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This study attempts to determine the common features and differences between the Latin language of the inscriptions of Aquincum, Salona, Aquileia and the provincial countries of Pannonia Inferior, Dalmatia and Venetia et Histria, compared with each other and the rest of the Latin speaking provinces of the Roman empire, and we intend to demonstrate whether a regional dialect area over the Alps–Danube–Adria region of the Roman empire existed, a hypothesis suggested by József Herman. For our research, we use all relevant linguistic data from the Computerized Historical Linguistic Database of Latin Inscriptions of the Imperial Age. We will examine the relative distribution of diverse types of non-standard data found in the inscriptions, contrasting the linguistic phenomena of an earlier period with a later stage of Vulgar Latin. The focus of our analysis will be on the changes in the vowel system and the grammatical cases between the two chronological periods within each of the three examined cities. If we succeed in identifying similar tendencies in the Vulgar Latin of these three cities, the shared linguistic phenomena may suggest the existence of a regional variant of Latin in the Alps–Danube–Adria region.

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with no empty convex 7-gons, Canadian Math. Bull. 26 482 484 Katchalski, M. and Meir, A., On empty triangles determined by points in the plane, Acta. Math. Hungar. 51 (1988), 323-328. MR 89f :52021 On empty triangles

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Summary  

Napoleon's original theorem refers to arbitrary triangles in the Euclidean plane. If equilateral triangles are externally erected on the sides of a given triangle, then their three corresponding circumcenters form an equilateral triangle. We present some analogous theorems and related statements for the isotropic (Galilean) plane.

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song translation and dubbing, as well as work on musicology, film studies, and literature studies, to develop an analytical model for animated musical films. This model, the triangle of aspects ( Reus 2017 ), allows researchers to generate a

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] Meyers , G. , Thinking Outside the Triangle , Paper presented to the 37th ASTIN Colloquium, Florida, Paper presented to the 37th ASTIN Colloquium, Florida 2007 . [16

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Abstract  

A polyhedron is a deltahedron if all its faces are equilateral triangles. It is isohedral if its symmetry group is transitive on the faces. The purpose of this paper is to list the known isohedral deltahedra.

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The Pons Asinorum , or the Bridge of Asses , refers to Proposition 5 of Book I of Euclid’s Elements . This proposition and its converse, Proposition 6, state that two sides of a triangle are equal if and only if the opposite angles are equal. Analogues of these propositions for higher dimensional d -simplices are considered in this paper, and satisfactory results are obtained for orthocentric d -simplices. These results do not hold for non-orthocentric d -simplices, thus supporting the point of view that orthocentric d -simplices and not arbitrary ones are the adequate generalization of triangles.

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More than two centuries ago Malfatti (see [9]) raised and solved the following problem (the so-called Malfatti’s construction problem): Construct three circles into a triangle so that each of them touches the two others from outside moreover touches two sides of the triangle too. It is an interesting fact that nobody investigated this problem on the hyperbolic plane, while the case of the sphere was solved simultaneously with the Euclidean case. In order to compensate this shortage we solve the following exercise: Determine three cycles of the hyperbolic plane so that each of them touches the two others moreover touches two of three given cycles of the hyperbolic plane.

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We remind some old packing problems, e.g. dense packing of spheres in the more-dimensional unit cube, maximization of the area of the union of triangles packed in the circle, potato bag problems, and briefly summarize the related known results.

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