# What is the direction along the edge of a circle called (in English and by chance German)?

Note: I am actually also searching for the term in German. That is why I posted this here (as opposed to the language SE's), besides me looking for this term in a mathematical/technical context.

I'd like to say "the points are shifted ______ly as the radius of the circle grows".
With "shifted" I aimed to convey the change of place to be discrete.

Searching I found "radial", "axial" and "circular", of which the first two are probably wrong, while the last one seems to be used predominantly in the sense of "circle-shaped" or "round". However, Merriam-Webster suggests "moving or going around in a circle" as an alternative definition—is this interpretation somewhat usual?

In German, the yield is even less, as can be seen from the Duden entry on "zirkulär".

• How about the points trace out spirals as the radius increases? – Brian M. Scott Jul 10 '15 at 1:22
• the points are shifted equidistantly farther from center as the radius of the circle grows. – mk.. Jul 10 '15 at 1:29
• @BrianM.Scott The change of place is discrete. Apparently I need a new participle, too. – 355durch113 Jul 10 '15 at 1:32
• something wrong with clockwise/anticlockwise? – Neil W Jul 10 '15 at 2:22
• The points move along the circle's circumference — in little jumps, though, because it is discrete. – Akiva Weinberger Jul 10 '15 at 3:11

"Radially" (in my experience) usually refers to a bunch of things spreading out in a circle, like if you drop a water balloon the water spreads out radially.

I'm pretty sure that the word you are looking for is "circularly" or "undergoes circular motion". I am a native english speaker and don't believe I've heard anything else.

Then there's just "circle" as a verb. As in "the points circle back around".

There's also "circumnavigate", although this usually is used in a more metaphorical, literary sense rather than actually moving on a circle.

Given your context, it seems like the best option is "the points rotate about the center as the radius of the circle grows"

• Thank you! I forgot to mention that the change of place is discrete, disqualifying "circle" and "rotate", and putting me in need of this specific term, which, in English however, seems to be "circular(ly)". – 355durch113 Jul 10 '15 at 1:36

The term "circumferential direction" is commonly used in engineering, but in physics the term "azimuthal direction" is used. I use "circumferential direction" when talking/writing to engineers and/or technical managers about something that is circular or cylindrical. I would use "azimuthal direction" with mathematicians and physicists.

A common example from engineering is the circumferential stress, which acts in the circumferential direction. One may also speak of the circumferential component of some object. I have seen the German phrases "Spannung in Umfangsrichtung", used to indicate the stress in the circumferential direction, and "Umfangskomponent" for the circumferential component, but I suspect these expressions are rare.

The term "azimutale Richtung" is common in German engineering and physics textbooks.

To keep it clear and simple, I would write "The points are displaced along the circumference as the radius of the circle increases." My German is poor, but perhaps something like "Wenn der Radius des Kreises sich vergrößert, die Punkte werden entlang dem Umfang verschoben" would get the idea across.

• Perhaps "Veränderungen des Radius führen zu Verschiebungen der Punkte auf dem Rand (die Verschiebungen sind nicht-stetig)" . This has also a causal notion. To remove this causal notion I'd say "Veränderungen des Radius gehen einher mit Verschiebungen der Punkte auf dem Rand (die Verschiebungen sind nicht-stetig)". The term "Rand" is here a short form for "auf dem Umfang" ("on the circumference"), and possibly is a bit outdated/today too little technical. – Gottfried Helms Jul 11 '15 at 4:01
• @GottfriedHelms Now those are two beautiful sentences. They are a pleasure to read. – LouisB Jul 11 '15 at 5:57
• Thank you! I'd like to say "mit wachsendem Radius werden die Punkte ______ versetzt"—I have yet to become familiar with the usage of "azimutal" in German, to know if inserting it above would be correct. One predominantly finds definitions in the sense of "concerning the Azimut(h)". @GottfriedHelms I can think of various periphrases, but I'd just like to know that one is not forced to resort to them in this case. – 355durch113 Jul 11 '15 at 17:43
• @Grantwalzer: Also "versetzt" is a better term than "verschieben" in this case - because "verschieben" is somehow felt to be a continuous motion while "versetzt" emphasizes the discreteness of the motion. However - why the limitation on "wachsend" (growing). For a general sentence is "verändert" better, because it doesn't imply only one direction of change of radius. Why should the problem for the reader be specialized to that case of "growing"/"expanding"? – Gottfried Helms Jul 11 '15 at 18:19
• @GottfriedHelms Well in this "application" (armature installation instructions for a slightly irregular reinforced concrete disk), the radius is only ever increasing (by choice). There are about 850 circles of steel, each of which is composed of two semicircles, and the points where those will be welded together must not be aligned. So, instead of declaring all of the 1698 positions separately, we want to provide an unambiguous directive. However, we settled with a periphrasis, while I remain curious. – 355durch113 Jul 12 '15 at 6:04

How about angularly? Is it implied in the context that the points are bound to the circle's edge?

Orbitally, tangentially, and transversely (in a non-Euclidean sense, i.e. the circle is flat and expanding "up", so sideways motion would be "transverse" to that motion) come to mind.

As for the discrete aspect of the "motion", changing the word "shifts" to "jumps", or something similar to better imply the discrete nature of the result.

The words clockwise (a.k.a. deasil)

and counter-clockwise (a.k.a. anti-clockwise, a.k.a. widdershins)

sound to me like what you're after, in English at least.