Euclidean vs Spherical

Front

What is the main difference between Euclidean and Spherical geometry regarding parallel lines?

Back

In Euclidean geometry, through a point not on a line, there exists one and only one line parallel to that line. In Spherical geometry, there are no parallel lines.

Front

How many points do two distinct lines intersect at in Euclidean geometry?

Back

In Euclidean geometry, two distinct lines intersect at one point.

Front

How many points do two distinct lines intersect at in Spherical geometry?

Back

In Spherical geometry, two distinct lines can intersect at two points.

Front

Can a triangle in spherical geometry have more than one right angle?

Back

Yes, a triangle in spherical geometry can have more than one right angle.

Front

What is the maximum number of obtuse angles a triangle can have in Spherical geometry?

Back

A triangle in Spherical geometry can have one obtuse angle.

Front

What is the relationship between the angles of a triangle in Euclidean geometry?

Back

The sum of the angles in a triangle in Euclidean geometry is always 180 degrees.

Front

What is the relationship between the angles of a triangle in Spherical geometry?

Back

The sum of the angles in a triangle in Spherical geometry is always greater than 180 degrees.

Front

How many lines can be drawn perpendicular to a given line through a point not on that line in Spherical geometry?

Back

In Spherical geometry, there are infinitely many lines that can be drawn perpendicular to a given line through a point not on that line.

Front

What is the definition of a great circle in Spherical geometry?

Back

A great circle is the largest circle that can be drawn on a sphere, representing the shortest path between two points on the surface.

Front

What is the definition of a line in Euclidean geometry?

Back

A line in Euclidean geometry is a straight one-dimensional figure that has no thickness and extends infinitely in both directions.