I never got beyond calculus in school, and I’ve heard this term thrown around by smart math and science people bit have no clue what it means or why it’s special.
In: Mathematics
Non-Euclidean geometry is the geometry for non-flat surfaces. Most of the rules we learn in geometry only apply to Euclidean geometry. Parallel lines never intersect, the sum of the angles in a triangle always add up to 180 degrees, etc.
These rules do not hold true for non-Euclidean geometry. Look at the surface of the earth. Despite what a flat earther would tell you, the Earth is a globe. Lines of longitude are parallel lines. In a flat map representation of the Earth, you can see these are parallel. But those parallel lines all intersect at both the north and south poles. Similarly, if you were to pick three points far enough apart, say New York City, São Paulo in Brazil, and Tokyo in Japan, the triangle formed by these three would be greater than 180 degrees.
Similarly, you could think of the inside of a bowl. This would be another non Euclidean surface. A triangle between three points inside of a big enough bowl would have the angles of these lines be less than 180 degrees.
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