

# k
0

n

(
−
1

)

k
(
k
−
1
)

/

2

⟨
M

⟩

k

{\displaystyle {\tilde {M}}=\sum \_{k=0}^{n}(-1)^{k(k-1)/2}\langle M\rangle \_{k}}

## Clifford 켤레 연산

Clifford 켤레 연산은 주 도치 연산과 반전 연산의 합성 연산이다. 기호로는 바(bar)를 씌워 표시한다. 수식으로는 다음과 같이 표시할 수 있다.

M
¯

=

M
~

^

=

M
^

~

=

∑

# k
0

n

(
−
1

)

k
(
k
1
)

/

2

⟨
M

⟩

k

{\displaystyle {\bar {M}}={\widehat {\tilde {M}}}={\tilde {\widehat {M}}}=\sum \_{k=0}^{n}(-1)^{k(k+1)/2}\langle M\rangle \_{k}}

## 단계 특이적 사상

단계 특이적 사상은 특정 단계에 해당하는 부호를 반전시키는 연산이다. 예를 들어 두 개의 단계의 블레이드 부호를 바꾸는 연산의 경우 다음과 같이 표시할 수 있다.

m

j
¯

,

k
¯

(
M
# )
M
−
2
(
⟨
M

⟩

j

⟨
M

⟩

k

)
,
0
≤
j
,
k
≤
n

{\displaystyle m\_{{\bar {j}},{\bar {k}}}(M)=M-2(\langle M\rangle \_{j}+\langle M\rangle \_{k}),0\leq j,k\leq n}

해당 연산은 같은 방식으로 임의 개수의 단계가 주어졌을 때로도 확장할 수 있다.
쐐기곱

쐐기곱(혹은 외적, 영어: Wedge Product/Exterior Product)은 기하대수학에서 새롭게 정의되는 연산이다. 기하곱과 사영 연산을 통해서 다음과 같이 정의된다.

A

r

∧

B

s

=
⟨

A

r

B

s

⟩

r
s

{\displaystyle A\_{r}\wedge B\_{s}=\langle A\_{r}B\_{s}\rangle \_{r+s}}

두 벡터의 쐐기곱일 경우, 교환법칙 등에 의해 다음과 같이 나타낼 수도 있다.

a
∧
# b

1
2

(
a
b
−
b
a
)

{\displaystyle a\wedge b={\frac {1}{2}}(ab-ba)}

## 쐐기곱의 성질

연산의 정의에 의하여, 벡터 a에 대하여

a
∧
# a

1
2

(
a
a
−
a
a
# )
0

{\displaystyle a\wedge a={\frac {1}{2}}(aa-aa)=0}

이 성립한다. 또한 양쪽에 스칼라배를 해주면, 스칼라는 교환법칙이 성립하므로

k
a
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l
# a

1
2

(
k
a
a
−
a
l
a
# )

1
2

(
k
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a
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l
a
a
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1
2

(
k
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(
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0

{\displaystyle ka\wedge la={\frac {1}{2}}(kaa-ala)={\frac {1}{2}}(kaa-laa)={\frac {1}{2}}(k-l)(aa-aa)=0}

.

### 다중벡터의 평행

위 식에서 평행한 두 벡터의 쐐기곱은 0이라는 결과를 얻을 수 있다. 이를 일반적으로 정의로 이용하여, 임의의 두 다중벡터

a
,
b

{\displaystyle a, b}

에 대하여,

a
∧
# b
0

{\displaystyle a\wedge b=0}

이면 두 다중벡터가 평행이라고 정의하기로 한다. 평행한 두 벡터의 기하곱은 단순히

a
# b
a
⋅
b
a
∧
# b
a
⋅
b

{\displaystyle ab=a\cdot b+a\wedge b=a\cdot b}

로 두 벡터의 내적이 된다.
Caillou

**Caillou** was a contestant in Epic Character Elimination Reboot. He originates from the Animated series *Caillou*. Caillou was put into Still Deciding in Guess Who's Back (Back Again), and was eliminated in Fun on the Sun. Caillou got last place out of everyone, aka 22nd

## Personality

Caillou is a BITCH and a LITTLE FUCKER WHO NEEDS TO LEARN SOME GOD DAMN MANNERS (Will be edited later)

## Coverage

In Guess Who's Back (Back Again), Caillou is first seen after Edward Elric calls him a kid, where he starts crying about wanting to go home. When Weiss Schnee tells him to be quiet, he starts crying about her being mean to him.

During the challenge, Caillou shows his team a box of razors and says he's gonna put them in the cake, only to get frozen in a block of ice by Weiss

In Fun on the Sun, Caillou cries for help to be unfrozen but no one on the team helps. Later, Sasha Waybright calls him out for trying to sabotage the team, which he denies. Caillou is elimianted with 6 votes. The last thing he does before getting sent to the Shadow Realm is cry.

In Jimbo, the first thing he says is that he hopes everyone gets eliminated. Later while everyone is walking in silence, Caillou breaks the silence by whining to be carried. Everyone just tells him to suck it up or ignores his crying. His audition to rejoin is saying he deserves a second chance since he was eliminated first.

In Work at a Pizza Place, Caillou boasts about getting more votes than Tyler only for Host to reveal that he only got 1 vote.

In The Hosting Dead (Part 1), Caillou gets no votes to rejoin. When told to vote, he votes for Mr. Clean claiming that he is a meanie. He also makes Cassy vote for him, despite her wanting to vote for Ghostface.

## Trivia

* Caillou is the youngest contestant in ECER
* Due to his early elimination, Caillou was tied with Top Cat as the last character in the series to die, finally having a death when he alongside all of the noncompeting contestants were blown up by the nuclear bomb in the episode Bored Games.

## Votes

 11
 17
기하대수학

기하대수학(Geometric Algebra)은 기하적 대상들을 대수학적 방식으로 분석하는 학문이다. 다루는 대상은 다중벡터들이며, 대표적으로 사용되는 연산은 기하곱, 내적, 쐐기곱 등이 있다.

