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A geometric property of the roots of Chebyshev polynomials

Wituła R., Hetmaniok E., Słota D.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 1

143--148

In this text a new property of geometric nature of the Chebyshev polynomials is given. It is proven that the lengths of diagonals of a regular n-gon with the side of length equal to one are the sums of positive roots of the respective renormalized Chebyshev polynomials of one from among four types. Some new special decompositions of differences of values of the Chebyshev polynomials are also presented.