Колесо Аристотеля

Парадокс «колесо Аристотеля»

«Колесо Аристотеля» — физико-математический парадокс, описанный в книге «Механика», которая считается трудом Аристотеля (IV век до н. э.). Рассмотрим два соединённых колеса, одно внутри другого, с общим центром (см. рисунок). Когда внешнее колесо движется без скольжения по плоскости и описывает полный оборот, его путь равен длине его окружности. При этом путь внутреннего колеса точно такой же, из чего можно сделать ошибочный вывод, что их окружности (а, следовательно, и диаметры) равны.

Этот парадокс обсуждали многие выдающиеся физики и математики, в том числе Галилей, Декарт и Ферма[1]. Первым правильный анализ дал Жан-Жак Дорту де Меран в 1715 году. Ошибка заключается в предположении, что внутреннее колесо, подобно внешнему, движется без скольжения[2].

См. также

Примечания

  1. ↑ Гарднер, 1988, с. 13—15.
  2. ↑ Bunch, Bryan H. Mathematical Fallacies and Paradoxes (англ.). — Van Nostrand Reinhold, 1982. — P. 3—9. — ISBN 0-442-24905-5.

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