running / gradient / progressing
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running
Describes a line, shape, or path that continues in a particular direction or in a particular way.
Die schräg verlaufende Naht gibt dem Kleid ein besonderes Design.
The diagonally running seam gives the dress a special design.
'Verlaufend' (running/progressing) is the present participle of the verb 'verlaufen' (to run, proceed, or develop). It is used like an adjective and describes something that is currently in a process of 'Verlaufen' (running/progressing) or is characterized by a course or progression.
Die entlang der Küste verlaufende Straße bietet eine wunderbare Aussicht.
The road running along the coast offers a wonderful view.
The context helps you recognize the meaning: If it is about geometry or paths (line, border), meaning 1 is intended. With colors and patterns, meaning 2 is intended. With illnesses or projects (process, development), meaning 3 is intended.
Die Grenze verläuft quer durch den Wald.
The border runs straight through the forest.
In this meaning, 'verlaufend' (running) is often combined with an adverb that specifies the direction or form. Typical examples are 'gerade verlaufend' (running straight), 'parallel verlaufend' (running parallel), or 'im Bogen verlaufend' (running in an arc).
Zwei parallel verlaufende Linien schneiden sich nie.
Two parallel-running lines never intersect.
When it is about processes or illnesses, 'verlaufend' (progressing) is often evaluated by adverbs. Common combinations are 'normal verlaufend' (progressing normally), 'erfolgreich verlaufend' (proceeding successfully), or 'komplikationslos verlaufend' (progressing without complications).
Nach einer komplikationslos verlaufenden Schwangerschaft kam das Baby gesund zur Welt.
After a pregnancy that progressed without complications, the baby was born healthy.
leading
'führend' and 'verlaufend' look similar, but they normally describe different things. 'führend' says that someone or something is at the top in a field or has an important leading role. 'verlaufend', on the other hand, describes how a process, a development, or even an illness progresses. The words can be confused because both end in '-end' and are formed from verbs. In terms of meaning, however, they are not interchangeable. For success, influence, or leadership, use 'führend'. For the way something happens or develops, use 'verlaufend'.
Die Ärztin spricht von einer mild verlaufenden Krankheit.
The doctor speaks of a mild illness.
Die Firma ist in Europa führend bei Solartechnik.
The company is a leader in Europe in solar technology.