
der Ball
ball
A round or oval piece of sports equipment used in many sports and games by throwing, catching, or kicking it.
Die Kinder spielen im Park mit einem Ball.
The children are playing with a ball in the park.
ball
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ball
A round or oval piece of sports equipment used in many sports and games by throwing, catching, or kicking it.
Die Kinder spielen im Park mit einem Ball.
The children are playing with a ball in the park.

ball
A large, festive, and formal dance event.
Sie trug ein elegantes Abendkleid zum Wiener Opernball.
She wore an elegant evening dress to the Vienna Opera Ball.

to stick with it
An idiom that means to stay engaged and active in something and not give up.
Wenn du die neue Sprache lernen willst, musst du am Ball bleiben.
If you want to learn the new language, you have to stick with it.

ball of the foot
The front, lower part of the foot directly behind the toes.
Beim Laufen sollte man auf dem Ball des Fußes landen, nicht auf der Ferse.
When running, you should land on the ball of your foot, not on your heel.
Although they are spelled the same, 'der Ball' (ball, sports equipment) and 'der Ball' (formal dance) are two words with different origins. The context, such as sports or a formal invitation, always makes clear which meaning is intended.
Die Kinder kicken den Ball über die Wiese.
The children kick the ball across the meadow.
In the meaning 'Spielgerät' (piece of sports equipment), Ball is used with typical sports verbs. These include: 'einen Ball werfen' (to throw a ball), 'fangen' (to catch), 'treten' (to kick), 'schießen' (to shoot), or 'prellen' (to bounce).
Der Torwart konnte den Ball gerade noch fangen.
The goalkeeper was just able to catch the ball.
When Ball means a dance event, you go 'auf einen Ball' (to a ball) or 'besucht einen Ball' (attend a ball). It is often part of compound words such as Abschlussball (graduation ball/prom), Opernball (opera ball), or Kostümball (costume ball).
Der Abschlussball unserer Schule findet dieses Jahr im Rathaus statt.
Our school's graduation ball is taking place in the town hall this year.
The idiom 'am Ball bleiben' means that you keep going with something in an engaged way. The preposition 'an' requires the dative here.
Das Projekt ist schwierig, aber wir müssen jetzt am Ball bleiben.
The project is difficult, but we have to stick with it now.
dance
Both words can refer to an event where people dance. A Ball is usually a large, festive, and often formal occasion, while „Tanz“ as the name of an event is more general and sounds somewhat dated. Use „Ball“ for an elegant formal occasion and „Tanz“ as a more general term.

Am Samstag besucht das Paar den festlichen Ball im alten Rathaus.
On Saturday, the couple is attending the formal ball at the old town hall.
Am Samstag besucht das Paar den Tanz im örtlichen Vereinshaus.
On Saturday, the couple is attending the dance at the local community center.