공식,formula

Difference between r1.34 and the current

@@ -1,4 +1,5 @@
[[수학,math]]에서 formula는 '''mathematical formula, 공식.'''
[[수학,math]]에서 formula는 대체로 '''mathematical formula, 공식.'''
공식이 아닌 formulae도 대체로 '식'으로 번역되는 듯, due to KmsE:formula

Sub:
[[해석기하_공식]]
@@ -88,11 +89,27 @@
Sub:

[[open_formula]]
한 개 이상의 [[자유변수,free_variable]]를 가진 formula
{
한 개 이상의 [[자유변수,free_variable]]를 가진 formula.
a formula that contains at least one free variable.
[[WpEn:Well-formed_formula#Atomic_and_open_formulas]]
WpEn:Open_formula
WtEn:open_formula x [[Date(2024-01-17T04:38:23)]]
} // open formula Ggl:"open formula"
(위아래비교)
Ggl:"open formula closed formula"
Naver:"open formula closed formula"

[[closed_formula]]
{
'''closed formula'''
[[WpEn:Well-formed_formula#Closed_formulas]]
WtEn:closed_formula
syn. WtEn:ground_formula (x) liked to: WpEn:ground_formula (redir. to WpEn:Ground_expression ... 저기서 ground term / ground formula / ground expression 설명함.) // ground_term / ground_formula / ground_expression
} // closed formula Ggl:"closed formula" Naver:"closed formula"

tbw: '''formula'''는 [[식,expression]] / [[명제,proposition]] / [[항,term]] / [[문장,sentence]] / .... 과 어떤 관련과 차이가?
{
@@ -102,27 +119,38 @@
}

[[sentential_formula]]
{
'''sentential formula'''
mklink [[문장,sentence]] [[sentential_variable]]
https://mathworld.wolfram.com/SententialFormula.html
Sub:
closed sentential formula
https://mathworld.wolfram.com/ClosedSententialFormula.html
"a sentential formula in which none of the variables are free (i.e., all variables are bound)."
open sentential formula
https://mathworld.wolfram.com/OpenSententialFormula.html
"A sentential formula that contains at least one free variable"
// Ggl:"closed open sentential formula"
} // sentential formula Ggl:"sentential formula"

[[propositional_formula]] - 작성중, [[명제,proposition]] [[명제논리,propositional_logic]]

[[atomic_formula]]
'''atomic formula'''
''원자논리식, 원자식?''
AKA 간단히 '''atom''' (wpen)
Cmp: [[atomic_sentence]] [[atomic_expression]]
WtEn:atomic_formula
[[WpEn:Well-formed_formula#Atomic_and_open_formulas]]
[[WpEn:Atomic_formula]]
AKA prime_formula ... via WtEn:prime_formula
http://foldoc.org/formula
https://everything2.com/title/formula (세번째)
} // 논리학의 formula
} // formula (논리학의 formula)

formula와 비슷한 spell: - 관계가 있는지 없는지, 비교할만한지, etc.
formulation (of math/logic)
@@ -137,6 +165,7 @@
http://foldoc.org/formula
https://mathworld.wolfram.com/Formula.html

Up: [[수학,math]]
pl. '''formulas, formulae = formulæ'''(Latinate)

Up: [[수학,math]]


수학,math에서 formula는 대체로 mathematical formula, 공식.
공식이 아닌 formulae도 대체로 '식'으로 번역되는 듯, due to KmsE:formula


chk
{
일변수 다항방정식(다항식,polynomial 방정식,equation)의 해,solution/근 ,root 을 구하는
1차방정식 ?
2차방정식 quadratic_equation - quadratic_formula // 이차방정식,quadratic_equation
3차방정식 cubic_equation - cubic_formula
4차방정식 quartic_equation - quartic_formula
5차방정식 quintic_equation - quintic_formula ... 5차 이상의 방정식은 일반적인 근의 공식이 없다
etc

이것들 페이지가 필요한가? 방정식 페이지로 족할듯?
-> 근의공식, - 근,루트,root의 공식 페이지가 필요할지도?





