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In this paper, we propose an elementary proof of Niven's Theorem in which the tangent function will have a primary role.

In this paper, we give possible suggestions for a classroom lesson about an application of probability using basic mathematical notions. We will approach to some combinatoric results without using "induction", "polynomial identities" nor "generating functions", and will give a proof of the "Vandermonde Identity" using elementary notions of probability.

In this paper, we will show a characterization for pairs of commensurable diagonals of regular n-gons. This result gives a positive answer to a recent question. [ABSTRACT FROM AUTHOR]

In this paper, we propose an elementary proof of Niven's Theorem in which the tangent function will have a primary role. [ABSTRACT FROM AUTHOR]

In this paper, we give possible suggestions for a classroom lesson about an application of probability using basic mathematical notions. We will approach to some combinatoric results without using ‘induction’, ‘polynomial identities’ nor ‘generating functions’, and will give a proof of the ‘Vandermonde Identity’ using elementary notions of probability. [ABSTRACT FROM AUTHOR]

This note is motivated by Whitehead's researches in inclusion- based point-free geometry as exposed in An Inquiry Concerning the Principles of Natural Knowledge and in The concept of Nature. More precisely, we observe that Whitehead's definition of point, based on the notions of abstractive class and covering, is not adequate. Indeed, if we admit such a definition it is also questionable that a point exists. On the contrary our approach, in which the diameter is a further primitive, enables us to avoid such a drawback. Moreover, since such a notion enables us to define a metric in the set of points, our proposal looks to be a good starting point for a foundation of the geometry metrical in nature (as proposed, for example, by L.M. Blumenthal). [ABSTRACT FROM AUTHOR]