Circles, Spheres and Spherical Geometry

Hiroshi Maehara is an emeritus professor of mathematics at Ryukyu University in Japan. He obtained his Ph.D. in mathematics from Tokyo University in 1986. He was a guest professor at the Institute of Statistical Mathematics in Tokyo from 1994 to 2005. He also held professor position at the Research Institute of Education Development of Tokai University in Tokyo from 2009 to 2012. His main research interests lie in discrete geometry and combinatorics.

Horst Martini is a distinguished retired professor of mathematics from the Chemnitz University of Technology in Germany. He obtained his Ph.D. in mathematics from the University of Dresden 1988, followed by his Habilitation from the University of Jena in 1993. His research interests include convex geometry, discrete geometry, functional analysis, and classical subfields of geometry, as well as applications in optimization and related fields. His scholarly pursuits also extend to certain fields in history of mathematics. He previously served as editor in chief of the Springer journal Contributions to Algebra and Geometry. In 2015, he received an honorary professorship from the Harbin University for Science and Technology in China. His passions include travelling to interesting places of geographical and historical significance and studying different genres of good music.

- Inversion and stereographic projection.- Bend formulas.- Graphs and circle-systems.- Spherical geometry I.- Spherical geometry II.- The problem of thirteen balls.- Spherical geometry III.- Geometric probability on the sphere.- Intersection graphs of spherical caps.- Quartets on a sphere.- Higher dimensions.- The Cayley-Menger determinant.- Casey's theorem.- Solutions to the selected exercises.