Golden Section and Evolving Systems

We present a body of results that demonstrate that the golden section can be implemented in the design of evolving systems. Albeit we only develop the mathematics, both mathematician and computer expert should find the concept clear. Perhaps of particular interest to the number theorist is the observation that the sequence defined by known as the Teleois number system, crops up in our results. Having shown in previous works how this sequence is closely related to the golden section, this manuscript gives further confirmation and the fact that Teleois numbers penetrate the golden section renders it a proportion of great splendour. Our results can find a wide range of applications from information technology to manufacturing.

Touched by the Goddess

A recent film starring Dev Patel and Jeremy Irons depicts Srinivasa Ramanujan’s fantastically original mathematical achievements and tragically early death at 32. Number theorist and expert on Ramanujan’s work Krishnaswami Alladi reviews The Man Who Knew Infinity.

On the Mean Value of a New Arithmetical Function

To study one of the problems that Romania number theorist F. Smarandache has proposed and to generalize it. For any positive integer let denotes the natural sequence where each number is repeated times. Based on the general term formula, the asymptotic properties of this sequence and some hybrid functions are studied using the elementary method, the asymptotic formulae are obtained ,thus enriching the study and application of this sequence.