Add to ORKGLet us begin with a two-dimensional problem. Consider an equilateral triangular region T with edges of unit length. What is the minimum length of a smooth curve that partitions T into two subregions of equal area? Assuming the vertices of T are (1=2; 0), (0;p3=2), (1=2; 0), a solution is given by one-sixth of the circumference of the circle x2 +
We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bou...
Let ABC be a triangle and E a point on AC. Let D be on AB such that DE is parallel to BC and F be on...
Given an arbitrary polygon with $n$ vertices, we wish to partition it into $p$ connected pieces of g...
Consider the family of generalized parabolas {y=−axr+c|a,r,c,x>0,risafixedconstant} that pass throug...
We consider the problem of partitioning (in a certain manner) a rectangle into n regions of equal ar...
Let an edge cut partition the vertex set of an n-dimensional quadratic grid with the side length a i...
The Isoperimetric Theorem states that for a planar region of given perimeter, the circle encloses th...
Let $K$ be a closed polygonal curve in $\RR^3$ consisting of $n$ line segments. Assume that...
summary:We define a proper triangulation to be a dissection of an integer sided equilateral triangle...
In this paper we provide an estimate from above for the value of the relaxed area functional A¯(u, Ω...
We describe briefly the problem of partitioning a con-tinuous curve into N parts with equal chords. ...
Given a simple polygon P on n vertices vq,vi,…, vn-i with each edge assigned a non-negative weight W...
In this paper we study the following problem: we are given a set of imprecise points modeled as para...
Given a set S of n points in the plane and a fixed angle 0 < ω < pi, we show how to find all t...
An example of using integration to find the area of a region that is bounded by 2 curve
We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bou...
Let ABC be a triangle and E a point on AC. Let D be on AB such that DE is parallel to BC and F be on...
Given an arbitrary polygon with $n$ vertices, we wish to partition it into $p$ connected pieces of g...
Consider the family of generalized parabolas {y=−axr+c|a,r,c,x>0,risafixedconstant} that pass throug...
We consider the problem of partitioning (in a certain manner) a rectangle into n regions of equal ar...
Let an edge cut partition the vertex set of an n-dimensional quadratic grid with the side length a i...
The Isoperimetric Theorem states that for a planar region of given perimeter, the circle encloses th...
Let $K$ be a closed polygonal curve in $\RR^3$ consisting of $n$ line segments. Assume that...
summary:We define a proper triangulation to be a dissection of an integer sided equilateral triangle...
In this paper we provide an estimate from above for the value of the relaxed area functional A¯(u, Ω...
We describe briefly the problem of partitioning a con-tinuous curve into N parts with equal chords. ...
Given a simple polygon P on n vertices vq,vi,…, vn-i with each edge assigned a non-negative weight W...
In this paper we study the following problem: we are given a set of imprecise points modeled as para...
Given a set S of n points in the plane and a fixed angle 0 < ω < pi, we show how to find all t...
An example of using integration to find the area of a region that is bounded by 2 curve
We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bou...
Let ABC be a triangle and E a point on AC. Let D be on AB such that DE is parallel to BC and F be on...
Given an arbitrary polygon with $n$ vertices, we wish to partition it into $p$ connected pieces of g...