  Recently, W. M. Schmidt and L. Summerer developed a new theory called
Parametric Geometry of Numbers which approximates the behaviour of the
successive minima of a family of convex bodies in $\mathbb{R}^{n}$ related to
the problem of simultaneous rational approximation to given real numbers. In
the case of one number, we show that the qualitative behaviour of the minima
reflects the continued fraction expansion of the smallest distance from this
number to an integer.
