EuDML | Browse

Denote by Kₘ the mirror image of a planar convex body K in a straight line m. It is easy to show that K*ₘ = conv(K ∪ Kₘ) is the smallest by inclusion convex body whose axis of symmetry is m and which contains K. The ratio axs(K) of the area of K to the minimum area of K*ₘ over all straight lines m is a measure of axial symmetry of K. We prove that axs(K) > 1/2√2 for every centrally symmetric convex body and that this estimate cannot be improved in general. We also give a formula for axs(P) for...

Currently displaying 1 – 20 of 203

Page 1 Next

Displaying 1 – 20 of 203

3D illustrations to Chapter 8 of Cromwell's Polyhedra

A Characterization of Sets of Constant Width.

A conjecture of Grünbaum on common transversals.

A correction to my paper:"Some topological extensions of plane geometry"

A Gallai-Type Transversal Problem in the Plane.

A generalization of the Erdös-Szekeres convex n-gon theorem.

A Helly number for unions of two boxes in $ℝ^{2}$ .

A Linear-Time Algorithm for Computing the Voronoi Diagram of a Convex Polygon.

A linear-time construction of Reuleaux polygons.

A measure of asymmetry for domains of constant width.

A measure of axial symmetry of centrally symmetric convex bodies

A measure of symmetry for ovals

A New Necessary Condition for the Vertex Visibility Graphs of Simple Polygons.

A non local quantitative characterization of ellipses leading to a solvable differential relation.

A normed space with the Beckman-Quarles property.

A note on convexly independent subsets of an infinite set of points.

A Note on the Circle Containment Problem.

A point set everywhere dense in the plane.

A Polynomial Solution for the Potato-peeling Problem.

A seperation property of plane convex sets.

Currently displaying 1 – 20 of 203