## 기하대수의 기초

기하대수에서 다루는 기하적 대상들의 예로는 스칼라, 벡터, 이중벡터 등이 있으며, 이들의 선형결합이 다중벡터이다. 스칼라와 벡터는 흔히 알려진 방식대로의 기하적 의미를 가진다. 이중벡터 및 다른 다중벡터들의 경우 스칼라나 벡터에서는 관찰되지 않는 새로운 성질을 갖는다.

### 표준기저로의 표현

다중벡터는 표준기저들로 나타내어질 수 있다. 기하대수학에서 표준기저를 표기하는 방식으로는

e

1

,

e

2

,

e

3

,
⋯

{\displaystyle e\_{1},e\_{2},e\_{3},\cdots }

,

x
^

,

y
^

,

z
^

,
⋯

{\displaystyle {\hat {x}},{\hat {y}},{\hat {z}},\cdots }

 등이 있다. 표준기저는 정규직교벡터들의 집합으로 볼 수 있으며, 이들의 쐐기곱(또는 이들이 직교하므로 기하곱)으로 이중벡터 및 그 이상의 단계(grade)를 갖는 다중벡터들을 만들어낼 수 있다. 예를 들어,

e

1

∧

e

2

=

e

1

e

2

{\displaystyle e\_{1}\wedge e\_{2}=e\_{1}e\_{2}}

는 두 벡터

e
1

,

e
2

{\displaystyle e\_1, e\_2}

를 순서대로 잇고 그 방향으로 평행사변형(이 경우 정규직교이므로, 정사각형)을 만들어서 나오는,

e
1

,

e
2

{\displaystyle e\_1, e\_2}

 벡터가 있는 평면상의 회전으로 해석할 수 있는 이중벡터가 된다. 또,

e

1

∧

e

2

∧

e

3

=

e

1

e

2

e

3

{\displaystyle e\_{1}\wedge e\_{2}\wedge e\_{3}=e\_{1}e\_{2}e\_{3}}

는 세 벡터를 잇고 나머지 변들을 이어서 나오는 평행육면체(이 경우 정규직교이므로, 정육면체)에 해당하는, 삼차원상의 어떠한 기하적 대상을 나타내는 삼중벡터가 나오게 된다. 참고로 비슷한 방식으로

n

{\displaystyle n}

개의 서로 다른 벡터들(벡터들끼리 정규직교일 필요는 없다)을 뽑아 쐐기곱을 하여 만들어지는 다중벡터를

n

{\displaystyle n}

-블레이드라고 한다. 같은 기저의 벡터를 하나라도 뽑게 되면 쐐기곱의 성질로 인하여 값이

0

{\displaystyle 0}

이 되며, 따라서

n

{\displaystyle n}

차원상에서

n
1

{\displaystyle n+1}

개 이상의 기저벡터를 뽑아 만든 블레이드는 항상 0이 됨 또한 확인할 수 있다.

이렇게 만들어진

n

{\displaystyle n}

-블레이드들의 선형결합을 일반적인 다중벡터로 부르기로 한다. 이 때 스칼라와 벡터의 합처럼 계산이 되지 않을 것으로 보이는 두 블레이드들도, 마치 복소수에서 실수부와 허수부가 덧셈으로 연결되고 더 이상 계산을 하지 않는 것처럼, 다중벡터의 덧셈도 그냥 스칼라부/벡터부/이중벡터부/...를 각각 계산한 후 합으로 연결하는 것으로 한다.

이들 다중벡터들의 기하곱도 마찬가지로 표준기저로 표현한 후, 기하곱의 분배법칙 및 직교하는 두 다중벡터의 기하곱은 반교환법칙이 성립함을 이용하여 계산할 수 있다.

### 다중벡터들의 기하적 의미

스칼라는 음수 및 양수의 '양'을 의미하는 대상이다. 우리가 흔히 다루는 실수와 같다.

벡터는 길이가 유한한 화살표로 표현될 수 있는, 길이와 방향을 갖는 대상이다. 선형대수학에서 다루는 벡터의 기하적 표기를 생각하면 된다.

이중벡터는 두 벡터로 만들어지는 평행사변형의 변을 따라 방향성을 갖는, 넓이와 회전성을 갖는 대상이다. 선형대수학에서 두 벡터의 외적(cross product)으로 얻어지는 벡터가 그 크기는 두 벡터로 만들어지는 평행사변형의 넓이와 같고, 방향은 두 벡터에 수직이면서 오른나사 법칙을 만족하는 방향으로 정의되는 것과 비슷하다. 실제로 삼차원에서 정의된 이중벡터는 이 벡터와 쌍대 관계에 있다. 그러나 선형대수학의 외적은 삼차원 이외에는 정의되지 않지만, 이중벡터는 정의되는 공간의 차원에 상관없이 넓이와 회전성을 갖는 대상으로 잘 정의된다.

삼중벡터는 세 벡터로 만들어지는 평행육면체의 면을 따라 방향성을 갖는, 부피와 사차원상의 어떤 움직임을 표현할 수 있는 대상이다.(추가 조사 필요)
사영 연산

(단계) 사영 연산은 다중벡터에서 특정 단계의 다중벡터를 뽑아내는 연산자로, 다중벡터의 내적 및 쐐기곱을 일반화하는 과정에서 사용된다. 예시로, 다중벡터 A의 스칼라 부분과 벡터 부분은 각각

⟨
A

⟩
0

,
⟨
A

⟩
1

{\displaystyle \langle A \rangle\_0, \langle A \rangle\_1}

로 나타낼 수 있다. 임의의 다중벡터는 스칼라, 벡터 및 블레이드들의 합으로 구성된다. 일반적으로 다중벡터 A는 다음과 같이 각 단계의 블레이드들의 합으로 나타낼 수 있다.

