dimitris sardelis

The aim of the present article is to explore the possibilities of representing positive integers as sums of other positive integers and highlight certain fundamental connections between their multiplicative and additive properties. In particular, we shall be concerned with the representation of positive integers as arithmetic series of the simplest kind, i.e., either as sums of successive odd positive numbers, or as sums of successive even positive numbers (both treated as Problem 1), or as sums of consecutive positive integers (treated as Problem 2).

The aim of the present article is to treat the Greek public debt issue strictly as a curve fitting problem. Thus, based on Eurostat data and using the Mathematica technical computing software, an exponential function that best fits the data is determined modelling how the Greek public debt expands with time. Exploring the main features of this best fit model, it is concluded that the Greek public debt cannot possibly be serviced in the long run unless a radical growth is implemented and/or part of the debt is written off.

The method of application of areas as presented in Euclid's Elements, is employed to generate the three conics as the loci of points with Cartesian coordinates satisfying quadratic equations with coefficients defined by the initial settings of the geometric constructions produced by the applications method. This conceptual reconstruction supports the view that the conics were most probably discovered as plane curves by fusing the method of the application of areas with the concept of locus, long before Apollonius studied them as conic sections.

The aim of the present article is to offer a strictly mathematical, statistical treatment of the current account balances in EU and in the Eurozone. Based on Eurostat data, an overview of the total and annual balances is first made for different collections among the EU countries. Then, using the Mathematica technical computing software, curve fitting is employed to determine the functions which best reflect how surpluses and deficits accumulate with time. It is shown that both EU and the Eurozone economies ultimately have to pass through a critical, turning point beyond which the accumulation of deficits exceeds the accumulation of surpluses thus marking a period of instability. An interval estimate at a ninety eight percent degree of confidence, yields that EU is found in a phase of instability since 2011 while the instability turning point for the Eurozone is bound to occur any year from 2015 to 2018.

The method of application of areas as presented in Euclid's Elements, is employed to generate the three conics as the loci of points with Cartesian coordinates satisfying quadratic equations with coefficients defined by the initial settings of the geometric constructions produced by the applications method. This conceptual reconstruction supports the view that the conics were most probably discovered as plane curves by fusing the method of the application of areas with the concept of locus, long before Apollonius studied them as conic sections.

The aim of the present article is to treat the Greek public debt issue strictly as a curve fitting problem. Thus, based on Eurostat data and using the Mathematica technical computing software, an exponential function that best fits the data is determined modelling how the Greek public debt expands with time. Exploring the main features of this best fit model, it is concluded that the Greek public debt cannot possibly be serviced in the long run unless a radical growth is implemented and/or part of the debt is written off.

The aim of the present article is to offer a strictly mathematical, statistical treatment of the current account balances in EU and in the Eurozone. Based on Eurostat data, an overview of the total and annual balances is first made for different collections among the EU countries. Then, using the Mathematica technical computing software, curve fitting is employed to determine the functions which best reflect how surpluses and deficits accumulate with time. It is shown that both EU and the Eurozone economies ultimately have to pass through a critical, turning point beyond which the accumulation of deficits exceeds the accumulation of surpluses thus marking a period of instability. An interval estimate at a ninety eight percent degree of confidence, yields that EU is found in a phase of instability since 2011 while the instability turning point for the Eurozone is bound to occur any year from 2015 to 2018.