Roundness of metric spaces was introduced by Per Enflo as a tool to study uniform structures of linear topological spaces. The present paper investigates geometric and topological properties detected by the roundness of general metric spaces. In particular, we show that geodesic spaces of roundness 2 are contractible, and that a compact Riemannian manifold with roundness > 1 must be simply conn...

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify several large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual path metric (SSTs...

Some forty years ago Per Enflo introduced the nonlinear notions of roundness and generalized roundness for general metric spaces in order to study (a) uniform homeomorphisms between (quasi-) Banach spaces, and (b) Hilbert’s Fifth Problem in the context of non locally compact topological groups (see [24], [25], [26], and [27]). Since then the concepts of roundness and generalized roundness have ...

We describe a roundness classiication procedure , that is, a procedure to determine if the roundness of a planar object I is within some 0 from an ideal circle. The procedure consists of a probing strategy and an evaluation algorithm working in a feedback loop. This approach of combining probing with evaluation is new in computational metrology. For several deenitions of roundness, our procedur...

A number of subjective and objective methods have been proposed, and are in use, to determine the roundness of sedimentary rock particles. Roundness, which is one of three properties describing the shape of a particle, is a measure of the extent to which the corners and edges of a particle have been worn away. The objective roundness measures are mainly based on the Fourier transform. In this p...

The aim of this study was to investigate differences in shape and size characteristics between developmental opacities and post-orthodontic white enamel lesions using computerized image analysis. Material, in the form of 35 mm slides, was obtained from the archive of photographic patient records in the orthodontic clinic at the Charles Clifford Dental Hospital. Images of 30 teeth with developme...

A new concept referred to as the batch roundness is presented in this paper. This concept is derived to illustrate the worst possible form error for a batch of circular features machined under the same conditions. It is to be used as a statistical quality measure for such a batch of circular features and evaluated by analyzing their systematic and random form error components. The definition of...

Talyrond-TR is a modern sensitive instrument in nanometrology. The performance of Talyrond-TR machine is very important to find an optimal result in roundness measurement. In this paper, the experimental evaluation method of Talyrond-TR 73 machine is designed by using reference standard hemisphere. The influence of Talyrond machine performance in roundness measurement is presented. Signal respo...

In this paper, we propose a new roundness parameter R, to denote circularity corrected by aspect ratio. The basic concept of this new roundness parameter is given by the following equation: R = Circularity + (Circularity perfect circle Circularity aspect ratio) where Circularityperfect circle is the maximum value of circularity and Circularityaspect ratio is the circularity when only the aspect...

Sphericity and roundness have been employed in sedimentological and geomorphological studies to represent the gross shape of a gravel particle. The original complex definitions of gravel sphericity and roundness led to the use of visual charts or simplified parameters. Although the accurate derivation of sphericity requires the surface area of a gravel particle, manual measurement of the area i...