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Could someone explain the circumstance in which one would use такой for "this" instead of one of the forms of этот?

Reverso gives me this: такой вид трансформации (this kind of transformation), but такой is often used as "such".

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I think you missed the point. Такой in your example wasn't used for this, it was correctly used for this kind. And since this kind is more or less synonymous with such a, the same applies.

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Reverso gives me this: такой вид трансформации (this kind of transformation), but такой is often used as "such".

I'm guessing you're referring to this excerpt from Reverso:

Следовательно, такой вид трансформации всегда выполним. // In a way, this kind of transformation was always destined to happen.

First of all, that's not a translation. Reverso is trying to harvest texts available online and algorithmically reconcile sentences in these texts based on semantic similarities. When two sentences are similar enough, it marks them as translations of one another. This process can yield false positives, as in this case. These two particular phrases seem to originate from two completely unrelated sources: English, Russian.

Could someone explain the circumstance in which one would use такой for "this" instead of one of the forms of этот?

Translations are not done word-for-word. The English phrase "this kind of" is idiomatic. It's used as a set phrase which is pretty much synonymous to "such". "This kind of transformation" and "such a transformation" mean almost the same thing.

You can translate "this kind of transformation" using a similar Russian set phrase подобного рода метаморфоза, but the latter is much less widespread in Russian. A more simple такая метаморфоза would likely be a preferred choice.

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  • And I'd like to add that this kind/sort of is neutral and can be used in any register, but such a is normally reserved for more emphatic situations, and, consequently, is generally mis-/overused by Russian speakers. For instance, someone accused of spreading rumors might say I never said such a thing! in their defense. Or ask "Where'd you find such a gorgeous car?!" or "I've never *seen*(!) such a car." All with significant emphasis. By the same token, saying "I never thought he'd make that kind of transformation" is nowhere as emphatic as "...such a transformation(!)."
    – CocoPop
    Feb 7 at 20:34
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It's simple: use "этот" to refer to a concrete object, use "такой" to refer to its category!

Consider:

1/2, 1/3, n/m - такие числа называют натуральными
1/2, 1/3, n/m - such numbers are called natural

взять 1/2 и 1/3 из множества {sqrt(3), 1/2, 1/3, sqrt(3)} - эти числа принадлежат к рациональным
taking 1/2 and 1/3 from {sqrt(3), 1/2, 1/3, sqrt(3)} set - these numbers belong to rational

Looking at your example такой вид трансформации, we see вид is already a kind of category. Case closed : )

P.S. By the way, этот вид трансформации also looks legit enough at first glance. You can provide a larger context for the sure.

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You should not discount the fact that mathematicans use their own jargon which changes the acceptable word use.

Математики "показывают", а не объясняют; "такой", а не этот вид; условия "даны", а не поставлены; предел "существует", а не находится и не вычисляется; признак "применяется", а не используется.

One may even be mistaken to think that since they mention "such" kind of transformation, there are also other similar ways of transformation. But in this case it is actually not hinted by such word use.

In a regular non-scientific text, and not literature, you may not see the use такой in this context.

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