8 research outputs found
A História da Alimentação: balizas historiogråficas
Os M. pretenderam traçar um quadro da HistĂłria da Alimentação, nĂŁo como um novo ramo epistemolĂłgico da disciplina, mas como um campo em desenvolvimento de prĂĄticas e atividades especializadas, incluindo pesquisa, formação, publicaçÔes, associaçÔes, encontros acadĂȘmicos, etc. Um breve relato das condiçÔes em que tal campo se assentou faz-se preceder de um panorama dos estudos de alimentação e temas correia tos, em geral, segundo cinco abardagens Ia biolĂłgica, a econĂŽmica, a social, a cultural e a filosĂłfica!, assim como da identificação das contribuiçÔes mais relevantes da Antropologia, Arqueologia, Sociologia e Geografia. A fim de comentar a multiforme e volumosa bibliografia histĂłrica, foi ela organizada segundo critĂ©rios morfolĂłgicos. A seguir, alguns tĂłpicos importantes mereceram tratamento Ă parte: a fome, o alimento e o domĂnio religioso, as descobertas europĂ©ias e a difusĂŁo mundial de alimentos, gosto e gastronomia. O artigo se encerra com um rĂĄpido balanço crĂtico da historiografia brasileira sobre o tema
On Incidences Between Points and Hyperplanes
We show that if the number I of incidences between m points and n planes in RÂł is sufficiently large, then the incidence graph (that connects points to their incident planes) contains a large complete bipartite subgraph involving r points and s planes, so that rs â„ I2 mn âa(m+n), for some constant a> 0. This is shown to be almost tight in the worst case because there are examples of arbitrarily large sets of points and planes where the largest complete bipartite incidence subgraph records only I2 m+n mn â 16 incidences. We also make some steps towards generalizing this result to higher dimensions. On the way, we slightly improve upon a result of Brass and Knauer [BK] about the representation complexity of incidences between m points and n hyperplanes in Rd, and get rid of the logarithmic factor in their upper bound
Repeated angles in three and four dimensions
Abstract. We show that the maximum number of occurrences of a given angle in a set of n points in ïżœ 3 is O(n 7/3), and that a right angle can actually occur âŠ(n 7/3) times. We then show that the maximum number of occurrences of any angle different from Ï/2 in a set of n points in ïżœ 4 is O(n 5/2 ÎČ(n)), where ÎČ(n) = 2 O(α(n)2) and α(n) is the inverse Ackermann function
Similar Simplices in a d-Dimensional Point Set
We consider the problem of bounding the maximum possible number fk,d(n) of ksimplices that are spanned by a set of n points in R d and are similar to a given simplex. We first show that f2,3(n) = O(n 13/6), and then tackle the general case, and show that fdâ2,d(n) = O(n dâ8/5) and 1 fdâ1,d(n) = O â (n dâ72/55), for any d. Our technique extends to derive bounds for other values of k and d, and we illustrate this by showing that f2,5(n) = O(n 8/3)
Points with large quadrant depth
Given a set P of points in the plane we are interested in points that are `deep' in the set in the sense that they have two opposite quadrants both containing many points of P. We deal with an extremal version of this problem. A pair (a,b) of numbers is admissible if every point set P contains a point p in P that determines a pair (Q,Qop) of opposite quadrants, such thatQ contains at least an a-fraction and Qop contains at least a b-fraction of the points of P. We provide a complete description of the set F of all admissible pairs (a,b). This amounts to identifying three line segments and a point on the boundary of F. In higher dimensions we study the maximum a, such that (a,a) is opposite-orthant admissible. In dimension d we show that 1/(2Îł)â€aâ€1/Îł for γ=22d-12d-1.Finally we deal with a variant of the problem where the opposite pairs of orthants need not be determined by a point in P. Again we are interested in values a, such that all subsets P inRd admit a pair (O,Oop) of opposite orthants both ontaining at least an a-fraction of the points. The maximum such value is a=1/2d. Generalizations of the problem are also disussed