MAGAZINES - POPULAR SCIENCE - Мир математики №41 (2014). Шар бесконечного объема. Пар...
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458395
458395
Мир математики №41 (2014). Шар бесконечного объема. Парадоксы измерения
Year: 2014
Format: PDF
File size: 50,3 MB
Language: RU
Format: PDF
File size: 50,3 MB
Language: RU
Is it possible to cut a ball into several parts so that two balls equal to the original can be assembled from them? Common sense dictates no. However, in 1924, Stefan Banach and Alfred Tarski mathematically proved that a ball could be doubled simply by cutting it into eight pieces and then redistributing them. In this issue, we will look at this and other amazing problems and try to answer questions that arise when measuring volume, length or area. One of them is what are objects that have more than two, but less than three dimensions?