Math Talks Seminar Series

Speaker: Dr. Maheshan Ekanayaka, Kennesaw State University
Title: "Stereographic Projection and Applications"
Abstract: In mathematics, Stereographic Projection is a perspective projection that maps 3D objects onto 2D planes, specifically applied to the sphere. By selecting a fixed point on the sphere, known as pole, one can project all other points onto plane through this fixed point. The plane onto which all the points are projected is perpendicular to the diameter passing through the fixed point. Excluding the pole, this projection is a smooth conformal (angle-preserving) function that maps circle on the sphere to circles or lines on the plane. It is believed that ancient Greek used this projection to map the celestial sphere onto the plane so that motions of the stars could be analyzed using the plane geometry. This presentation explores the process of calculating Cartesian coordinates on the plane from the coordinates of a sphere, and vice versa. The discussion begins with the derivation of the Stereographic Projection of the unit circle (S¹) onto the real line using a parametric line equation. Building on this, the formula for the Stereographic Projection of the unit sphere (S²) onto the complex plane is derived. Stereographic Projection finds applications in Cartography, particularly creating maps in navigating Earth due to its angle preserving property. Moreover, it is utilized in Crystallography, Geology, even in the Photography.

References: Rozenfel’d, B. A., & Sergeeva, N. D. (1986). Stereographic Projection. AMS :: Feature Column :: Stereographic Projection. (2020). American Mathematical Society.

The Department of Mathematics Math Talks Seminar Series is open to all KSU faculty, students, and invited visitors to present any math or math-related topic. Seminars typically require little or no advanced mathematical knowledge and are open to anyone.