# r
0

N

⟨
A

⟩
r

{\displaystyle A = \sum\_{r=0}^N \langle A \rangle\_r}

다중벡터를 구성하는 모든 블레이드가 같은 단계를 가질 때 이 다중벡터를 동형(Homogeneous)이라고 한다. 즉, 다음 식이 성립할 경우 이를 r-단계 동형 다중벡터라고 한다.

# A
⟨
A

⟩
r

{\displaystyle A = \langle A \rangle\_r}

## 내적과 쐐기곱의 일반적 정의

사영 연산을 통해 다중벡터의 내적과 쐐기곱을 일반화할 수 있다. 각각 단계 r, s인 두 동형 다중벡터

A
r

,

B
s

{\displaystyle A\_r, B\_s}

의 기하곱을 계산해보자. 두 다중벡터들을 구성하는 기저들이 서로 선형 독립이라면 결과는 (r+s)-단계 다중벡터일 것이고, 기저들 중 한 쌍의 벡터들이 동일하다면 두 벡터가 소거되어 (r+s-2)-단계 다중벡터가 나온다. 같은 방식으로 계속 내려가다가 최종적으로 한 기저가 다른 기저에 포함되는 경우의 결과인 |r-s|-단계 다중벡터가 나올 수 있다. 즉, 사영벡터를 이용해 나타내면 다음과 같이 나타낼 수 있다.

A
r

B
s

=
⟨

A
r

B
s

⟩

r
s

⟨

A
r

B
s

⟩

r
s
−
2

.
.
.
⟨

A
r

B
s

⟩

r
−
s

{\displaystyle A\_r B\_s = \langle A\_rB\_s \rangle\_{r+s} + \langle A\_rB\_s \rangle\_{r+s-2}+...+\langle A\_rB\_s \rangle\_{|r-s|}}

이 때 최고 단계의 동형 다중벡터

⟨

A
r

B
s

⟩

r
s

=

A
r

∧

B
s

{\displaystyle \langle A\_rB\_s \rangle\_{r+s} = A\_r \wedge B\_s}

로, 최소 단계의 동형 다중벡터

⟨

A
r

B
s

⟩

r
−
s

=

A
r

⋅

B
s

{\displaystyle \langle A\_rB\_s \rangle\_{|r-s|}=A\_r \cdot B\_s}

로 정의한다. 이 정의와 내적 및 쐐기곱의 분배 법칙을 이용해서, 일반적인 다중벡터 사이의 내적과 쐐기곱을 정의할 수 있게 된다.

위 식의 예시로 r=s=1이라면 두 벡터 간의 연산으로

a
# b
⟨
a
b

⟩
0

⟨
a
b

⟩
2

=
a
⋅
b
a
∧
b

{\displaystyle ab = \langle ab \rangle\_0 + \langle ab \rangle\_2 = a \cdot b + a \wedge b}

가 되어 두 벡터 사이의 내적 및 쐐기곱이 기존 공식을 만족함을 알 수 있다.
NYPD Bureau of Patrol Services

## NYPD Bureau HQ Commanding Officers

* NYPD Bureau Chief - (S1 - S5)
* NYPD Bureau Chief - (S6 - S10)
* NYPD Bureau Chief - (S11 - S15)
* NYPD Bureau Chief - (S16 - S20)
* NYPD Bureau Chief - (S21 - Present)

## NYPD Borough Commanding Officers

* NYPD Manhattan South Borough Commander: Assistant Chief -
	+ NYPD Manhattan South Deputy Borough Commander: Deputy Chief -
* NYPD Manhattan North Borough Commander: Assistant Chief -
	+ NYPD Manhattan North Deputy Borough Commander: Deputy Chief -
* NYPD Brooklyn South Borough Commander: Assistant Chief -
	+ NYPD Brooklyn South Deputy Borough Commander: Deputy Chief -
* NYPD Brooklyn North Borough Commander: Assistant Chief -
	+ NYPD Brooklyn North Deputy Borough Commander: Deputy Chief -
* NYPD Queens South Borough Commander: Assistant Chief -
	+ NYPD Queens South Deputy Borough Commander: Deputy Chief -
* NYPD Queens North Borough Commander: Assistant Chief -
	+ NYPD Queens North Deputy Borough Commander: Deputy Chief -
* NYPD Staten Island Borough Commander: Assistant Chief -
	+ NYPD Staten Island Deputy Borough Commander: Deputy Chief -
* NYPD Bronx Patrol Borough Commander: Assistant Chief -
	+ NYPD Bronx Patrol Deputy Borough Commander: Deputy Chief -

## NYPD Borough's Command

* Manhattan South Borough
	+ 04th Patrol Precinct - (Manhattan South Homicide Task Force)
	+ \_\_\_ Patrol Precinct - (Manhattan South Special Victims Unit)
	+ \_\_\_ Patrol Precinct
* Manhattan North Borough
	+ 27th Patrol Precinct - (Manhattan North Homicide Task Force)
	+ \_\_\_ Patrol Precinct - (Manhattan North Special Victims Unit)
	+ \_\_\_ Patrol Precinct
* Brooklyn South Borough
	+ \_\_\_ Patrol Precinct
	+ \_\_\_ Patrol Precinct
	+ \_\_\_ Patrol Precinct
* Brooklyn North Borough
	+ \_\_\_ Patrol Precinct
	+ \_\_\_ Patrol Precinct
	+ \_\_\_ Patrol Precinct
* Queens South Borough
	+ \_\_\_ Patrol Precinct
	+ \_\_\_ Patrol Precinct
	+ \_\_\_ Patrol Precinct
* Queens North Borough
	+ \_\_\_ Patrol Precinct
	+ \_\_\_ Patrol Precinct
	+ \_\_\_ Patrol Precinct
* Staten Island Borough
	+ \_\_\_ Patrol Precinct
	+ \_\_\_ Patrol Precinct
	+ \_\_\_ Patrol Precinct
* Bronx Patrol Borough
	+ 56th Patrol Precinct
	+ 55th Patrol Precinct - (Bronx Special Victims Unit)
	+ \_\_\_ Patrol Precinct

