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Biegen vs. beugen vs. krümmen vs. verbiegen

While the German words biegen, beugen, krümmen, and verbiegen all translate to the English verb to bend, their usage depends heavily on the context. The choice of word is determined by what exactly is being bent, the resulting shape of the object, and whether the action implies intentional shaping, body movement, natural curvature, or accidental damage.

Biegen

The word biegen is the most general term for bending physical objects, such as wire, metal, or branches, usually to change their shape intentionally. It can also describe a flexible object reacting to force, or the action of a road curving and a vehicle turning around a corner.
Der Handwerker muss das dicke Kupferrohr biegen.
(The craftsman has to bend the thick copper pipe.)
Sie können den Draht einfach in eine runde Form biegen.
(You can simply bend the wire into a round shape.)
Die alten Bäume biegen sich stark im heftigen Wind.
(The old trees bend heavily in the fierce wind.)
Das rote Auto ist schnell um die Ecke gebogen.
(The red car bent around the corner quickly.)
Mit etwas Hitze lässt sich dieses Plastik sehr gut biegen.
(With a little heat, this plastic can be bent very well.)

Beugen

The verb beugen is primarily used when bending body parts, particularly joints like knees or the neck, and often implies a bowing or leaning motion. In a figurative sense, beugen means to submit, yield, or bow to authority, rules, or external pressure.
Bitte beugen Sie Ihre Knie leicht bei dieser Übung.
(Please bend your knees slightly during this exercise.)
Er musste den Kopf beugen, um durch die niedrige Tür zu passen.
(He had to bend his head to fit through the low door.)
Die neugierige Frau beugte sich weit über das Geländer.
(The curious woman bent far over the railing.)
Wir werden uns den unfairen Forderungen des Chefs nicht beugen.
(We will not bend to the unfair demands of the boss.)
Das Volk musste sich dem Willen des neuen Königs beugen.
(The people had to bend to the will of the new king.)

Krümmen

The word krümmen describes bending something into a continuous curve, arc, or crooked shape, rather than creating a sharp angle. It is frequently used for natural shapes, bad posture, or the physical reaction of a body curling up due to intense pain or extreme laughter.
Der lange Fluss krümmt sich malerisch durch das tiefe Tal.
(The long river curves picturesquely through the deep valley.)
Der Patient krümmte sich vor Schmerzen auf dem harten Boden.
(The patient bent over in pain on the hard floor.)
Die ängstliche Katze krümmt ihren Rücken zu einem Buckel.
(The frightened cat arches its back into a hump.)
Du solltest deinen Rücken beim Arbeiten am Computer nicht so krümmen.
(You should not hunch your back so much when working at the computer.)
Eine reife Banane ist von Natur aus leicht gekrümmt.
(A ripe banana is naturally slightly curved.)

Verbiegen

The term verbiegen means to bend something out of its proper shape, usually resulting in accidental damage, distortion, or unwanted deformation. Figuratively, verbiegen is used to describe a person compromising their core principles or changing their personality just to please others.
Ich habe meinen Haustürschlüssel im Schloss völlig verbogen.
(I completely bent my front door key out of shape in the lock.)
Der billige Löffel verbiegt sich, wenn das Eis zu hart ist.
(The cheap spoon bends out of shape when the ice cream is too hard.)
Bei dem schweren Unfall wurde der Rahmen des Fahrrads verbogen.
(During the severe accident, the frame of the bicycle was bent.)
Ich werde mich für diesen neuen Job auf keinen Fall verbiegen.
(I will absolutely not bend my principles for this new job.)
Pass gut auf, dass du die dünnen Nadeln der Maschine nicht verbiegst.
(Be very careful that you do not bend the thin needles of the machine.)

Summary

To summarize, use biegen for the general and often intentional shaping of physical objects like wires. Choose beugen when referring to the bending of body parts, such as knees, or when talking about submitting to authority. Opt for krümmen to describe natural, continuous curves or a body curling up in pain. Finally, use verbiegen when an object is accidentally damaged and bent out of shape, or when describing a person who compromises their true self.