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Navigators have been taught for centuries to estimate the location of their craft on a map from three lines of position, for redundancy. The three lines typically form a triangle, called a cocked hat. How is the location of the craft related to the triangle? For more than 80 years navigators have also been taught that, if each line of position is equally likely to pass to the right and to the left of the true location, then the likelihood that the craft is in the triangle is exactly 1/4. This is stated in numerous reputable sources, but was never stated or proved in a mathematically formal and rigorous fashion. In this paper we prove that the likelihood is indeed 1/4 if we assume that the lines of position always intersect pairwise. We also show that the result does not hold under weaker (and more reasonable) assumptions, and we prove a generalisation to $n$ lines. [ABSTRACT FROM AUTHOR]

Abstract: A random polygon is the convex hull of uniformly distributed random points in a convex body . General upper bounds are established for the variance of the area of a random polygon and also for the variance of its number of vertices. The upper bounds have the same order of magnitude as the known lower bounds on variance for these functionals. The results imply a strong law of large numbers for the area and number of vertices of random polygons for all planar convex bodies. Similar results had been known, but only in the special cases when K is a polygon or where K is a smooth convex body. The careful, technical arguments we needed may lead to tools for analogous extensions to general convex bodies in higher dimension. On the other hand one of the main results is a stronger version in dimension of the economic cap covering theorem of Bárány and Larman. It is crucial to our proof, but it does not extend to higher dimension. [Copyright &y& Elsevier]

Bárány, Hubard, and Jerónimo recently showed that for given well-separated convex bodies S1,..., S d in R d and constants β i∈[0,1], there exists a unique hyperplane h with the property that Vol ( h+∩ S i)= β i⋅Vol ( S i); h+ is the closed positive transversal halfspace of h, and h is a “generalized ham-sandwich cut.” We give a discrete analogue for a set S of n points in R d which are partitioned into a family S= P1∪ ⋅⋅⋅∪ P d of well-separated sets and are in weak general position. The combinatorial proof inspires an O( n(log n) d−3) algorithm which, given positive integers a i≤| P i|, finds the unique hyperplane h incident with a point in each P i and having | h+∩ P i|= a i. Finally we show two other consequences of the direct combinatorial proof: the first is a stronger result, namely that in the discrete case, the conditions assuring existence and uniqueness of generalized cuts are also necessary; the second is an alternative and simpler proof of the theorem in Bárány et al., and in addition, we strengthen the result via a partial converse. [ABSTRACT FROM AUTHOR]

The Borsuk–Ulam theorem has many applications in algebraic topology, algebraic geomtry, and combinatorics. Here we study some combinatorial consequences, typically asserting the existence of a certain combinatorial object. An interesting aspect is the computational complexity of algorithms that search for the object. The study of these algorithms is facilitated by direct combinatorial existence proofs that bypass Borsuk–Ulam. [ABSTRACT FROM AUTHOR]

This article focuses on the definition of comprehensive medicine. The people who are concerned with the teaching of comprehensive medicine find a real need for a precise definition of it. The definitive terms found in the literature, such as the whole person, the person behind the disease and so on are too imprecise. Even if they convey the 'what is' of comprehensive medicine, they do not tell the 'how to.' The comprehensiveness of medicine arises out of the incorporation into medical thinking, teaching and practice of the applicable knowledge of dynamic psychiatry, psychology and sociology. Comprehensive medicine, then, is the conviction, born out of experience, that the medical care of patients can be improved now by the utilization of psychodynamic knowledge and sociological knowledge, along with the generally available biological skills. Perhaps the most significant feature of comprehensive medicine is that it is patient-oriented as opposed to the disease orientation of most of present day medicine.

Presents a letter to the editor in response to the article "Public-health preparedness requires more than surveillance," in the November 6, 2004 issue.

Presents a letter to the editor in response to a January 31 editorial on obesity and the goal of the Department of Health and Human Services in the United States.

The article discusses the manner and ways of a doctor while treating patients. The doctor in a white coat, pushed open the door in which the patient was lying. The door had no lock or latch so that he needed only to push it and felt no need to knock. He announced of being a doctor and stood and standing, surveyed the patient-thing with a practiced eye. The patient quickly, crushed out his half-smoked cigarette. The doctor asked about the problem from the patient and added several questions related to the duration of the trouble, exact location of the pain, previous illness, marital status, children, smoking or drinking habit and job. He adviced for certain tests and said that the details of trouble can be revealed only after the test.