Сумма углов треугольника не всегда равна 180º #vertdider #veritasium

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·Nov 3, 2024

В плоской геометрии мы ожидаем, что в сумме углы треугольника без осечек дадут 180°. Но в сферической геометрии в сумме три угла дадут больше. Гиперболической и напротив, если сложить все углы треугольника, получим меньше 180°. В этом нет ничего удивительного.

Посмотрите на этот шарик. Представим, что это сфера. Нарисую здесь небольшой треугольник; он оказался практически на плоской поверхности, и сумма его углов составит, грубо говоря, 80°. Только если я нарисую очень большой треугольник, сумма углов поменяется из-за искривления поверхности, и мы, измерив их, получим больше 180°.

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Сумма углов треугольника не всегда равна 180º #vertdider #veritasium

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