In the present work, the inverse stereographic projection of Fibonacci points onto quadric surfaces of revolution is investigated. The construction of Fibonacci points from Fibonacci numbers, together with the one-to-one and invertible nature of stereographic projection, enables the establishment of new mathematical relations on quadric surfaces.} Cassini and Catalan identities are analyzed and mapped onto quadric surfaces to demonstrate how classical identities transform under this mapping, thereby opening new application areas for Fibonacci numbers on the surface of quadrics. In two dimensional plane, in addition to points, special Fibonacci related grids, circles, and spirals are considered. Their inverse stereographic projections are obtained. It is shown that the surfaces of quadrics can be partitioned into special domains whose boundaries can be fully expressed in terms of Fibonacci related curves. Because quadric surfaces frequently appear in botanical structures, these new relations may provide new insights into the biological applications of Fibonacci numbers in developmental biology.
Barış Ateş (Fri,) studied this question.