## NYPD Auxiliary Section

* Supervising Lieutenant - \_\_\_\_ Brody, (Law & Order S18 E8)
* Auxiliary P. Officer - Victor Rodchenko, (Law & Order S18 E8)

## NYPD Manhattan

* NYPD Police Captain - Donald Cragen, Manhattan S/N Special Victims Unit
* NYPD Police Captain - Olivia Benson, Manhattan S/N Special Victims Unit

## NYPD Precincts

* John F. Kennedy Precinct
* 116th Patrol Precinct -
* 110th Patrol Precinct -
* 22nd Patrol Precinct -
* 74th Patrol Precinct -
* 29th Patrol Precinct -
* 26th Patrol Precinct -
* 27th Patrol Precinct
* 16th Patrol Precinct - (Manhattan South/North Special Victims Unit)
* 15th Patrol Precinct -
* 31st Patrol Precinct
* 21st Patrol Precinct -
NYPD Vice Enforcement Division

## Vice Enforcement Division Commanders

* NYPD Deputy Inspector -
* NYPD Deputy Inspector -
* NYPD Deputy Inspector -
* NYPD Police Captain - Igor Gerbic, , Unknown Borough Vice Enforcement Squad - (L&O: SVU SS17 E17)
* NYPD Police Captain -
* NYPD Police Captain -

## Vice Enforcement Division Supervisors

* NYPD Lieutenant -
* NYPD Lieutenant -
* NYPD Lieutenant -
* NYPD Sergeant - Edward Dericco, Unknown Borough Vice Enforcement Squad - (Law & Order: SVU S4 E1)
* NYPD Sergeant - Phoebe Backer, Manhattan North Vice Enforcement Squad - (Law & Order: SVU S20 E15, S22 E4, E11 & E14)
* NYPD Sergeant -

## Vice Enforcement Division Detectives

* Detective First Grade
	+ Detective -
* Detective 2nd Grade
	+ Detective -
* Detective 3rd Grade
	+ Detective -
* Unknown Grade
	+ Detective - Anton Jefferson, Unknown Borough Vice Enforcement Squad - (L&O: SVU S17 E17 - E18)
	+ Detective - Thomas Russo, Unknown Borough Vice Enforcement Squad - (L&O: SVU S17 E17 - E18)

## Vice Enforcement Division Officers

* 31st Patrol Precinct (Unknown Borough) - Vice Enforcement Squad
	+ NYPD Officer - Peter F. Ridley, (Law & Order: SVU S1 E4) / 6 Blue Stripes = 30 Years of Services / Badge Number: Unknown
	+ NYPD Officer - Sal D`Angelo, (Law & Order: SVU S1 E4) / 4 Blue Stripes = 23 Years of Services / Badge Number: Unknown
Timeline of Crowen

Present Time: 4443

* Approximately -10,000: Simori creates the Cosmos and Phene
* 0: Humanity arrives on the eastern shores of the continent, in present Hadwisa, and found Feros.
* 20: The first Kingdom of Man, Ferrrosian Balkcis, is founded.
* 41: Humanity comes across the wandering Idione, and construct a city for her worship.
* 68: The Ferrrosian Balkcis Kingdom fragments following a terrible typhoon, creating the Kingdom of Diderio
* 177: The Formation of the Binjani Kingdom of Man
* 199: Binjani/Czit Conflicts begin
* 211: The Drow emerge from the Underdark
* 216: The Kingdom of Vadoniasque is founded
* 249: The Necromatic Wars Begin in Eastern Zokar
* 420: Francis goes dry
* 547: The Second Elven Kingdom of Vadonint
* 666: Francis causes another problem.
* 952: Moonlight Kingdom
* 1839: The restructuring into the Empire of Vadonia.
* 2222: The Countess becomes the first person to arrive from Viotis.
* 2223: The Age of Darkness Begins
* 2673: Nasato is formed following the end of the Magic Rift Conflicts.
* 2888: The Age of Heros Begins
* 3444: The Age of Giants Begins
* 3999: The Age of The Hunt Begins
* 4343: Ruby Arrives to Crowen
* 4443: The Age of Revolutions Begins
NYPD Forensic Investigation Division

## Forensic Investigation Division Commanders

* NYPD Assistant Chief -
* NYPD Assistant Chief -
* NYPD Assistant Chief -
* NYPD Assistant Chief -

## Forensic Investigation Division Executives

* NYPD Deputy Chief -
* NYPD Deputy Chief -
* NYPD Deputy Chief -
* NYPD Deputy Chief -
* NYPD Inspector -
* NYPD Inspector -
* NYPD Inspector -
* NYPD Inspector -

## Division Squads & Units

* Firearms Analysis Section:
	+ Detective - Evan Underberg, (Law & Order S14 E8)
* Police Laboratory
* Crime Scene Unit - Deputy Inspector is the Commanding Officer
* DNA Liaison Unit
* Latent Print Unit
* Ballistics Unit
* Bomb Squad

## F-Tech's

* Forensic Technician - Pat Fisher, (L&O: SVU S5 E23)
TheBigAppleFranchise Wiki

**Welcome to the TheBigAppleFranchise Wiki!**
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NYPD Crime Scene Unit

## CSU Commanders

* NYPD Deputy Inspector -
* NYPD Police Captain - Judith Siper

## CSU Supervisors

* NYPD Lieutenant -
* NYPD Sergeant -

## CSU Detectives

* NYPD Detective - Clifton Montgomery, (Law & Order: SVU S12 E14)
* NYPD Detective - Ryan O'Halloran,
* NYPD Detective - \_\_\_\_ DiGraita, (Law & Order S19 E19 & S20 E6)
* NYPD Detective - \_\_\_\_ Halpern, (Law & Order S18 E4)
* NYPD Detective - \_\_\_\_ Brown, (Law & Order S9 E12)
* NYPD Detective - Adrian Sung, (L&O: SVU S12 E11 - E12 & E16 & E21 - E22 & E24, S13 E5

