A New Constant Arising in Approximation Theory, Chaos Theory and Number Theory

Plouffe studied the recurrences , and (defined below). Plouffe's constant [1] arises from the recurrence . We present a closely related constant, ç, arising from the recurrence and like Plouffe's constant it has a feasible algorithm (more efficient) for its th digit and can be constructed by a compass and ruler (this construction is described). We give a partial proof that ç is irrational and discuss its relation to the full logistic map [2] and the tent map [3]. We give the relation of ç* for Chebyshev polynomials.We give a new property of Chebyshev polynomials we think this is unexpected since they have been studied for many years see [4].We sketch a possible proof of the unsolved problem of if the digits of are normal