4 поворота

*

Сложность: 

Квадрат повёрнут 4 раза, каждый поворот на 90 градусов. Оказалось, что эти четыре поворота можно заменить одним и также на 90 градусов. Как это можно сделать?

Решение

Повернём квадрат сначала вокруг диагонали AC на 180° (или два раза на 90°):

В результате вершины B и D поменяются местами:

Теперь повернём квадрат на 180° вокруг стороны AB:

В результате квадрат примет следующее положение:

Очевидно, что точно такой же результат получился бы, если бы мы повернули квадрат один раз на 90° по часовой стрелке вокруг вершины A (в плоскости квадрата).




Комментарии

разве получится?

последний рисунок вроде нереальный

Да, была ошибка в рисунке. Исправил.

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