👉 One of the most surprising aspects of mathematics is the concept of non-Euclidean geometry, particularly hyperbolic geometry, where the sum of angles in a triangle is less than 180 degrees. This seems counterintuitive because, in our everyday experience and the familiar Euclidean geometry we learn in school, angles in a triangle always add up to exactly 180 degrees. The unexpected twist is that this property holds true in hyperbolic spaces, which can be visualized as a saddle-shaped surface where parallel lines diverge. This challenges our intuitive understanding of space and has profound implications in fields like relativity and topology, revealing that the rules we take for granted in flat spaces don't always apply universally.
