AlpsThe Alps (ælps) are the highest and most extensive mountain range that is entirely in Europe, stretching approximately across eight Alpine countries (from west to east): Monaco, France, Switzerland, Italy, Liechtenstein, Germany, Slovenia, and Austria. The Alpine arch extends from Nice on the western Mediterranean to Trieste on the Adriatic and Vienna at the beginning of the Pannonian Basin. The mountains were formed over tens of millions of years as the African and Eurasian tectonic plates collided.
IsometryIn mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος isos meaning "equal", and μέτρον metron meaning "measure". Given a metric space (loosely, a set and a scheme for assigning distances between elements of the set), an isometry is a transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between the elements in the original metric space.
Guttman scaleIn the analysis of multivariate observations designed to assess subjects with respect to an attribute, a Guttman scale (named after Louis Guttman) is a single (unidimensional) ordinal scale for the assessment of the attribute, from which the original observations may be reproduced. The discovery of a Guttman scale in data depends on their multivariate distribution's conforming to a particular structure (see below).
Nash embedding theoremsThe Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded into some Euclidean space. Isometric means preserving the length of every path. For instance, bending but neither stretching nor tearing a page of paper gives an isometric embedding of the page into Euclidean space because curves drawn on the page retain the same arclength however the page is bent.
Detention basinA detention basin or retarding basin is an excavated area installed on, or adjacent to, tributaries of rivers, streams, lakes or bays to protect against flooding and, in some cases, downstream erosion by storing water for a limited period of time. These basins are also called dry ponds, holding ponds or dry detention basins if no permanent pool of water exists. Detention ponds that are designed to permanently retain some volume of water at all times are called retention basins.
