
kontinuierlich
continuous
Describes a process or development that proceeds without interruption, evenly, and steadily.
Die Firma ist in den letzten zehn Jahren kontinuierlich gewachsen.
The company has grown continuously over the last ten years.
continuous
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continuous
Describes a process or development that proceeds without interruption, evenly, and steadily.
Die Firma ist in den letzten zehn Jahren kontinuierlich gewachsen.
The company has grown continuously over the last ten years.

continuous
In mathematics and physics, a property of functions or quantities that have no discontinuities. The transition between values occurs without gaps.
Die Bewegung des Planeten lässt sich durch eine kontinuierliche Funktion beschreiben.
The planet's motion can be described by a continuous function.
'Kontinuierlich' (continuously) is very often used like an adverb to describe a verb. It answers the question 'How does something happen?' and then usually stands directly with the verb.
Wir arbeiten kontinuierlich an der Verbesserung unserer Dienstleistungen.
We are continuously working to improve our services.
The word 'kontinuierlich' (continuous / continuously) belongs more to written language or formal contexts, such as business, science, or reports. It often sounds more formal and precise.
Die Daten werden kontinuierlich erfasst und ausgewertet.
The data is continuously recorded and analyzed.
In its general meaning, 'kontinuierlich' (continuously) is often combined with verbs of change or development. Typical phrases are: 'sich kontinuierlich verbessern' (to improve continuously), 'kontinuierlich steigen/sinken' (to rise/fall continuously), or 'etwas kontinuierlich fortsetzen' (to continue something continuously).
Die Preise für Rohstoffe sind kontinuierlich gestiegen.
Raw material prices have risen continuously.
You can recognize the technical meaning from the context. When 'Funktion' (function), 'Kurve' (curve), 'Signal' (signal), or other terms from mathematics and physics are mentioned, the gapless property is meant.
Ein kontinuierliches Signal kann zu jedem Zeitpunkt einen Wert annehmen.
A continuous signal can take on a value at any point in time.
constant
When describing a process that continues for some time, konstant and kontinuierlich can seem similar. Konstant primarily emphasizes that a value or rate remains the same. Kontinuierlich emphasizes that the process proceeds without interruption, even though the values may change during it.

Die Pumpe arbeitet eine Stunde lang kontinuierlich, obwohl sich ihre Leistung verändert.
The pump operates continuously for one hour, even though its output changes.
Die Pumpe arbeitet eine Stunde lang mit einer konstanten Leistung von 500 Watt.
The pump operates at a constant output of 500 watts for one hour.