Search results for "Euclidean distance matrix"

Covering and differentiation

1995

Finite linear spaces in which any n-gon is euclidean

1986

Abstract An n-gon of a linear space is a set S of n points no three of which are collinear. By a diagonal point of S we mean a point p off S with the property that at least two lines through p intersect S in two points. The number of diagonal points is called the type of S. For example, a 4-gon has at most three diagonal points. We call an n-gon euclidean if (roughly speaking) it contains the maximal possible number of 4-gons of type 3. In this paper, we characterize all finite linear spaces in which, for a fixed number n ⩾ 5, any n-gon is euclidean. It turns out that these structures are essentially projective spaces or punctured projective spaces.

Some inequalities involving the euclidean condition of a matrix

1960

Isolated roundings and flattenings of submanifolds in Euclidean spaces

2005

We introduce the concepts of rounding and flattening of a smooth map $g$ of an $m$-dimensional manifold $M$ to the euclidean space $\R^n$ with $m<n$, as those points in $M$ such that the image $g(M)$ has contact of type $\Sigma^{m,\dots,m}$ with a hypersphere or a hyperplane of $\R^n$, respectively. This includes several known special points such as vertices or flattenings of a curve in $\R^n$, umbilics of a surface in $\R^3$, or inflections of a surface in $\R^4$.