Andrei B Nov 6, 2010:

To seadeer: on relevance Let me point to the fact that reference to calculus textbooks is not quite relevant because contexts like the present one are encountered in physics rather than calculus proper.
To be sure, I've just checked two classical American texts on calculus:
Apostol, 2nd edition (best for math geeks) and Stewart, 5th edition (best for "pedestrians"). If you doubt that these references are good enough, you'd rather consult with someone who has really studied calculus (for at least two years, as I have in my time at Fiztech); e.g., a civil engineer's opinion won't count here, excuse me. Both contain lots of "squares" and "quadratics," but neither offers anything like "varies with / as"
The reason is simple: examples of some (physical) quantity varying as another quantity squared generally lie outside the scope of pure maths
However, I agree with your remark on "quadratically": I'd even make a point here: it is a typical Russianism (or Germanism, for that matter, because it seems to have been borrowed from German).
Anyway, style must be consistent with the context, which is obviously one of engineering physics here

seadeer (X) Nov 6, 2010:

I have consulted with someone who is a native speaker and a mathematician, and both "quadratically" and "as the square of" are perfectly fine with him. In the Thomas calculus textbook (one of the most commonly used calc textbooks in the US), the terms "quadratic function" and all other things quadratic came up in the index and in the text, although I did not find the phrase "vary quadratically". My husband did note that not all people might know the term "quadratically", so from that perspective "square" might make more sense, even if it's a text for engineers or other technical specialists. But overall it looks like choosing one or the other is a matter of style and slightly depends on the background of your reader.

rns Nov 6, 2010:

"носители языка могут научить только если являются специалистами или опытными переводчиками в области, к которой относится контекст" — другие здесь мне не встречались.

Andrei B Nov 6, 2010:

reference see
http://microheat.stanford.edu/publications/A29.pdf
page 222
line 5 from bottom

rns Nov 6, 2010:

"quadratic" is so lateen.

Andrei B Nov 6, 2010:

@носители языка могут научить только если являются специалистами или опытными переводчиками в области, к которой относится контекст
В противном случае носитель может забраковать вариант, который ему "режет ухо" на родном языке, но не поможет в выборе стандарта, принятого в современных учебниках, монографиях и др. публикациях авторов-носителей языка (по приведенному выше определению)

Anton Konashenok Nov 6, 2010:

A few more subtleties "Square" can be found in popular literature, "quadratic" remains in specialist usage only. Also, the former is discrete and unmodifiable - something can vary either as the square of something, or in some other way, while the latter can take a modifying prefix: a value can vary "quasiquadratically", or "supralinearly but subquadratically", etc.
This is similar to the difference between "exact" and "accurate": you can be more accurate or less accurate, but you are either exact or inexact, with no gradations.

rns Nov 6, 2010:

По приведенному выше определению стандартов, носители языка знают лучше и нам необходимо просто поучиться у них.

Andrei B Nov 6, 2010:

@depends on the square + addition Fully agree with Anton:
"depends on the square of" may be any function of "the square of"
Note also that
"varies as the square of X" is equivalent to "varies as X squared"
The latter wording, also widely used in physics and mathematics, can hardly be checked by googling

Anton Konashenok Nov 5, 2010:

Just a small note regarding David's observation "Depends on the square of" is not the same as "varies as/with the square / quadratically". It's a much weaker assertion, as the type of dependence is unspecified.

David Knowles Nov 5, 2010:

Google says: (all examples with quotes round them)
"varies quadratically with": 12,600
"varies with the square of": 456,000
"varies as the square of": 262,000
"varies according to the square of": 131,000
"depends on the square of": 7,860,000

Nik-On/Off (asker) Nov 5, 2010:

Понятно спасибо

Andrei B Nov 5, 2010:

стандарты это не сборник норм и правил
Это - как пишут носители языка, например в учебниках и монографиях
Существуют пособия по англ. математичесому языку (mathematical writing guides или что-то в этом роде)
Лучший способ - эмпирический (просто чтение), как при освоении грамоты и вообще языка. Правила приходится "учить", а при чтении правильная лексика "впитывается" сама. Занимает время, но дает "чувство языка" на уровне подкорки
Если носитель языка не начитан в математике, он может не отличать стандартный вариант от "нестандарта", когда оба звучат одинаково хорошо. Тем не менее, он предпочтет varies quadratically вместо depends quadratically, т.к. широкое употребление depends on - типичный русизм (калька с русского), а по-английски обычная конструкция - varies with / as
Гораздо более частое использование as the square of или squared, чем quadratically - просто эмпирический факт, т.е. в этом смысле и есть стандарт (см. выше)

Nik-On/Off (asker) Nov 5, 2010:

See http://en.wikipedia.org/wiki/Quadratic for the usage of the word "quadratic"

Anton Konashenok Nov 5, 2010:

David, I beg to differ "A varies quadratically with B" is fairly common in scientific literature.

David Knowles Nov 5, 2010:

Quadratic equations are the only common use of the word "quadratic". Otherwise "square" is normally used. So I would expect "depends on the square of the thickness" or "varies according to the square of the thickness"

Nik-On/Off (asker) Nov 5, 2010:

A какие стандарты нарушаются в случае с "depends quadratically"?

Andrei B Nov 5, 2010:

можно написать и так (и как угодно), если игнорировать стандарты английской математической лексики
Гугл даст много примеров, но среди авторов будет мало носителей языка, если вообще будут

Nik-On/Off (asker) Nov 5, 2010:

Так может можно написать the displacement depends quadratically on the thickness?