Parabolic Numbers: A New Perspective

Thus far, many studies have been conducted on $p$-complex numbers. Depending on the sign of $p$, there are three cases: hyperbolic, dual, and elliptic. In the literature, dual numbers are called parabolic numbers, but they do not parameterize parabolas. Therefore, a number system that parameterizes parabolas is worth studying. This paper defines $p$ as a function of the coordinate $y$ and obtains a number system named parabolic numbers whose circles are parabolas. These parabolic numbers complete the set of number systems where circles are conic sections. Finally, this paper discusses the prospect of further research.