Cardiohelicoidal surfaces

Abstract

Geometers have been working the curve theory and the surface theory for hundreds of years. We see good works for the theories in the literature. In this work, we introduce cardiohelicoidal surface in the three dimensional Euclidean space E^3. We indicate basic notions of Euclidean geometry. Then, stating a helicoidal surface, we obtain cardiohelicoidal surface, and calculate its Gauss map, the Gaussian curvature and the mean curvature. In the end, we find some corollaries of the Gaussian curvature and the mean curvature of the cardiohelicoidal surface in E^3.