Local preposition 'an' (to/onto, Wohin?/where to? + accusative)

an with movement means to / onto a vertical surface or up to something - you move a thing against a wall, to the window, to the river. As a two-way preposition, an takes the accusative for movement towards (question Wohin?).

The rule:

• Wohin? (movement onto/towards) → an + Akkusativ
• Wo? (position) → an + Dativ

Accusative articles after an: an den (m), an die (f), an das (n). The neuter form contracts: an das → ans.

Paired examples:

• Ich hänge das Bild an die Wand. - I hang the picture on the wall. (Wohin? → Akkusativ)
• Das Bild hängt an der Wand. - The picture hangs on the wall. (Wo? → Dativ)
• Wir gehen ans Fenster. - We go to the window. (Wohin? → Akkusativ, an das → ans)
• Er setzt sich an den Tisch. - He sits down at the table. (Wohin? → Akkusativ)

Common mistakes:

• Using the dative when something moves: Ich hänge das Bild an der Wand is wrong - say an die Wand.
• Confusing an (vertical surface) with auf (horizontal surface).

'an' (to / onto a vertical surface) takes the accusative for movement (Wohin?).

'an' takes the accusative for direction towards a vertical surface (Wohin?); an das → ans.

'an' steht bei einer Richtungsangabe (Wohin?) mit dem Akkusativ.