Q: Show great circles are geodesics on the sphere. Find distance NYC to London. Great circle: intersection with plane through center! Geodesic curvature zero: straightest path! NYC (40.7°N,74°W), London (51.5°N,0.1°W). Central angle: cos c = sinφ₁sinφ₂+cosφ₁cosφ₂cosΔλ. = sin40.7 sin51.5+cos40.7 cos51.5 cos73.9 ≈ 0.505+0.471×0.277 ≈ 0.635. c ≈ 50.6° = 0.883 rad. Distance: 6371×0.883 ≈ 5626 km! (Shortest flight path!)