Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.

27346 Results for the subject "Geometry":

Publisher SummaryThis chapter is a preface to the book, “Handbook of Differential Geometry Volume II,” discussing some problems on Finsler geometry, foliations, symplectic geometry, metric Riemannian geometry, contact geometry, complex differential geometry, compendium on the geometry of Lagrange spaces, and certain actual topics on modern Lorentzian geometry. Some contributions emphasize the basics, some emphasizes the classical results, and others the recent developments.

Franki Dillen Publication date: 2006/01/01SummariesThe researches into non-Euclidean geometry from Saccheri 1733 to Riemann 1854 and Beltrami 1868 can best be understood not merely as foundational enquiries, but also as a progressive elaboration of the methods of analysis and later of differential geometry. The hyperbolic trigonometry of Lobachevskii and J. Bolyai was not generally taken as a conclusive demonstration of the existence of non-Euclidean geometry until it was given a foundation in the study of intrinsic Riemannian geometry.

Jeremy Gray Publication date: 1979/08/01AbstractThe aim of this study was to investigate the relationship between geometry attitude scores and self-efficacy scores towards geometry. Thus, correlational model was used in the process of the study and convenience sampling method was used. The research was conducted with 126 pre-service elementary mathematics teachers studying at Aksaray University Education Faculty in 2010-2011 academic year. In investigating the relationship between geometry attitudes and self-efficacy beliefs about geometry “Self-efficacy scale towards geometry” developed by Cantürk-Günhan and Başer and “Geometry attitude scale” developed by Bindak were used. The results of the study revealed that, pre-service teachers’ geometry attitude scores and self-efficacy scores towards geometry is high. In addition, there is a strong positive relationship between pre-service teachers’ geometry attitudes and self-efficacy beliefs towards geometry.

Melihan Ünlü Publication date: 2010/01/01AbstractIt has long been an open problem whether or not there exists a partial geometry with parameters (s,t,α)=(4,27,2). Such a partial geometry, which we call a McLaughlin geometry, would have the McLaughlin graph as point graph. In this note we use tools from computational group theory and computational graph theory to show that a McLaughlin geometry cannot have certain automorphisms, nor can such a geometry satisfy the Axiom of Pasch.

Leonard H. Soicher Publication date: 2006/06/01AbstractPart of the attraction of Euclid geometry is that almost all of its theorems can be pictorially confirmed. In this study; focusing on the concept of area in the plane geometry it has been showed that the areas have been invariant with various arrangements made without the data of a geometric figure making use of area axioms.

S. Hizarci Publication date: 2004/06/04AbstractThis paper traces the ebbs and flows of the history of geometry at Cambridge from the time of Cayley to 1940, and therefore the arrival of a branch of modern mathematics in Great Britain. Cayley had little immediate influence, but projective geometry blossomed and then declined during the reign of H.F. Baker, and was revived by Hodge at the end of the period. We also consider the implications these developments have for the concept of a school in the history of mathematics.

June Barrow-Green Publication date: 2006/08/01AbstractThe effective action method for calculation of pair creation in an anisotropic universe is studied. The transition amplitudes are given in terms of a metric called the “effective geometry”, which is complex because of the back reaction of the produced pairs. We establish a formula which relates the “real geometry”, i.e., the real observable metric, to the effective geometry at the lowest nontrivial order in the perturbation expansion.

Hideaki Aoyama Publication date: 1981/12/03Highlights•1-D model is proposed to calculate complete geometry of ejector.•Novel concepts are introduced to accurately predict the dimensions of ejector.•Primary and secondary nozzle is influenced by generator and condenser respectively.•Performance and operating range of ejector depend on the geometry of ejector.•Effect of ejector inputs are found on its geometry.

Vikas Kumar Publication date: 2018/12/15Publisher SummaryThis chapter introduces incidence geometry. Incidence geometry arises from the points, lines, and planes of elementary geometry, based on properties stated in terms of inclusion and intersection. An example of such a property is the fact that two distinct points are elements of (are incident with) a unique line. The subject generalizes in various directions with various degrees of abstraction. As in many other mathematical subjects, the incidence may be somehow compatible with more structure. This leads in particular to ordered (incidence) geometry based on the properties related to segments of lines, half-lines, half-planes and half-spaces in elementary geometry, to topological (incidence) geometry when closed and open subsets of elementary geometry are taken into account and to metric (incidence) geometry based on the additional structure provided by perpendicularity, distance and motion.

