Research work suggestions

I have been working on a new approach to analyzing unit vector transformations since one month. The professor of mathematics has assured that the solution is logical and has urged me to begin my presentation before publishing it in Rose Hulman Institute of Technology's undergraduate math journal. The technique incorporates a geometric approach to reduce the level of abstractness. Below is a pre-transformation image of the 'Cartesian to Cylindrical coordinate system transformation' I had drawn using AutoCAD 2015.

I would be happy to receive suggestions on improving my work.