  Consider an analytic map of a neighborhood of 0 in a vector space to a
Euclidean space. Suppose that this map takes all germs of lines passing through
0 to germs of circles. Such a map is called rounding. We introduce a natural
equivalence relation on roundings and prove that any rounding, whose
differential at 0 has rank at least 2, is equivalent to a fractional quadratic
rounding. A fractional quadratic map is just the ratio of a quadratic map and a
quadratic polynomial. We also show that any rounding gives rise to a quadratic
map between spheres. The known results on quadratic maps between spheres have
some interesting implications concerning roundings.
