J Math Chem (2011) 49:2244–2249 DOI 10.1007/s10910-011-9883-7 ORIGINAL PAPER Geometry of n-dimensional Euclidean space Gaussian enfoldments Ramon Carbó-Dorca · Emili Besalú Received: 12 May 2011 / Accepted: 7 July 2011 / Published online: 20 July 2011 © Springer Science+Business Media, LLC 2011 Abstract In this study the geometric features and relationships of the points con- tained into a Gaussian enfoldment of n-dimensional Euclidean space are analyzed. Euclidean distances and angles are described by means of a simple formulation, which demonstrates the topological change underwent by n-dimensional Euclidean spaces upon Gaussian enfoldment, transforming the Euclidean points into enfoldment points lying in a closed sphere of unit radius. This property relates Gaussian enfoldments with the holographic electronic density theorem. Keywords Gaussian enfoldment of n-dimensional Euclidean spaces · Geometry of Gaussian enfoldment · Multivariate Gaussian functions · Enfoldment points · Generalized distances and angles in Gaussian enfoldments · Holographic electronic density theorem (HEDT) 1 Introduction The concept of an n-dimensional Euclidean space Gaussian enfoldment has been recently described [1]. The idea basic about any enfoldment mathematical construct is simple enough and easy to describe. In fact, an enfoldment is the same as to con- sider that at every n-dimensional Euclidean point, there is located a vector or vectors belonging to some ∞-dimensional function space. 1 1 In fact, at every n-dimensional Euclidian point one can also consider the possibility that there lies a whole 8-dimensional Hilbert or functional space of any kind, whose elements are centered at the enfoldment point. R. Carbó-Dorca (B ) · E. Besalú Institut de Química Computacional, Universitat de Girona, 17071 Girona (Catalonia), Spain e-mail: quantumqsar@hotmail.com 123