Convex Quotes
Colour is the place where our brain and the universe meet. That's why colour appears so entirely dramatic, to true painters. Look at Sainte-Victoire there [the hill, which Cézanne painted again and again] How it soars, how imperiously it thirsts for the sun!.. For a long time I was quite unable to paint Sainte-Victoire; I had no idea to go about it because, like others who just look at it, I imagined the shadow to be concave, whereas in fact it's convex, it disperses outward from the center. Instead of accumulating, it evaporates, becomes fluid, bluish, participating in the movements of the surrounding air. Just as over there to the right, on the Pilon du Roi, you can see the contrary effect, the brightness gently rocking to and fro, moist and shimmering. That's the sea.... That's one needs to depict. What one needs to know. That's the bath of experience, so to speak...
Paul Cézanne
A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Lotfi A. Zadeh
One of the many importants ideas introduced by Minkowski into the study of convex bodies was that of gauge function. Roughly, the gauge function is the equation of a convex body. Minkowski showed that the gauge function could be defined in a purely geometric way and that it must have certain properties analogous to those possessed by the distance of a point from the origin. He also showed that conversely given any function possessing these properties, there exists a convex body with the given function as its gauge function.
Carl Ludwig Siegel
The mysterious musicality, the organic intermarriage of its forms convex and concave, the high singing phrase of a straight line bordering a plane and its sudden dropping into a scarcely traceable curve, and feel deeply, sharply, the profound peace, the philosophy awakened by the even distribution of light and shade, wandering from one curved plane into a deep clarity of light, enriching a carefully carved stone plane. One will understand at once that those awakened sensation have nothing to do with anatomical considerations, exactitudes observed or not.
Ossip Zadkine
The effective inventor of the telescope and compound microscope was Galileo... Galileo's account of the path of the rays through the concave eye-piece and convex objective which he used was not satisfactory and was considerably improved by Kepler, who suggested the use of two convex lenses which became the basis of later instruments. Kepler had already written an important optical treatise in the form of a commentary on Witelo's Perspectiva... His improvements to the telescope may be regarded as what he had learned from the thirteenth-century writer.
Johannes Kepler
