Title: Theory / Unimportant / Math / Geometry/ / Moise{ / Euclidean
Tags: récupéré fromImplication typConjDef

Name: The Euclidean Parallel Postulate
Definition: Given a line \(L\) and a point \(P\) not on \(L\), there is exactly one line which contain \(P\) and are parallel to \(L\).
Page: 139
Chapter: 9

Name: A triangular/square/rectangular region
Definition: The union of a triangle/square/rectangle and its interior.
Page: 184
Chapter: 13
Section: 1

Name: The edges of \(R\)
Definition: The sides of the triangle \(T\)
Page: 184
Chapter: 13
Section: 1
Variables: \(R=\)
Context: Triangular region

Name: The vertices of \(R\)
Definition: The vertices of the edges of \(R\)
Page: 184
Chapter: 13
Section: 1
Variables: \(R=\)

Name: A polygonal region
Definition: the union of the elements of a complex
Page: 184
Chapter: 13
Section: 1
Denoted by: \(R\)

Name: The set of polygonal regions
Page: 185
Chapter: 13
Section: 1
Notation: \(\mathcal R\)

Name: A measure of polygonals
Definition: Congruence Postulate
Page: 185
Chapter: 13
Section: 1
Definition2: the Additivity Postulate
Conjdef: satisfying all of
Definition3: the measure of a square of side \(a\) is \(a\)
Denoted by: \(\alpha\)
DefType: A function \(\mathcal R\to\mathbb R^{>0}\)

Question: The measure of the rectangle is
Answer: the product of its base and its altitude
Page: 186
Chapter: 13
Section: 2
Variables: \(R\) a rectangle
Name: The rectangle formula

Question: The measure of is
Answer: \(\frac{AC\times AB}{2}\).
Page: 187
Chapter: 13
Section: 2
Index: 1
Kind: Theo

Name: Its (formula) area
Definition: Half of the product of the length of a base and the corresponding altitude.
Page: 205
Chapter: 14
Section: 1
Variables: \(\triangle ABC\)
Kind: Def

Name: A complex
Definition: A set of triangular region such that \(R\cap R'\) is either a side, a singleton or the emptyset for each \(R,R'\) in this set.
Page: 205
Chapter: 14
Section: 2
Example: \(\{T_1, T_2, T_3, T_4, T_5\}\)
Denoted by: \(K\)

Name: A triangulation of \(R\)
Definition: A complex whose union is \(R\)
Page: 205, 25
Chapter: 14, 0 classical topology
Section: 2, 2.4
Variables: \(R\in\mathcal R\)
Name2: A simplicial decomposition of \(R\)

Name: The formula area of \(K\)
Definition: The sum of the area of the elements of \(K\)
Page: 205
Chapter: 14
Section: 2
Variables: \(K\) a complex
Kind: Def

Name: A strip complex
Definition: A complex \(K\) whose vertices lie on two parallel lines.
Page: 205
Chapter: 14
Section: 2
Kind: Def

Question: The formula area of \(S\)
Answer: \(\frac{h}{2}\left(\sum e_i+\sum f_i\right)\)
Page: 205
Chapter: 14
Section: 2
Variables: \(S\=)
Index: 1
Kind: Theo

Smaller0: \(r_1,r_2,c\) satisfies the triangular inequality
Greater0: \(C,C'\) intersect in two points
Page: 238
Chapter: 16
Section: 5
Variables: \(C_i\) circles of radius \(r_i\)
\(c\) the distance between their centers
Index: 1
Kind: Theo
Name: The two-circle theorem

Question: The two points in which \(C,C'\) intersect
Answer: lies on opposite sides of the line of centers
Page: 238
Chapter: 16
Section: 5
Variables: \(C_i\) circles of radius \(r_i\)
\(c\) the distance between their centers
Index: 1
Kind: Theo
Assuming: \(r_1,r_2,c\) satisfies the triangular inequality
Euclidean geometry
Name: The two-circle theorem

Smaller0: \(a_1,a_2,a_3>0\) satisfy the triangle inequality
Greater0: there is a triangle whose sides are \(a_i\)
Page: 239
Chapter: 16
Section: 5
Variables: \(a_1,a_2,a_3>0\)
Index: 2
Kind: Theo
Smaller to greater: iff
Assuming: Euclidean geometry
Name: The Triangle Theorem

Name: A strip decomposition of \(T\)
Definition: A decomposition of \(T\) into triangle and trapezoid.
Page: 206
Chapter: 14
Section: 2
Variables: \(T\) a trapezoid