On a theorem of Radon - Hurwitz
The classical Hurwitz - Radon theorem states on the unit sphere Sn of (n+1)-dimensional Euclidean space (in case of odd n) there exists at least r(n) tangent orthonormal vector fields, where r(n) is the Hurwitz - Radon number. In the paper a new proof of the Hurwitz - Radon theorem is given. The proof is based on the construction of the above mentioned vector fields.