## CSU Unknown

* Unknown Rank - \_\_\_\_\_\_ Jackson, (Law & Order S09 E02)
* Unknown Rank - \_\_\_\_\_\_ \_\_\_\_\_, (Law & Order S20 E17)
* Unknown Rank - \_\_\_\_\_\_ Barrett, (Law & Order S12 E11 & E19, S13 E15)
* Unknown Rank - \_\_\_\_\_\_ Persky, (Law & Order S9 E06)
* Unknown Rank - \_\_\_\_\_\_ Rivera, (Law & Order S1 E12)
* Unknown Rank - Frank Bremmer, (L&O: SVU S1 E1 Only)
* Unknown Rank - Donna Richter, (Law & Order S9 E05)
* Unknown Rank - \_\_\_\_\_\_ Hsu, (Law & Order S9 E02)
* Unknown Rank - Dale Stuckey, (Law & Order S\_ E\_\_)
New York City Office of Chief Medical Examiner (OCME)

## Chief Medical Examiner's

* Chief - Dr. Melinda Warner, (2018 - Present)

## Assistant Chief Medical Examiner's

* Assistant Chief - Dr. Elizabeth Rodgers

## Assistant Medical Examiner's

* Assistant - Dr. \_\_\_\_\_ Ackerman, (Law & Order S16 E19)
* Assistant - Dr. \_\_\_\_\_ Manning, (Law & Order S5 E7 & S6 E3)
* Assistant - Dr. \_\_\_\_\_ \_\_\_\_\_, (Law & Order S20 E20)
* Assistant - Dr. \_\_\_\_\_ \_\_\_\_\_, (Law & Order S20 E5)
* Assistant - Dr. \_\_\_\_\_ Morean, (Law & Order S19 E18)
* Assistant - Dr. \_\_\_\_\_ Thorne, (Law & Order S18 E1)
* Assistant - Dr. Judy Summers, (Law & Order S09 E2)
* Assistant - Dr. \_\_\_\_\_ Hoeck, (Law & Order S05 E6)
* Assistant - Dr. \_\_\_\_\_ Steele, (Law & Order S19 E17)
* Assistant - Dr. \_\_\_\_\_ Torres, (Law & Order S18 E13)
* Assistant - Dr. \_\_\_\_\_ Brody, (Law & Order S12 E19, S13 E2 & E19, S14 E1 & E13 & E18, S15 E2 - E3 & E15, S16 E6 & E20 - E21)
* Assistant - Dr. Stan Palchuck, (Law & Order S19 E08 & S20 E06)
* Assistant - Dr. \_\_\_\_\_ Wong, (Law & Order S18 E9)
* Assistant - Dr. \_\_\_\_\_ Cook, (Law & Order S13 E14)
* Assistant - Dr. Janet Glynn, (Law & Order S9 E05)
* Assistant - Dr. Carla Birch, (Law & order S15 E24, S16 E13 & S17 E15)
* Assistant - Dr. Cho Shen, (L&O S18 E6 & E8, S19 E12, S20 E22)
표준기저

표준기저(영어: Standard basis)는 다중벡터들을 표기하는 방식 중의 하나로, 좌표계가 주어진 기하학적 대상들을 다룰 때 계산을 용이하게 해준다.

## 표준기저의 표기

일반적으로

{

x
^

,

y
^

,

z
^

,

w
^

}

{\displaystyle \{{\hat {x}},{\hat {y}},{\hat {z}},{\hat {w}}\}}

와 같이 좌표계의 표기를 따라가거나, 차원이 높아질 경우

{

e

1

,

e

2

,
.
.
.
,

e

n

}

{\displaystyle \{e\_{1},e\_{2},...,e\_{n}\}}

와 같이 아래첨자로 숫자를 적어서 표시한다.

## 표준기저의 성질

표준기저의 각 원소는 벡터이며, 크기가 1이고 서로 수직인 정규직교기저이다.

임의 차원에서 정의된 다중벡터의 표준기저

{

e

1

,

e

2

,
.
.
.
,

e

n

}

{\displaystyle \{e\_{1},e\_{2},...,e\_{n}\}}

에 대하여,

e

i

e

j

=

{

1
,

if

# i
j

−

e

j

e

i

,

if

i
≠
j

{\displaystyle e\_{i}e\_{j}={\begin{cases}1,&{\text{if }}i=j\\-e\_{j}e\_{i},&{\text{if }}i\neq j\end{cases}}}

가 성립한다. 이는 표준기저일 때 서로 다른 두 기저벡터끼리는 서로 수직이며, 같은 두 기저벡터끼리는 평행이기 때문에 성립한다.
31st Patrol Precinct

The 31st Precinct is located in the Manhattan South/North Borough at ????. It has a Patrol Services Division and a Vice Enforcement Squad.

## NYPD Precinct Commanders

* NYPD Deputy Inspector -
* NYPD Deputy Inspector -
* NYPD Deputy Inspector -
* NYPD Deputy Inspector -
* NYPD Deputy Inspector -
* NYPD Police Captain -
* NYPD Police Captain -
* NYPD Police Captain -
* NYPD Police Captain -
* NYPD Police Captain -

## NYPD Precinct Supervisors

* NYPD Lieutenant -
* NYPD Lieutenant -
* NYPD Lieutenant -
* NYPD Lieutenant -
* NYPD Lieutenant -
* NYPD Sergeant - Michael Lucas, (Law & Order S9 E11)
	+ 6 Blue Stripes = 30 Years of Service / Badge Number: 9218
* NYPD Sergeant - Karen Smythe, (L&O: SVU S2 E14)
	+ \_ Blue Stripes = \_ - \_ Years of Services / Badge Number: ??
* NYPD Sergeant -
* NYPD Sergeant -
* NYPD Sergeant -

