die Krümmung
curvature
The state of being bent or curved; a deviation from a straight line or a flat plane.
EXAMPLE
Die starke Krümmung der Straße erfordert eine langsame Fahrweise.
The strong curvature of the road requires driving slowly.
die Krümmung
curvature
die Krümmung, die Krümmungen
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Meanings
die Krümmung
curvature
In mathematics and physics, a measure of how strongly a curve or surface deviates from a straight line or plane.
EXAMPLE
Die allgemeine Relativitätstheorie beschreibt die Gravitation als eine Krümmung der Raumzeit.
The general theory of relativity describes gravity as a curvature of spacetime.
die Krümmung
curvature
A natural or pathological bending of a body part, especially the spine.
EXAMPLE
Eine seitliche Krümmung der Wirbelsäule wird als Skoliose bezeichnet.
A sideways curvature of the spine is called scoliosis.
Forms
Forms adapted from the German Wiktionary entry Krümmung, by Wiktionary contributors, licence CC BY-SA 4.0.
At a glance
| gender | feminine die |
|---|---|
| plural | die Krümmungen |
| genitive | der Krümmung |
The four cases
| singular | plural | |
|---|---|---|
| nominative | die Krümmung | die Krümmungen |
| accusative | die Krümmung | die Krümmungen |
| dative | der Krümmung | den Krümmungen |
| genitive | der Krümmung | der Krümmungen |
The article changes with the case; it is shown in colour.
Usage tips
Word family
The noun 'die Krümmung' (curvature) belongs to the word family around the verb 'krümmen' (to bend something) and the adjective 'krumm' (crooked, not straight). The ending '-ung' turns the verb into a feminine noun that describes the process or result of bending.
EXAMPLE
Der alte Baum krümmt sich im Wind.
The old tree bends in the wind.
Diese Gurke ist ziemlich krumm gewachsen.
This cucumber has grown quite crooked.
Use with the genitive
To describe what is curved, 'Krümmung' (curvature) is very often combined with a noun in the genitive or with the preposition 'von' + dative.
EXAMPLE
Die Krümmung des Raumes ist ein zentrales Konzept der Physik.
The curvature of space is a central concept in physics.
Man erkannte die Krümmung von dem Fluss erst aus der Luft.
You could only see the curvature of the river from the air.
Context clues
The context makes the meaning clear: words like 'Straße' (road) or 'Fluss' (river) point to a geographical bend. In connection with 'Wirbelsäule' (spine) or 'Rücken' (back), a medical meaning is intended. Terms like 'Raumzeit' (spacetime) indicate a scientific context.
EXAMPLE
Die Krümmung der Banane ist ganz natürlich.
The curvature of the banana is completely natural.
Der Arzt diagnostizierte eine leichte Krümmung seiner Wirbelsäule.
The doctor diagnosed a slight curvature of his spine.
Typical adjectives
To describe the degree of bending, 'Krümmung' (curvature) is often combined with adjectives such as 'stark' (strong), 'leicht' (slight), 'sanft' (gentle), or 'scharf' (sharp).
EXAMPLE
Die Straße macht eine scharfe Krümmung nach links.
The road makes a sharp curve to the left.
Der Weg folgt der sanften Krümmung des Hügels.
The path follows the gentle curvature of the hill.
In real life
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