Distinguish, differentiate, compare and explain what is the Difference between Euclidean geometry and Spherical geometry. Comparison and Differences.

Difference between Euclidean geometry and Spherical geometry

S.No. Euclidean geometry Spherical geometry
1 Lines extends indefinitely and has no thickness or width. Line is a great circle that divides the sphere into two equal half­-spheres
2 A line is the shortest path between two points. There is a unique great circle passing through any pair of non­polar points.
3 A straight line is infinite. A great circle is finite and returns to its original starting point.
4 Given three collinear points, one point is always between the other two. Given three collinear points, each point could be in the middle of the other two.
5 Perpendicular lines intersect at one point. Perpendicular lines intersect at two points.
6 Perpendicular lines form four right angles. Perpendicular lines form eight right angles.

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Euclidean geometry vs Spherical geometry

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