  In this research-expository paper we recall the basic results of reduction
theory of positive definite quadratic forms. Using the result of Ryskov on
admissible centerings and the result of Tammela about the determination of a
Minkowski-reduced form, we prove that the absolute values of coordinates of a
minimum vector in a six-dimensional Minkowski-reduced basis are less or equal
to three. To get this little sharpening of the result which can be deduced
automatically from Tammela's works we combine some elementary geometric
reasonings with the mentioned theoretical results.
