hem / edge
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hem
The sewn-over edge of a piece of fabric, for example on clothing or curtains, which prevents fraying.
Der Saum an ihrem Rock war aufgegangen und musste neu genäht werden.
The hem of her skirt had come undone and had to be sewn again.
edge
The edge or boundary of an area, especially of a forest, meadow, or desert.
Wir spazierten am Saum des Waldes entlang und sammelten Pilze.
We walked along the edge of the forest and collected mushrooms.
The noun 'der Saum' (hem / edge) is closely related to the verb 'säumen'. 'Säumen' means to create an edge or to surround something, which fits both meanings of the noun: sewing a fabric edge or forming the edge of a landscape.
Die Schneiderin säumt das Kleid sorgfältig.
The tailor hems the dress carefully.
You can easily tell from context whether it is about fabric or a landscape. Words like 'Kleid' (dress), 'Hose' (pants), 'nähen' (to sew), or 'Stoff' (fabric) point to the edge of textiles. Words like 'Wald' (forest), 'Wiese' (meadow), or 'Wüste' (desert) point to the edge of an area.
Der Saum des Vorhangs war ausgefranst.
The hem of the curtain was frayed.
In connection with clothing, 'Saum' (hem) is often used with the verbs 'kürzen' (to shorten) or 'verlängern' (to lengthen). A very common phrase is also that a hem 'aufgeht', which means that the seam comes undone.
Kannst du mir bitte den Saum an meiner Hose kürzen?
Could you please shorten the hem of my pants?
When 'Saum' (edge) describes the edge of a landscape, the preposition 'an' with the dative is almost always used, often in the form 'am Saum'. This describes a position directly at the boundary of the area.
Wir machten ein Picknick am Saum einer großen Wiese.
We had a picnic at the edge of a large meadow.
edge / margin
Rand is the general term for the outer edge of a piece of fabric or an item of clothing. Saum is more specific: it refers to a folded-over and sewn fabric edge. Before sewing, Rand is therefore more likely; for the finished edge, Saum is the appropriate term.
Nach dem Nähen prüft sie den unteren Saum des Rocks.
After sewing, she checks the skirt's lower hem.
Vor dem Nähen markiert sie den unteren Rand des Stoffes.
Before sewing, she marks the lower edge of the fabric.
