vicinity / circumcircle
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vicinity
An area or region located within a certain distance around a central point.
Wir suchen eine neue Wohnung im Umkreis von zehn Kilometern um meine Arbeitsstelle.
We are looking for a new apartment within a ten-kilometer radius of my workplace.
The word is made up of the preposition 'um' (around) and the noun 'der Kreis' (circle). So it literally describes a circle around something, which is the basic idea in all meanings.
Im weiten Umkreis gab es kein einziges Haus.
There was not a single house in the wider vicinity.
To describe a geographic area, the fixed expression 'im Umkreis von' (within a radius of) is almost always used, followed by a distance. The central point is introduced with 'um' (around).
Alle Filialen im Umkreis von 50 Kilometern um Hamburg werden heute beliefert.
All branches within a 50-kilometer radius of Hamburg will be supplied today.
When referring to the social environment, 'Umkreis' (circle) is often combined with adjectives like 'eng' (close), 'persönlich' (personal), or 'familiär' (family-related). It then describes the group of people who are close to someone.
Diese Information ist nur für den engsten Umkreis der Geschäftsführung bestimmt.
This information is intended only for the innermost circle of the management.
This meaning belongs to the technical language of geometry. You can recognize it from words like 'Dreieck' (triangle), 'Polygon' (polygon), 'Mittelpunkt' (center), or 'konstruieren' (to construct).
Jedes Dreieck besitzt genau einen Umkreis.
Every triangle has exactly one circumcircle.
area / field
'der Bereich' and 'der Umkreis' can both mean an area. 'Bereich' is general: it can be a defined part of a place, for example in a city, a building, or on a site. 'Umkreis' means an area around a specific point, often with a distance. The words can be confused when talking about places. If the central point is important, you are more likely to say 'Umkreis'. If you just mean a zone or a part, 'Bereich' is more natural.
Im Umkreis von zehn Kilometern gibt es keinen Bahnhof.
There is no train station within a ten-kilometer radius.
Dieser Bereich des Parks ist nur für Kinder und Familien gedacht.
This area of the park is intended only for children and families.