Key Concepts: Spherical Geometry ⭐

Lines in Spherical Geometry

In spherical geometry, "lines" are great circles. There are no parallel lines — every pair of great circles intersects at two points.

Triangles on a Sphere

• The sum of angles in a spherical triangle is greater than 180° and less than 540°.
• The excess over 180° is related to the triangle's area.

Comparing Euclidean and Spherical Geometry

• Euclidean: through a point not on a line, exactly one parallel exists (Parallel Postulate).
• Spherical: no parallels exist — all great circles intersect.
• Euclidean: triangle angle sum = 180°. Spherical: triangle angle sum > 180°.