There are many students who do not completely grasp the complicated concepts of geometry. They are unable to relate it to real life, and have a hard time absorbing abstract concepts. They wonder what good learning the intricacies of sin and tan will have on their lives. That is why they pay little attention in geometry class and just do enough to get through the subjects.
However, if they were to learn the history behind the various formulas and how they came into being then they will grasp the concepts much better. This is why knowing the history of any subject is a good idea and geometry is no different. In this context doing a dissertation on the history of modern geometry is a plan worth considering.
Students can start with the history of projective geometry and they can continue their research into the discovery of non-Euclidean geometry, which covers the time period from the 1820s to the 1830s. Students can write on the developments in algebra and the influence that they had on projective geometry. It is also a good idea to consider the works done on abstract axiomatic geometry.
While doing the project the students can discuss the differential geometric aspects of non-Euclidean geometry. Einstein was influenced a lot by this subject and researchers can look into what the extent of his interest was and what role it played in his work.
Another angle that can be explored by the researchers is the relationship between geometry and physics. There is much truth to be gained by doing a dissertation on this subject. During the course of the investigation many more truths will be revealed. It will also pave the way for the students to grasp some very complicated concepts a lot easier.