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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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