[edit]

적분공식

[edit]

헤론_공식,Heron_s_formula

세 변의 길이가 $a, b, c$ 인 삼각형의 넓이 $S$ 는
$S = \sqrt{s(s-a)(s-b)(s-c)}$
단,
$s=(a+b+c)/2$

Pf.
$\sin^2A=1-\cos^2A$
$=1-\left(\frac{b^2+c^2-a^2}{2bc}\right)^2$
$=\frac{(a+b+c)(b+c-a)(a-b+c)(a+b-c)}{4b^2c^2}$
여기서 $a+b+c=2s$ 이므로, $b+c-a=2(s-a),\,a-b+c=2(s-b),\,a+b-c=2(s-c)$ 를 대입하면
$=\frac{4s(s-a)(s-b)(s-c)}{b^2c^2}$
$sin A > 0$ 이므로
$\sin A=\frac{2\sqrt{s(s-a)(s-b)(s-c)}}{bc}$
따라서
$S=\frac{1}{2}bc\sin A=\sqrt{s(s-a)(s-b)(s-c)}$

Pf. 코사인법칙,cosines_law을 쓴 증명 - Stewart Appendix D 참조.

[edit]

See also


formula의 다른 뜻
화학,chemistry: chemical formula: 화학식; 제조법, 조제법
논리,logic:
{
//tmp; chk; from wpko
wpko 사용 번역어는 '논리식'. 즉 식,expression의 일종으로 보는 번역?
논리식,formula = 정형논리식,well-formed_formula,wff{ RR:적형식,wff }라 하는데... rly? chk
논리식이라 하면 Srch:well-form을 갖출 수밖에 없어서 저 둘이 같은 뜻인건지? chk
아님 단순히 wff를 줄여서 formula라 하는건지?
WpKo:논리식
WpEn:Well-formed_formula


[https]수학백과: 형식논리학에서도 마찬가지
"논리식(formula), 부분논리식(subformula)"

명제,proposition와 mklink



Sub:

open_formula
{
한 개 이상의 자유변수,free_variable를 가진 formula.
a formula that contains at least one free variable.

WpEn:Well-formed_formula#Atomic_and_open_formulas
WpEn:Open_formula

WtEn:open_formula x 2024-01-17
} // open formula Ggl:open formula

(위아래비교)
Ggl:open formula closed formula
Naver:open formula closed formula

closed_formula
{
closed formula
WpEn:Well-formed_formula#Closed_formulas
WtEn:closed_formula
syn. WtEn:ground_formula (x) liked to: WpEn:ground_formula (redir. to WpEn:Ground_expression ... 저기서 ground term / ground formula / ground expression 설명함.) // ground_term / ground_formula / ground_expression
} // closed formula Ggl:closed formula Naver:closed formula

tbw: formula는 식,expression / 명제,proposition / 항,term / 문장,sentence / .... 과 어떤 관련과 차이가?
{
closed_formula = sentence.


sentential_formula
{
sentential formula
mklink 문장,sentence sentential_variable

https://mathworld.wolfram.com/SententialFormula.html

Sub:
closed sentential formula
https://mathworld.wolfram.com/ClosedSententialFormula.html
"a sentential formula in which none of the variables are free (i.e., all variables are bound)."
open sentential formula
https://mathworld.wolfram.com/OpenSententialFormula.html
"A sentential formula that contains at least one free variable"
// Ggl:closed open sentential formula

} // sentential formula Ggl:sentential formula

propositional_formula - 작성중, 명제,proposition 명제논리,propositional_logic

atomic_formula
atomic formula
원자논리식, 원자식?
AKA 간단히 atom (wpen)
Cmp: atomic_sentence atomic_expression
WtEn:atomic_formula
WpEn:Well-formed_formula#Atomic_and_open_formulas
WpEn:Atomic_formula
AKA prime_formula ... via WtEn:prime_formula
http://foldoc.org/formula
https://everything2.com/title/formula (세번째)
} // formula (논리학의 formula)

formula와 비슷한 spell: - 관계가 있는지 없는지, 비교할만한지, etc.
formulation (of math/logic)
공식화? 형식화?
WtEn:formulation
WpEn:Formulation
logic에 대한 링크가 WpEn:Formula_(mathematical_logic)(redir. to wff)로 되어 있는 것을 보면 분명 관련 있음.
... Ndict:formulation Google:formulation math Google:formulation logic math


pl. formulas, formulae = formulæ(Latinate)