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Окружность внутри и снаружи фигур проходит разное расстояние #vertdider #veritasium

less than 1m read
·Nov 3, 2024

[музыка] Если окружность катится по контуру фигуры, её центр двигается снаружи, что увеличивает пройденное им расстояние на одну длину окружности. Таким образом, расстояние, которое преодолел центр кружка, - это периметр фигуры плюс длина окружности.

Когда мы делим эту величину на длину окружности, чтобы узнать количество оборотов, у нас получается N = P / L. Если кружок катится внутри фигуры, то его центр преодолевает расстояние на одну длину окружности меньше. Тогда количество оборотов будет N - 1.

Если кружок катится по прямой линии, расстояние, которое преодолевает его центр, равно величине отрезка. Поделив её на длину окружности, получаем N. Это правило не просто любопытная закономерность.

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