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

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The sum of angles in a triangle on a spherical surface exceeds 180 degrees, challenging the traditional understanding taught in schools. This phenomenon varies based on the triangle's size, making flat triangles the exception rather than the rule. The discussion highlights a common misconception about geometry in real-world applications. Participants express surprise at this revelation, indicating it was not commonly taught. Understanding this concept is crucial for grasping the complexities of geometry beyond flat surfaces.
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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?
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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