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Abstract  

Suppose a convex body wants to pass through a circular hole in a wall. Does its ability to do so depend on the thickness of the wall? In fact in most cases it does, and in this paper we present a sufficient criterion for a polytope to allow an affirmative answer to the question.

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NURMELA, K. J. and ÖSTERGÅRD, P. R. J., Packing up to 50 equal circles in a square, Discrete Comput. Geom. 18 (1997), 111-120. MR 98e :52020 Packing up to 50 equal circles in a square

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.167.1109 . [3] Chen , W. 1995 On the polynomials with all their zeros on the unit circle J. Math. Anal. Appl. 190 714 – 724 10.1006/jmaa.1995

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Metcalf Th. R. Advancing celestial circles of position, Navigation , Vol. 38, No. 3, 1991. Kaplan G. H. The motion of the observer in celestial navigation , Astronomical Applications

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Abstract  

Some theorems from inversive and Euclidean circle geometry are extended to all affine Cayley-Klein planes. In particular, we obtain an analogue to the first step of Clifford’s chain of theorems, a statement related to Napoleon’s theorem, extensions of Wood’s theorem on similar-perspective triangles and of the known fact that the three radical axes of three given circles are parallel or have a point in common. For proving these statements, we use generalized complex numbers.

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Abstract  

Let R be a ring and define x ○ y = x + y - xy, which yields a monoid (R, ○), called the circle semigroup of R. This paper investigates the relationship between the ring and its circle semigroup. Of particular interest are the cases where the semigroup is simple, 0-simple, cancellative, 0-cancellative, regular, inverse, or the union of groups, or where the ring is simple, regular, or a domain. The idempotents in R coincide with the idempotents in (R, ○) and play an important role in the theory developed.

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Elekes, GY., n points in the plane can determine n 3/2 unit circles, Combinatorica 4 (1984), 131. MR 86e :52015 n points in the plane can determine n 3/2 unit circles

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and between the two world wars, when ethnic nationalism continued to shape the Czechoslovak Republic. Rooted in the late middle ages, literary societies had been widespread in almost every town and city of Europe ever since the first such circles

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We prove that every nilpotent group of class 2 and exponent 4 is the circle group of a nilpotent ring of index 3 and characteristic 2.

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