## NYPD Precinct Detectives

* Detective First Grade -
	+ Detective -
	+ Detective -
* Detective 2nd Grade -
	+ Detective -
	+ Detective -
* Detective 1st Grade -
	+ Detective -
	+ Detective -

## NYPD Precinct Officers

* NYPD Officer - \_\_\_\_\_ Galetta, (L&O: SVU S6 E23)
* NYPD Officer - Michael Towne,
* NYPD Officer - Peter F. Ridley, (L&O: SVU S1 E4)
* NYPD Officer - Mitch Murray,
* NYPD Officer - Sal D`Angelo, (L&O: SVU S1 E4)
* NYPD Officer - Austin Bates, ()
NYPD Bureau of Organised Crime Control

## Bureau Commanding Officers

* NYPD Bureau Chief -
* NYPD Bureau Chief -
* NYPD Bureau Chief -
* NYPD Bureau Chief -
* NYPD Bureau Chief -

## Bureau Executive Officers

* NYPD Assistant Chief -
* NYPD Assistant Chief -
* NYPD Assistant Chief -
* NYPD Assistant Chief -
* NYPD Assistant Chief -
* NYPD Deputy Chief -
* NYPD Deputy Chief -
* NYPD Deputy Chief -
* NYPD Deputy Chief -
* NYPD Deputy Chief -
* NYPD Inspector -
* NYPD Inspector -
* NYPD Inspector -
* NYPD Inspector -
* NYPD Inspector -

## Supervising Officers

* NYPD Deputy Inspector -
* NYPD Deputy Inspector -
* NYPD Deputy Inspector -
* NYPD Deputy Inspector -
* NYPD Deputy Inspector -
* NYPD Police Captain -
* NYPD Police Captain -
* NYPD Police Captain -
* NYPD Police Captain -
* NYPD Police Captain -

## Supervising Officers

* NYPD Lieutenant - William Brewster, (Organised Crime S2 E7 - Present)
* NYPD Lieutenant - Marv Moennig, (Organised Crime S1 E1 - S2 E7)
* NYPD Lieutenant -
* NYPD Lieutenant -
* NYPD Lieutenant -
* NYPD Sergeant - William Brewster, (Organised Crime S2 E1 - S2 E7)
* NYPD Sergeant -
* NYPD Sergeant -
* NYPD Sergeant - Ayanna Bell, (Organised Crime S1 E1 - Present)
* NYPD Sergeant -

## Bureau Detectives

* Detective First Grade:
	+ Detective - Freddie Washburn, (Organised Crime S1 E2 - S1 E8)
	+ Detective - Elliot Stabler, Sr, (Organised Crime S1 E1 - Present)
	+ Detective - Victoria Cho, (Organised Crime S2 E2 - Present)
* Detective 2nd Grade:
	+ Detective - Diego Morales, (Organised Crime S2 E2 - Present)
* Detective 3rd Grade:
	+ Detective - Carlos Maldonado, (Organised Crime S1 E2 - S1 E8)
	+ Detective - Jet Slootmaekers, (Organised Crime S1 E1 - Present)
		- Technology Expert
	+ Detective - Gina Cappelletti, (Organised Crime S1 E2 - S1 E7)
	+ Detective - Carmen Riley, (Organised Crime S2 E1 - Present)
* Unknown Grade
	+ Detective - \_\_\_\_\_ Ostrover, (Law & Order S16 E12)

## Bureau Officers

* NYPD Officer -
* NYPD Officer -
* NYPD Officer -
* NYPD Officer -
* NYPD Officer -

## Bu. Divisions

* Organized Crime Investigation Division
* Firearms Suppression Division
* Investigative Support Division
* Field Control Division
* Narcotics Division:
	+ Narcotics Borough Manhattan South
	+ Narcotics Borough Manhattan North
	+ Narcotics Borough Brooklyn South
	+ Narcotics Borough Brooklyn North
	+ Narcotics Borough Staten Island
	+ Narcotics Borough Queens
	+ Narcotics Borough Bronx
* Gang Division:
	+ Brooklyn South Gang Squad
	+ Brooklyn North Gang Squad
	+ Staten Island Gang Squad
	+ Manhattan Gang Squad
	+ Queens Gang Squad
	+ Bronx Gang Squad

## Ex. Links

* https://en.wikipedia.org/wiki/New\_York\_City\_Police\_Department\_Organized\_Crime\_Control\_Bureau
Акула-Факел

### Ещё известная как "арбузная акула"

(Превратиться в Акулу-факел можно только во время блекаута и отключения енергии.)

что-бы превратиться в Акулу-факел нужно пойти в столовку. (или-же иначе кухню)

в столовке, на верху кое-какой полки есть Арбуз,который надо взять в инвентарь игрока.

После этого, надо держа арбуз в руке стать на акулу, которая находиться в бассейне.
Guerra do Mar Interno

## Básico

A Guerra do Mar Interno foi um dos maiores conflitos militares de todos os tempos, centrada no Mar Interno, envolveu dois lados distintos, O Império de Recan Sor e o Reino de For'qin, contra a coalizão formada por Forkfhein, Monkharia, Vayureta, Esthu'Arbool, Coetaqi, Odut e Tenwab. Comahi, Edawah e Etânia também aderiram à Coalizão nos últimos meses de guerra. Também houve a participação de Cledwyn e seus homens.

## Causas

A guerra começou a ser desenhada no ano 609, quando Aetive Cordot Fresano Iesande Recan, Imperador de Recan Sor na época, descobriu que seu maior projeto náutico, o Grande Soberano dos Mares, havia sido descoberto e vazado para outras civilizações do Mar Interno, por um espião de Forkfhein, que estava disfarçado de cidadão Odut. Aetive enfurecido, visitou então Forkfhein, Vayureta, Esthu'Arbool e Monkharia, perguntando a cada líder sobre quem havia realmente vazado os documentos.

