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It is not the right angle that attracts me.
nor the straight line, tough, inflexible,
created by man.
what attracts me is the free, sensual curve.
the curve I find in the mountains of my country,
in the sinuous course of its rivers,
in the waves of the sea,
in the clouds of the sky,
in the body of the favourite woman.
Of curves is made all the universe.
--
As quoted on a Photo page on the Museum of Contemporary Art over Baia da Guanabara

 

Oscar Niemeyer

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It is not the right angle that attracts me, nor the straight line, hard and inflexible, created by man. What attracts me is the free and sensual curve — the curve that I find in the mountains of my country, in the sinuous course of its rivers, in the body of the beloved woman.

 

Oscar Niemeyer

 

I was attracted by the curve — the liberated, sensual curve suggested by the possibilities of new technology yet so often recalled in venerable old baroque churches.

 

Oscar Niemeyer

 

A thrown-stone trajectory is a good metaphor for so many phenomena: the curve of an event, any event; the curve of a life, any life; the curve of a hypothesis; the curve experienced in the manufacture of a work of art; the curve of interest experienced in the manufacture of a catalogue.

 

Peter Greenaway

 

But if some mind very different from ours were to look upon some property of some curved line as we do on the evenness of a straight line, he would not recognize as such the evenness of a straight line; nor would he arrange the elements of his geometry according to that very different system, and would investigate quite other relationships as I have suggested in my notes.
We fashion our geometry on the properties of a straight line because that seems to us to be the simplest of all. But really all lines that are continuous and of a uniform nature are just as simple as one another. Another kind of mind which might form an equally clear mental perception of some property of any one of these curves, as we do of the congruence of a straight line, might believe these curves to be the simplest of all, and from that property of these curves build up the elements of a very different geometry, referring all other curves to that one, just as we compare them to a straight line. Indeed, these minds, if they noticed and formed an extremely clear perception of some property of, say, the parabola, would not seek, as our geometers do, to rectify the parabola, they would endeavor, if one may coin the expression, to parabolify the straight line.

 

Roger Joseph Boscovich

 

...the relation of betweenness on the torus is undetermined for curves that cannot be contracted to a point [e.g., circles around a doughnut hole], i.e., for three of such curves it is not uniquely determined which of them lies between the other two. ..This indeterminateness... has the consequence that such a curve [alone] does not divide the surface of the torus into two separate domains; between points to the "right" and to the "left" of the line.

 

Hans Reichenbach