Should we use in academic writing the word "respectively" for the following case:
Consider circles 1 and 2. These circles have radii r1 and r2, respectively.
Maybe because it is obvious here (1 -> r1; 2 -> r2), then we do not need to use respectively? (I am non native English speaker)
I read about the issue here and got confused about the case above, as it states: "respectively .. should only be used if your sentence would be unclear without it."
(I've edited for Springer, Elsevier, and other families of journals for about 15 years.) A common, consistent, and reasonable convention in academic writing is that "respectively" is used to indicate a one-to-one correspondence between the elements of two or more (equal-length) lists in the same sentence.
The two circles were labeled A and B.
Consider circles 1 and 2. Their corresponding radii are r1 and r2.
Consider circles 1 and 2 with radii r1 and r2, respectively.
The radii of circles 1 and 2 are respectively r1 and r2.
Other conventions exist, but this one is particularly easy to apply because you need only consider a single sentence at a time and because you need not assume anything regarding the reader's knowledge. As above, "respectively" can be placed directly following the verb without commas or at the end of the sentence with a comma:
G and E respectively represent the shear and Young moduli and ri and ro the inner and outer diameters.
G and E are the shear and Young moduli, and ri and ro are the inner and outer diameters, respectively.
It's only obvious if you know that a circle has one radius (as opposed to, say, an ellipse) and that interpreting the sentence as "circle 1 has radii r1 and r2, and circle 2 has radii r1 and r2" is nonsensical.
While this is grade school knowledge, it still requires the reader to stop and think about the semantic sense of the sentence to parse it correctly. Using respectively avoids that and makes it easier for the reader to parse the sentence, as they don't have to recall mathematical knowledge to do so. As such, while not necessarily required depending on your audience, it's more natural to use it.
The use of "respectively" in your example sentence about the two circles is correct.
The article you cited at springer.com is partly right and partly wrong.
It's right that all the "GOOD" and "BAD" sentences are good and bad respectively.
It's wrong about the reason. "Respectively" is correct if it is used to correlate two lists of things in order. Notice that all the "GOOD" examples either have two lists of things correlated with "respectively", or one list of things without "respectively". The "BAD" example sentences have only one list of things, and then the word "respectively".
