When applications follow these definition, the two most common ones are
that the altitude to the hypotenuse of a right triangle is the geometric mean between
the segments into which the hypotenuse is divided, (figure 1, formula 1) and that
each leg is the geometric mean between the hypotenuse and the segment on the
hypotenuse that is adjacent to the leg (figure 1, formula 2). Students then apply the
formula, and find the lengths that are required, but the question remains as to
whether the students have any notion of the underlying concept of geometric mean,
or its connection to other mathematics.