Balancing on the edge, the golden ratio, the Fibonacci sequence and\n their generalization

The golden ratio and Fibonacci numbers are found to occur in various aspects\nof nature. We discuss the occurrence of this ratio in an interesting physical\nproblem concerning center of masses in two dimensions. The result is shown to\nbe independent of the particular shape of the object. The approach taken\nextends naturally to higher dimensions. This leads to ratios similar to the\ngolden ratio and generalization of the Fibonacci sequence. The hierarchy of\nthese ratios with dimension and the limit as the dimension tends to infinity is\ndiscussed using the physical problem.\n