So I'm trying to prove the Jordan curve theorem for polygons, but I'm not sure how to show that a line segment that does not intersect the boundary has all points of the same parity. I'm also not sure how to show that all the external points are connected by a polygonal path and all the internal points are connected by a polygonal path.
2026-03-27 02:39:11.1774579151
Proof of Jordan Curve Theorem for Polygons
374 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in POLYGONS
- Can the relocation of one control point of a NURBS curve be compensated by an adjustment of some weights?
- Need a hint regarding this question...
- How do I detect if a circle overlaps with a polygon or not?
- A peculiar Diophantine equation
- Looking for Regular Polygons with a Side to Diagonal ratio Equaling a Metallic Mean
- Calculating the value of $\pi$
- Bounding Numbers for $N>2$
- Generalizing Odom's construction of the golden ratio
- Integrating difficult function over a polygon
- Existence and uniqueness of a Riemann-Hilbert problem involving a polygon
Related Questions in DISCRETE-GEOMETRY
- Properties of triangles with integer sides and area
- Discrete points curvature analysis
- Is it a tetrahedron, 5-cell, or something else?
- Is there a volume formula for hyperbolic tetrahedron
- Size of $X\setminus g(X)$ for $g(x)$ the closest $y$ to $x$ with $X_k\sim Unif(A)$
- The permutations of (1,1,0,0), (-1,1,0,0), (-1,-1,0,0) are vertices of a polytope.
- What means the modular operator in that proof?
- Schlegel diagram and d-diagram
- volumetric discrete Laplacian
- What are some examples of 2-polytope/3-polytope that are not simple?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Here is a paper which explain the Jordan curve theorem for polygons.