This is a difficult question! I want to make the material
interesting to a wide range of people from 11 year old school
children to professors of mathematics. This is impossible! On
the whole I have tried to avoid technical mathematics but
inserted a few words for those who know enough mathematics to
appreciate it. Gauss had a major interest in differential
geometry, and published many papers on the subject.
Disquisitiones generales circa superficies curva (1828) was his
most renowned work in this field. In fact, this paper arose from
his geodesic interests, but it contained such geometrical ideas
as Gaussian curvature. Here differential geometry is in our
glossary and so further information can easily be obtained by
those who want it. I then go on to talk about the difficulties
that Gauss was having with his family life over this period etc.
People who have no idea what differential geometry is seem quite
happy to read on, while those who do get a brief indication of
why Gauss was interested in it etc. Is th