Theorems of Spherical Geometry

Theorems of spherical geometry describe relationships on a curved, spherical surface, like Earth's. Unlike flat surfaces, straight lines become great circles (like Earth’s equator), and angles add differently. Key theorems include the sum of angles in a triangle being more than 180°, with the excess related to the triangle's area. The Law of Sines helps find side lengths and angles in spherical triangles, similar to flat geometry but adjusted for curvature. These principles are essential in navigation, astronomy, and understanding planetary surfaces, providing precise tools for calculations where flat geometry doesn't apply.