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 the material accurate?