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- W197970504 abstract "Geometric extremum problems were already investigated in ancient times, and the isoperimetric problem in particular attracted the attention of mathematicians. In the 19th century considerable progress was made by the work of Steiner, Lindelöf, Schwarz and Brunn, among others. Minkowski's research on convex bodies and the application of geometric methods to number-theoretic questions gave an enormous impetus to the field of geometric extremum problems. In the present century a great number of very important results were obtained by Blaschke, Steinitz, Hadwiger and Dinghas, among many others. Beginning in the forties, the fruitful ideas and the contributions of L. Fejes Tóth formed and advanced this area of geometry in a singular way. His books (L. Fejes Tóth 1972, 1964), to which we shall refer continually, turned out to be an abundant source of inspiration to workers in this field. In this chapter we shall be dealing with extremum problems for convex sets mainly in 2- and 3-dimensional Euclidean space. Limitations of space force us to make a selection of the problems to be considered. We shall give a survey of the results, including the pertinent references, but only occasionally indicate the methods of proof." @default.
- W197970504 created "2016-06-24" @default.
- W197970504 creator A5001061265 @default.
- W197970504 date "1993-01-01" @default.
- W197970504 modified "2023-10-18" @default.
- W197970504 title "Extremum Problems for Convex Discs and Polyhedra" @default.
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