Is this statement regarding mathematics true? (yes basic)

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The discussion centers on the relationship between mathematics and real-world applications, particularly in the context of non-Euclidean geometries. A statement from a website suggests that mathematical assumptions can differ from reality, exemplified by the behavior of angles in a triangle drawn around a massive object like the sun, where angles exceed 180° due to gravity's effect on space. This challenges the notion that mathematics is a straightforward representation of reality, highlighting its dependence on specific assumptions and contexts. The conversation acknowledges the complexity of these concepts, indicating that they are not as basic as initially thought. The realization that mathematics can diverge from intuitive understanding prompts a reevaluation of its foundational principles.
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I'm clueless on mathematics and will soon begin the long road into its academic study. I saw this statement on the following website:
http://everything2.com/title/the+difference+between+mathematics+and+physics

the last poster says this:

"sometimes mathematics makes assumptions different to what holds in the real world. If I draw a triangle around the sun, the angles will add up to more than 180° because gravity curves space. Mathematics works only within the assumptions you put into it."

Is this true? Kind of goes against what I would assume is the purpose of mathematics (I thought mathematics was a expression of reality not dependent upon variables of reality?)

Thanks, and yes I know this is basic!
 
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It's not really all that basic; no need to apologize. The poster appears to be talking about non-Euclidean geometries, specifically elliptic geometry. So yes, it's real.
 
Thanks =)

Well, that completely shattered any thoughts I had on mathematics haha
 

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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