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Abstract
In this article we made an attempt to connect Geometry and Number Theory in a very much interesting and beautiful way. The most irrational number turns out to be a number already known in geometry. It is Golden ratio i.e. Phi . The continued fraction representation of an irrational is unique.This article introduces Palash’s fraction ,which is a new continued fraction of Phi. Palash’s fraction is equal to Phi upto 12 decimal places. Here, we uses a recursive formula to show the convergence. The diagram gives a visualisation of convergence and shows that how Palash’s fraction is going to be an approximation of Golden ratio. Here, we suggests a generalized form of a special type of recursive continued fraction, to visualise it perfectly. In this paper we shows how Palash’s Fraction links with Fibonacci numbers and Fibonacci sequence.
