1,721,042 research outputs found
A characterization of regular n-gons whose pairs of diagonals are either congruent or incommensurable
No full textIt is well-known that the side length of a regular hexagon is half the length of its longest diagonals. From this property, one can easily see that for every positive integer m> 1 , any regular 6m-gon contains two non-congruent diagonals that are commensurable. In this paper, we show that if n is not a multiple of 6, then all pairs of diagonals of different lengths of a regular n-gon are incommensurable. This yields a characterization of regular n-gons whose pairs of diagonals are either congruent or incommensurable. The main result gives positive answers to some questions on this topic
Cubics, hyperbolas and steiner ellipses
No full textIn this article, we will show that for every choice of real num- bers a1 and a2, the set (loci) of solutions of all polynomials of the type x^3+a_2x^2+a_1x+d, where d ∈ R, can be characterized in terms of hyperbo- las. Furthermore, relations between such hyperbolas and Steiner ellipses (inellipses and circumellipses) associated with cubics will be pointed out
Maximizing the Area of Polygons via Quasicyclic Polygons
No full textBased on Peter’s work from 2003, quadrilaterals can be characterized in the following way: “among all quadrilaterals with given side lengths a, b, c and d, those of the largest possible area are exactly the cyclic ones”. In this paper, we will give the corresponding characterization for every polygon, by means of quasicyclic polygons properties
Caratterizzazione geometrica dei compressori a viti
No full textCondizionamento dell'Aria Riscaldamento e Refrigerazione, Anno 35 n.3, Marzo 199
An extension of lucas identity via pascal’s triangle
No full textThe Fibonacci sequence can be obtained by drawing diagonals in a Pascal’s triangle, and from this, we can obtain the Lucas identity. An investigation on the behavior of certain kinds of other diagonals inside a Pascal’s triangle identifies a new family of recursive sequences: the k-Padovan sequences. This family both contains the Fibonacci and the Padovan sequences. A general binomial identity for k-Padovan sequences which extends both the well-known Lucas identity and the less known Padovan identity is derived
An elementary proof of Niven's theorem via the tangent function
No full textIn this paper, we propose an elementary proof of Niven's Theorem in which the tangent function will have a primary role
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