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Deep, acute curves, on the other hand, suggest confusion, turbulence, even frenzy, as in the violence of waves in a storm, the chaos of a tangled thread, or the turmoil of lines suggested by the forms of a crowd. The complicated curves used to form the mother in the family group shown above suggest a fussy, frivolous personality.

Been googling for a while but couldn't find the answer. Google Translate also gave me a translation in my language that I could not understand.

Maybe if someone gave me the synonym of deep for the context above, Google Translate would provide a more obvious translation.

Copied from http://char.txa.cornell.edu/language/element/element.htm

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In this case 'elongated' seems to be an appropriate synonym. Though this could, in three dimensional pieces, relate to depth in relation to girth. –  dotsamuelswan Apr 11 '13 at 17:36
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Could it not just be the sense of "extending far in or back from the front or from an edge, surface, opening, etc., considered as the front" from a dictionary? U← Deep curve vs. shallow curve →u –  Tyler James Young Apr 11 '13 at 17:46
    
@TylerJamesYoung I agree, but I think the curves of D vs. ) might be a better visual representation, with D having a deeper curve than ). –  onomatomaniak Apr 11 '13 at 18:34
    
Deep in relation to a curve means exactly as it does in any other similar context. cf. shallow (also mentioned in the same page.) GR. –  Kris Apr 12 '13 at 7:05

1 Answer 1

The phrase “deep, acute curves” as used toward the end of a cornell.edu “Introduction to the Elements of Design” webpage, refers to curves or bends where the perimeter of the curve is large compared to the area the curve encloses or excludes. In the design that the text refers to, Saul Steinberg's “Cut-out Family”, the mother's narrow waist and her elaborate dress, hair and hat provide examples of deep curves in this sense. The man and the child, on the other hand, are portrayed with few deep curves.

Saul Steinberg Cut-out Family

Edit: In wiktionary, the adjective deep has a dozen senses shown. Which correspond most closely to its usage in the phrase deep curves? Literal senses like “A long way inside; situated far in or back”, or “Voluminous”, or “Having its bottom far down” may apply; but the figurative sense “To a significant, not superficial, extent” is perhaps more appropriate. As a practical matter, shallow curves (“Having little depth; significantly less deep than wide”) may be easier to recognize than deep curves, which we may then define as “not-shallow curves”.

Note, the definition I gave of deep acute curves as “curves or bends where the perimeter of the curve is large compared to the area the curve encloses or excludes” is related to definitions of high curvature as given in wikipedia's curvature article. The unit tangent vector T mentioned there (or the unit normal N) sweeps through more angular area per unit of time for a high-curvature curve than for a low-curvature curve.

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Isn't that what the word deep means in plain English? Does it need a specialized interpretation? –  Kris Apr 12 '13 at 7:04
    
@Kris, there is a small issue of which meaning applies. (See edit.) Some interpretation is needed, but not specialized interpretation. –  jwpat7 Apr 12 '13 at 14:57
    
In the case of artistic discussion, expect terms to be vague and more open to interpretation. Perhaps "higher amplitude" is a good analog. –  horatio Apr 12 '13 at 19:35

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