Francis Buekenhout Publication date: 1995/01/01Publisher SummaryThis chapter discusses how Gröbner basis method can be used to prove geometry theorems. One of the important applications of the Gröbner basis method is to decide ideal membership for polynomial ideals. The computation of the Gröbner basis is very sensitive to the variable ordering. The chapter discusses the relationship between geometry and algebra to show that the Cartesian product of the field of real numbers is not the only realistic geometry. There are two approaches for defining geometry. These are the algebraic approach and the axiomatic geometry approach. For each model of a theory of geometry, one can prove the existence of a number system inherent to that model. The chapter discusses possible formulations on the algebraic formulation of certain geometry statements and related issues. The discussion is confined to a metric geometry whose associated field E is algebraically closed.

SHANG-CHING CHOU Publication date: 1989/01/01AbstractTraffic safety and road geometry are strictly interlinked because road geometry deeply influences the drivers’ performance. So it is very important to know road alignments geometry. Road centreline data for the geometry definition can be generally collected from existing maps or by static measurements (traditional surveys) or by dynamic measurements (GPS receiver mounted on a car). The procedure to define the road geometry, independently from the survey technique and the data type, must be implemented considering the precision level necessary to road applications. This study tries to define intrinsic limits of this integrated data measurement and processing procedure, with the aim to define the reliability of road alignment geometry according to the final employing of road geometry recognition.

Paola Di Mascio Publication date: 2012/10/03AbstractWe present the construction of the standard model within the framework of non-associative geometry. For the simplest scalar product we get the tree-level predictions mw = 12mt, mH = 32mt and sin2θW = 38. These relations differ slightly from predictions derived in non-commutative geometry.

Raimar Wulkenhaar Publication date: 1997/01/02Highlights•The greatest changes in hip geometry occurred during the transmenopausal period, 2 years before the FMP to 1 year after FMP.•Changes in hip geometry across the menopausal transition parallel changed in BMD.•The observed changes in hip geometry could contribute to an increased fracture risk.

Nayana Nagaraj Publication date: 2019/05/01AbstractHyperbolic geometry and elliptic geometry are the best known of the non-Euclidean geometries. An earlier paper published in Computers & Graphics[8], described an implementation of the LOGO Turtle Graphics programming environment for hyperbolic geometry. This paper describes a continuation of the same work. It discusses: &#x02022;• How the existing system may be extended to allow the turtle to operate in elliptic geometry as well as hyperbolic geometry.&#x02022;• Some interesting conceptual problems brought up by the peculiarities of elliptic geometry.&#x02022;• Theoretical issues and practical implementation of elliptic LOGO.&#x02022;• Possible future work.

Helen Sims-Coomber Publication date: 1994/07/01AbstractA review is given of some recent developments in the differential geometry of quantum computation for which the quantum evolution is described by the special unitary unimodular group, SU(2n). Using the Lie algebra su(2n), detailed derivations are given of a useful Riemannian geometry of SU(2n), including the connection and the geodesic equation for minimal complexity quantum computations.

Howard E. Brandt Publication date: 2009/12/15AbstractIn the present paper we generalise transference theorems from the classical geometry of numbers to the geometry of numbers over the ring of adeles of a number field. To this end we introduce a notion of polarity for adelic convex bodies.

Carsten Thiel Publication date: 2012/08/01AbstractWe give some new representations of the partial geometry pg(6, 6, 2), which was constructed by van Lint and Schrijver, show a connection with a strongly regular graph based on the ternary Golay code, and determine the automorphism group of the geometry.

P.J Cameron Publication date: 1982/03/01AbstractThe mass attenuation coefficient of β-particles in aluminum is determined for five different β-emitters covering the end-point energy range from 0.4 to 2.3 MeV adopting two extreme geometries, namely the good geometry setup and the 2π geometry setup. The experimental and estimated values obtained using these geometries are compared with those values obtained using an intermediate geometry by Nathuram et al.,(1) and Gleason et al.(5) The effect of geometry on μ/ϱ values is discussed.

S.R. Thontadarya Publication date: 1984/10/01Highlights•Conceptual interest of long range “massive graviton” theories.•Permanent underdetermination from approximate empirical equivalence.•Conventionality of geometry reconsidered using Poincar׳s modal argument.•Explanatory priority of laws over geometry.•Conventionality of geometry not restricted to volumes.

J. Brian Pitts Publication date: 2016/02/01AbstractThis note is dedicated to the real Killing equation on three-dimensional Weyl manifolds. Any manifold admitting a real Killing spinor of weight 0 satisfies the conditions of a Gauduchon–Tod geometry. Conversely, any simply connected Gauduchon–Tod geometry has a two-dimensional space of solutions of the real Killing equation on the spinor bundle of weight 0.

Volker Buchholz Publication date: 2000/09/01