Sem respostas concretas, Aetive pouco depois descobriu que o espião era realmente de Forkfhein, e declarou guerra ao país, que foi então apoiado por seus aliados, Monkharia, Esthu'Arbool e Vayureta. Pouco tempo depois, Aetive anunciou que seu plano era destruir todas as civilizações do Mar Interno. Tal anúncio causou a entrada de outros países, como Coetaqi, Odut e Tenwab do lado de Forkfhein.

## Batalhas

Os primeiros combates dessa guerra ocorreram no Mar Interno entre 9 navios de Cledwyn junto com 20 navios de Coetaqi contra 22 navios de Recan e 1 de For'qin. Esse combate marcou o início da guerra e o início da Batalha do Mar Interno.

### Batalha do Mar Interno

A batalha do Mar Interno foi uma batalha marítima que aconteceu nos primeiros meses da guerra, em que os países da Coalizão tentavam impedir que a frota do Soberano dos Mares e Aetive desembarcassem em Vayureta. Essa batalha contou com as forças de Vayureta, Esthu'Arbool, Cledwyn/Hen'Ogledd, Monkharia, Recan Sor e For'qin.

Essa batalha se iniciou de vez quando forças navais de Esthu'Arbool e Vayureta interceptaram a frota do Soberano dos mares, que navegava rumo a Vayureta.

No início desse conflito diversos navios foram destruídos
The Learned Man

I once read a story about a man who got overthrown by his shadow.

It's not real, but I found someone close...

He came up to the door a month ago. Desperately pleading to be locked up.

"It's my shadow. It's screwed my life over ever since I went into that mansion."

I was going to tell him this isn't a paranormal investigation place... Yet shadows are always attached to us, right? So I let him in.

God. That was a mistake.

I'll tell the rest of the story of this ~~secksy~~ burden later. I'm on dinner break. - Alexandra, 3/23/22
Скины

**Скины** - одна из механик игры.

## Суть

Скин можно экипировать на оружие, и ваше это оружие будет отображаться как этот скин.

## Получение

Большинство скинов выпадают из ящиков, но есть некоторые, которые получаются иным способом.

## Редкости

Все скины имеют свою редкость, которая основывается на шансе выпадения в ящике. От редкости зависит «значение» скина, которое отображает, сколько кредитов можно получить продав скин.

• Элемент значка (зелёный) - можно получить за достижения

• Обычный (оранжевый) - 50%

• Необычно (белый) - 25%

• Редкий (жёлтый) - 17%

• Ультра-Редкий (голубой) - 6%

• Легендарный (розовый) - 2%

## Гитары

Гитары - это особые скины, которые играют музыку. Гитары всегда имеют редкость Легендарный. (искл: Архангел, Чхтхониан)
The Burnout Paradise Remastered Calvary Wiki

# **Welcome to the The Burnout Paradise Remastered Calvary Wiki!**

## The Other Guys.....

*Need help building out this community?*

* Rules of this wiki
* Getting Started
* How to Contribute
* Managing your new community
* Guides
* All Help articles

You can also be part of the larger Fandom family of communities. Visit Fandom's Community Central!

*Community Founders*: Write a good and paragraph-length description for your welcome section about your topic. Let your readers know what your topic is about and add some general information about it. Then you should visit the admin dashboard for more tips.
내적

내적(영어: Inner Product)은 교환 성질이 있는 연산이다. 선형대수학에서 벡터끼리의 내적만이 정의되었다면, 기하대수학에서는 기하곱을 사용하여 다음과 같이 다중벡터로 정의를 확장시켜 정의할 수 있다.

a
⋅
# b

1
2

(
a
b
b
a
)

{\displaystyle a\cdot b={\frac {1}{2}}(ab+ba)}

## 내적의 계산

위에서 소개된 내적의 정의와 함께, 각 다중벡터를 표준기저로 풀어 쓴 후 분배법칙을 이용한다. 예시로, 벡터와 이중벡터

# a
2

x
^

z
^

,
# b

y
^

z
^

{\displaystyle a=2{\hat {x}}+{\hat {z}},b={\hat {y}}{\hat {z}}}

의 내적을 구하면

a
⋅
b

=

1
2

(
a
b
b
a
)

=

1
2

(
(
2

x
^

z
^

)
(

y
^

z
^

)
(

y
^

z
^

)
(
2

x
^

z
^

)
)

=

1
2

(
2

x
^

y
^

z
^

z
^

y
^

z
^

2

y
^

z
^

x
^

y
^

z
^

z
^

)

=

1
2

(
2

x
^

y
^

z
^

−

y
^

2

y
^

z

y
^

)

=
2

x
^

y
^

z
^

{\displaystyle {\begin{aligned}a\cdot b&={\frac {1}{2}}(ab+ba)\\&={\frac {1}{2}}((2{\hat {x}}+{\hat {z}})({\hat {y}}{\hat {z}})+({\hat {y}}{\hat {z}})(2{\hat {x}}+{\hat {z}}))\\&={\frac {1}{2}}(2{\hat {x}}{\hat {y}}{\hat {z}}+{\hat {z}}{\hat {y}}{\hat {z}}+2{\hat {y}}{\hat {z}}{\hat {x}}+{\hat {y}}{\hat {z}}{\hat {z}})\\&={\frac {1}{2}}(2{\hat {x}}{\hat {y}}{\hat {z}}-{\hat {y}}+2{\hat {y}}{z}+{\hat {y}})\\&=2{\hat {x}}{\hat {y}}{\hat {z}}\end{aligned}}}

로, 삼중벡터가 나오는 것을 확인할 수 있다. 참고로,

a

{\displaystyle a}

에서

b

{\displaystyle b}

에 없는 성분인

x
^

{\displaystyle \hat x}

이 있는 부분은 살아남고,

b

{\displaystyle b}

에 있는 성분인

z
^

{\displaystyle \hat{z} }

이 있는 부분은 서로 상쇄됨을 확인할 수 있다.

