Georgy Feodosiyovych Voronoi (28.04.1868-20.11.1908) is one of the most well-known mathematicians that Ukrainian land gave to the world science.

His scientific achievements made an impression of brilliant outbursts of the thought on his contemporaries; he was recognized by experts as one of the brightest talents in the field of the number theory late XIX and early XX centuries. But the true value of his scientific heritage manifested itself only in our days in connection with the development of computerization, and of many other modern branches of science.

*Short biography*

Georgy Voronoi was born in the village of Zhuravka in Poltava Province of the former Russian Empire (now it is Varva District of Chernihiv Region), he graduated from the Pryluky Male Gymnasium (1885), the St. Petersburg University (1889, student of Andrey Markov). He was left at the university to prepare a Master thesis. After defending his thesis in 1894 he was appointed as a professor at the University of Warsaw. He defended his doctoral thesis in 1897 in which he generalized the algorithm for continuous fractions to the cubic domain, the best European mathematicians tried to solve this problem during the whole XIX century. He was awarded with the Bunyakovsky Prize for this research. Since autumn of 1898 Voronoi was also appointed a dean of the mechanical faculty of the Warsaw Polytechnic Institute. In 1903, Waclaw Sierpinski, a student of Warsaw University, was awarded with a gold medal for his paper on the Number Theory, the subject of which was suggested him by Voronoi.

In 1907, Voronoi was elected a corresponding member of the St. Petersburg Academy of Sciences. During the revolutionary events of 1905-1907, Warsaw University and the Warsaw Polytechnic Institute were closed, Voronoi tried to obtain a position as a professor of mathematics at the Kyiv University, but he was appointed a dean of the mechanical faculty of the Donskoy Polytechnic Institute founded at Novocherkassk.

Throughout his life, Georgy Voronoi kept in touch with his native village Zhuravka, every year he arrived there during his summer vacation time, thinking about his scientific works there. Voronoi suffered from an illness of the gallbladder, in the fall of 1908, his illness turned into its sharp stage, and Georgy Voronoi died on November 7 (20), 1908 in Warsaw. According to his will, Georgy Voronoi was buried in Zhuravka. His embalmed body was kept in a special crypt, but in the early 1930s the crypt was destroyed and the body of the scientist was reburied (by his fellow villagers) in the grave of his father, Theodosius Voronoi.

In more detail, the biography of G.F. Voronoi was presented in the paper: *“Life and Times of Georgy Voronoi (1868-1908)”.*

Manuscripts of G. Voronoi, several notebooks of his student and mathematical diaries were given by relatives to the Institute of Manuscripts of the V. Vernadsky National Library of Ukraine where they are kept now. In 1952-1953, the Institute of Mathematics of the Academy of Sciences of Ukraine published Proceedings of Voronoi (in three volumes) with detailed comments from leading scientists of that time (B. N. Delone, B.A.Venkov, Yu.V.Linnik, Y.B.Pohrebysky, Y.Z.Shtokalo).

Georgy Voronoi’s research work was remarkable by its depth and completeness of presentation. Voronoi’s scientific heritage consists of 12 main papers, mainly in the field of the Number Theory, but almost every one of his papers later on served as an impetus for further development of a new direction of research.

“Voronoi left us only six great and six small papers. Each of the great works is either capital in the given area, or opens a large field of research; even every small Voronoi’s paper is extremely original and sometimes directs research to a new way. ... The depth and importance of his extensive research left a profound impression to the modern Theory of Numbers. Along with Minkovsky, Voronoi is the creator of the Geometry of Numbers. Voronoi’s paper of 1903 on the number of points under hyperbole should be considered a milestone in which the modern analytic theory of numbers begins” - such a summary of Voronoi’s scientific heritage was written in 1947 by Boris Delone, one of the most talented followers of Voronoi. But Delone could not predict how significant Voronoi's theoretical results would be for the development of the science nowadays.

