Math Myth: The sum of all angles in a triangle is 180°

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SUMMARY

The discussion centers on the misconception that the sum of all angles in a triangle is always 180°. It highlights that on a spherical surface, such as the Earth, the angles of a triangle can sum to more than 180°, with the exact sum varying based on the triangle's size. This phenomenon illustrates that flat triangles are the exception rather than the rule in non-Euclidean geometry. The insights shared by @fresh_42 emphasize the importance of understanding geometry in different contexts.

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From @fresh_42's Insight
https://www.physicsforums.com/insights/10-math-things-we-all-learnt-wrong-at-school/

Please discuss!

We all live on a globe, a giant ball. The angles of a triangle on this ball add up to a number greater than ##180°##.

Kugeldreieck.png


And the amount by which the sum extends ##180°## isn't even constant. It depends on the size of the triangle. The flat triangle with angle-sum ##180°## is the exception, not the norm. The real world is crooked.
 
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This is something I never knew in school! Has anyone else heard of this before?
 

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