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PDF книги » Математика » Schouten J. A., Kulk W. V. D. - Pfaff's problem and its generalizations

Schouten J. A., Kulk W. V. D. - Pfaff's problem and its generalizations

Название: Pfaff's problem and its generalizations
Автор: Schouten J. A., Kulk W. V. D.
Категория: Математика
Тип: Книга
Дата: 04.01.2009 11:44:30
Скачано: 28
Описание: In olden times there was a slave, packing valuable leaves for his king. But he packed the leaves at random and the leaves came out badly damaged and the king was very angry and the head of the slave was cut off. Many other slaves came and went and the story was very sad. But at last there came one more intelligent than his predecessors, who packed the leaves nicely in layers, and they came out in a way that pleased the king. That slave not only saved his own life but he was the first man who faced and solved a Pfaff's problem. Now let us take the leaves very small and very thin, say, infinitesimal 'facets', and let us pack them so closely that there is one facet in every point of the occupied space. Then they may be arranged in such a way that they form a system of oo7 surfaces in space. That is the nice packing. But if the packing is at random, though continuous, no such surfaces can be built. That is the packing to be condemned if valuable leaves are concerned. But mathematically it is not less interesting. To handle all kinds of packing we need an exact mathematical formulation and this will be given at once for an w-dimensional space. A Pfaffian equation
Файл: 7.78 МБ