“About twenty years ago, Voronoi diagrams were introduced to theoretical computer science in an influential paper by Shamos and Hoey. Meanwhile, the Voronoi diagram has become so ubiquitous in geometric algorithms design that some people date the birth of computational geometry to this event. Indeed, a good percentage of papers in the computational geometry literature is directly or indirectly concerned with Voronoi diagrams and their related structures” (O. Aichholzer, F. Aurenhammer, Tech Univ., Graz, Austria, 1998).

Voronoi diagrams are used in a wide variety of fields: from molecular biology to space, in computer graphics, in problems related to pattern recognition and artificial intelligence, in ecology, radiation physics, cosmology, chemical technology, physical chemistry, and other fields, as well as in relief modeling, motion analysis and planning, collision detection, navigation and circumventing interference, network analysis etc. - in all these and many other areas Voronoi diagrams enable using mathematical models and calculations.

In recent decades, studies of Voronoi diagrams and their generalizations have been carried out in many countries of Europe, the USA, Canada, South America, Japan, China, Australia, and New Zealand.

In Seoul, Korea, there exists the Research Center for Voronoi diagrams. Since 2004, at the initiative of this Center, International Symposia on the Generalization of Voronoi Diagrams and their Applications (ISVD) have been held throughout the world for 10 years. Such symposia took place in:

Tokyo, Japan, 2004,

Seoul, South Korea, 2005,

Calgary, Canada, 2006,

Glamorgan, Great Britain, 2007,

Kyiv, Ukraine, 2008,

Copenhagen, Denmark, 2009,

Quebec, Canada, 2010,

Quinda, China, 2011,

Rutgers, USA, 2012,

St. Petersburg, Russia, 2013.

In Kiev, since 1993, five international conferences (once every five years) were held under the general name "International Conference on Analytic Numder Theory and Spatial Tessellations", and their participants were both mathematicians from many countries of the world and experts of various fields of science who use Voronoi diagrams. The topics of the conferences were not limited to the Voronoi diagrams, it included almost all Voronoi’s research. A significant number of links to these conferences (see Google's citation "International Conference on Analytic Numder Theory and Spatial Tessellations") is an evidence of success of these conferences.

Proceedings of Kyiv conferences entitled "Voronoi's Impact on Modern Science" are also used by experts, as evidenced by the large number of references to them in the literature (see citations on "Voronoi's Impact on Modern Science" in Google).

In 2008, the anniversary year for G. Voronoi (100 years of the memory of the scientist), at the suggestion of the organizers of the ISVD, the symposium was held in Kiev, along with the fourth Kyiv conference. Information leaflet about the 2008 conference can be found on the website: 5th Annual International Symposium on Vorono's Diagrams in Science and Engineering and The 4th International Kyiv Conference on Analytical Number Theory and Spatial Tessellations.

In addition to the conferences, there are also joint projects of experts from different countries that develop certain aspects of applications of Voronoi diagrams.

For example, in 2011-2013 the joint research project "Spatial Dissemination and Graphics" (short title "VORONOI"), which is included into the program of EuroGIGA of the European Science Foundation (ESF) was studied. This project consisted of programs presented by leading scholars who head the corresponding Research Schools in their countries, from 6 different European countries: Austria, Belgium, Germany, Poland, Switzerland and Spain. As an example, we nominate here the research report from the section headed by Franz Aurenhammer (Graz

University of Technology, Austria).

Voronoi diagrams are used in engineering structures, in design projects, as the method of Voronoi partitioning of a certain volume can create the most stable structures using the minimum amount of material. Here it is some examples of design projects, based on a three-dimensional Voronoi diagram: Chinese designer Hyun-Seok Kim built the yacht called "Voronoi yacht", Portuguese architect Andre Koelho created a mushroom- lamp "Voronoi", in 2005 during Seoul symposium ISVD there was an exhibition "the Art on Voronoi" at the Art Museum of Seoul, such exhibition was also opened in Calgary (Canada) in 2006.

The extremely widespread use of the Voronoi diagrams is evidenced by the dozens and hundreds of thousands of links in Wikipedia, and in Google for terms such as

Voronoi diagrams,

Voronoi tessellation,

Applications of Voronoi diagrams,

Voronoi art,

Voronoi diagrams nature,

Voronoi design,

Voronoi architecture design,

Voronoi urban design, etc.