Undergrad 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/

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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 'Leibniz Rule Videos on Digital-University'

Good morning I have been refreshing my memory about Leibniz differentiation of integrals and found some useful videos from digital-university.org on YouTube. Although the audio quality is poor and the speaker proceeds a bit slowly, the explanations and processes are clear. However, it seems that one video in the Leibniz rule series is missing. While the videos are still present on YouTube, the referring website no longer exists but is preserved on the internet archive...
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