## 내적의 성질

연산의 정의에 의하여,

a
⋅
# a

1
2

(
a
a
a
a
# a

a

2

{\displaystyle a\cdot a={\frac {1}{2}}(aa+aa)=aa=a^{2}}

이 성립한다. 일반적으로 다중벡터

a

{\displaystyle a}

에 대하여 이 값이 스칼라가 아니지만,

n

{\displaystyle n}

-블레이드를 위 식에 넣으면 항상 스칼라값이 나옴을 증명할 수 있다n-블레이드 제곱은 스칼라.

### 다중벡터의 수직

벡터간의 내적에서, 두 벡터

u
,
v

{\displaystyle u, v}

가 수직임을

u
⋅
# v
0

{\displaystyle u\cdot v=0}

로 정의하였다. 마찬가지로 두 다중벡터가 수직임을 내적을 이용해 정의하면, 임의의 다중벡터

a
,
b

{\displaystyle a, b}

에 대하여

a
⋅
# b
0

{\displaystyle a\cdot b=0}

이면 두 다중벡터가 수직이라고 정의하기로 한다. 이 경우 두 다중벡터의 기하곱은 단순히

a
# b
a
⋅
b
a
∧
# b
a
∧
b

{\displaystyle ab=a\cdot b+a\wedge b=a\wedge b}

로 두 다중벡터의 쐐기곱이 된다.

### 기존의 내적과의 관계

기존에 선형대수학에서 정의된 벡터끼리의 내적의 경우 결과가 같게 나온다. 이는 다음과 같이 표준기저로 벡터를 표현함으로써 확인할 수 있다.

# a

a

1

e

1

a

2

e

2

⋯

a

n

e

n

,
# b

b

1

e

1

b

2

e

2

⋯

b

n

e

n

{\textstyle a=a\_{1}e\_{1}+a\_{2}e\_{2}+\cdots a\_{n}e\_{n},b=b\_{1}e\_{1}+b\_{2}e\_{2}+\cdots b\_{n}e\_{n}}

일 때,

a
⋅
b

=
(

a

1

e

1

a

2

e

2

⋯

a

n

e

n

)
⋅
(

b

1

e

1

b

2

e

2

⋯

b

n

e

n

)

=

∑

i
,
j

n

a

i

b

j

e

i

⋅

e

j

=

∑

# i
1

n

a

i

b

i

=

a

1

b

1

a

2

b

2

⋯

a

n

b

n

{\displaystyle {\begin{aligned}a\cdot b&=(a\_{1}e\_{1}+a\_{2}e\_{2}+\cdots +a\_{n}e\_{n})\cdot (b\_{1}e\_{1}+b\_{2}e\_{2}+\cdots +b\_{n}e\_{n})\\&=\sum \_{i,j}^{n}a\_{i}b\_{j}e\_{i}\cdot e\_{j}\\&=\sum \_{i=1}^{n}a\_{i}b\_{i}\\&=a\_{1}b\_{1}+a\_{2}b\_{2}+\cdots +a\_{n}b\_{n}\end{aligned}}}
The Eyes Are Watching You.

## Story

Once upon a time, there was a young boy.

He had everything he could ask for, a sister, a house, food.. everything. Everything but his parents.

One day, the boy wandered deep into the woods with his sister, only finding something that wasn't a candied house, no, no. It was a strange little tree shaped like three triangles stacked on eachother, they thought nothing much of it, so they took it. But.. the brother, at the next hour, fell onto a patch of the dead, gray grass.

And thus, the brother took his last breath.

Some say his spirit is a gaurdian of his sister, others say the brother became some watcher.

But all we know.

Is that its eyes are watching you.

## Personality

Nothing important. But from the story, he was caring. And according to some more recently found documents of him, he was gay as hell.

I was always caring.. sure, I might’ve had feelings for someone, but that’s not really apart of my personality, I’m alittle too overprotective I might say..

No, you're definitely gay. Don't avoid the guilt.

## Appearance

We don't know, but from reports of this monster, it has no eyes.

When was I a monster?

….
--

U2lzdGVyLCwgSSBkb24ndCBmZWVsIHRoYXQgZ29vZA==

Oh. Let’s get you home.

U2lzdGVyLCwgSSBmZWVsIHRpcmVkLi4=

Brother…?

BROTHER. W-WAKE UP.

…. RG9uJ3QgZ28gbmVhciB0aGF0IHRyZWUu
Patient Zero and Broken Promise of Hope

We have new oddities! Isn't that fun? Here we have Patient Zero and Broken Promise of hope. These two were found separately, although they requested to be put in a book together as Patient Zero gets anxious when alone. Aren't I so nice? - Alexandra

## Broken Promise of Hope

We found him trying to break into the archives using some strange crystal powers along with some crystallized agents near him. However, we quickly managed to capture him and place him in a book. He dislikes cooperating with us and he's extremely rude, though he's quite protective of his brother, who we later found out was named "Citrine". We assume that he is one of The Swordsman's children. He wears an emerald green bandana with a peridot colored raincoat with dark brown rain boots.

## Patient Zero

I found him outside The Swordsman's cell, in a more condensed and squishy form. I mistook him for a kneadable eraser until I interviewed Axeton himself, where I found out he was actually another oddity; and his son. I have no idea how he got in, I swear, I locked the door... Anyways, they seem timid and dislike being alone, and they're always close to their brother, Peridot. They seem to be a humanoid figure made of some slimy orange substance wearing a hospital gown.

## Trivia

* Broken Promise of Hope and Patient Zero are actually our youngest oddities, awww...
* Patient Zero, according to their origin, seemed to have come from a hospital of some sort.
* I found a picture of a family photo including Axeton, Peridot, and what seems to be a normal Citrine, and another lady in yellow... Maybe she's an oddity, too? -Alexandra
* Due to strange circumstances that happened today, Patient Zero has been reclassified to Catalyst class.