Number Theory in a Newer Perspective: Introducing Realistic Concepts Through Genetic Approach

Number Theory has been presented in a newer perspective by introducing realistic concepts developed by genetic approach; it calls for approaching a problem by going into its genesis. This way the solution starts unfolding itself in a simpler and natural way. An alternative classification of sets giving due recognition to different kinds of numbers viz. positive and negative integers, zero, fractions, irrational numbers has been suggested to avoid complexity. Creation of natural numbers, irrational numbers of the form sqrt(n) and construction of right and left handed spirals have been made possible by Pythagorean Triangles with unit base and perpendicular. This concept / approach can be applied to explain the formation of galaxies. Two chapters are devoted to summarize the work on prime numbers and Fermat's Last Theorem, duly presented in LAP's First two publications in 2011, after their presentations at International Congress of Mathematicians held in 2006 and 2010.