die Regelmäßigkeit
regularity
The quality of something happening or being present at even, recurring intervals.
Die Regelmäßigkeit, mit der er Sport treibt, ist bewundernswert.
The regularity with which he exercises is admirable.

regularity
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regularity
The quality of something happening or being present at even, recurring intervals.
Die Regelmäßigkeit, mit der er Sport treibt, ist bewundernswert.
The regularity with which he exercises is admirable.

The word is derived from the adjective 'regelmäßig' (regular), which in turn goes back to 'die Regel' (the rule). The ending '-keit' turns the adjective into a noun. So the basic idea is always something that follows a rule.
Für ein gesundes Leben ist eine gewisse Regelmäßigkeit bei den Mahlzeiten wichtig.
For a healthy life, a certain regularity in meals is important.
To express how often or how consistently something happens, the phrase 'mit einer (gewissen/großen) Regelmäßigkeit' (with a certain/great regularity) is often used.
Er ruft seine Eltern mit einer beeindruckenden Regelmäßigkeit jede Woche an.
He calls his parents every week with impressive regularity.
The context makes the meaning clear: If it is about time and repetition, such as sports or visits, temporal regularity is meant. If it is about patterns, forms, or structures, such as crystals or architecture, uniformity is meant.
Die Regelmäßigkeit der Schneeflocken ist unter dem Mikroskop faszinierend.
The regularity of snowflakes is fascinating under the microscope.
law
'das Gesetz' and 'die Regelmäßigkeit' can both describe that something happens according to a fixed pattern. In science, a 'Gesetz' often means a general principle that always applies, or applies very reliably. 'Regelmäßigkeit' more often describes that you recognize a recurring pattern, for example in intervals, forms, or processes. A 'Gesetz' sounds stronger and more general. A 'Regelmäßigkeit' can also be just an observation. If you want to explain that something applies as a basic principle, 'Gesetz' fits. If you are only describing a pattern or repeated occurrence, 'Regelmäßigkeit' fits better.

In den letzten Wochen hat David eine Regelmäßigkeit in seinen Kopfschmerzen bemerkt.
In recent weeks, David has noticed a regularity in his headaches.
Im Physikunterricht lernen wir das Gesetz, nach dem ein Körper nach unten fällt.
In physics class, we learn the law that explains how a body falls downward.