To an ordered N -tuple (x 1 , . . . , x N ) of distinct points in the three-dimensional Euclidean space Atiyah has associated an ordered N -tuple of complex homogeneous polynomials (p 1 , . . . , p N ) in two variables x, y of degree N − 1, each p i determined only up to a scalar factor. He has conjectured that these polynomials are linearly independent. In this note it is shown that Atiyah's conjecture is true for two special configurations of N points. For one of these configurations, it is

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... own that a stronger conjecture of Atiyah and Sutcliffe is also valid. Key words. Atiyah's conjecture, Hopf map, Configuration of N points in the three-dimensional Euclidean space, Complex projective line.