[01] Qamar Afzal, Department of Mathematics, University of Lahore, Pakpattan, Pakistan. [02] Farkhanda Afzal, Department of Humanities and Basic Sciences, College of Telecommunication and Engineering, National University of Science and Technology, Islamabad, Pakistan.

Golden mean is an important feature of Aristotle’s' virtue theory consequently it is significant to understand and it should be easily applied to any problem. The abilities that surround Aristotle’s ethics are to be found within the Golden mean, which includes finding the balance among two means. The Golden mean, the Golden section and Golden ratio all the admired names for a mathematical concept which is defined as a number that is equal to its own reciprocal plus one. Suppose we have the extended complex plane and we define Möbius group which has order six and it is defined by linear functional transformations from extended complex plane to extended complex plane. In this paper we determine the existence of golden mean in the action on M real quadratic field and we give the orbit in which golden mean appears.

Golden Mean, Pisot Number, Salem Number, Orbit, Mobius Group

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