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Is spherical geometry a form of euclidean?
No, both spherical and hyperbolic geometries are noneuclidian.
Are the rules of parallel and perpendicular lines different in spherical geometry than in Euclidean geometry?
yes
Is it true that in the nineteenth century Euclidean geometry was disproved by spherical geometry which was in turn disproved by hyperbolic geometry?
False.
In the nineteenth century Euclidean geometry was disproved by spherical geometry which was in turn disproved by hyperbolic geometry.g?
No. Spherical geometry did not disprove Euclidean geometry but demonstrated that more than one geometries were possible. Different circumstances required different geometries. Similarly hyperbolic geometry did not disprove either of the others.
Did Lobachevsky negation created spherical geometry?
Lobachevsky's work did not create spherical geometry; rather, he is known for developing hyperbolic geometry, which deviates from Euclidean principles. Spherical geometry, on the other hand, is based on the properties of figures on the surface of a sphere and includes concepts such as great circles and the sum of angles in a triangle exceeding 180 degrees. Both geometries are non-Euclidean, but they arise from different fundamental assumptions about space. Lobachevsky's contributions helped to expand the understanding of non-Euclidean geometries, including both hyperbolic and spherical forms.
What is Non euclidean geometry?
Geometry that is not on a plane, like spherical geometry
Does the parallel postulate in Euclidean geometry work in spherical geometry?
No.
What is non euclidean?
Geometry that is not on a plane, like spherical geometry
Is spherical geometry a form of euclidean?
No, both spherical and hyperbolic geometries are noneuclidian.
Where do parallels meet?
In Euclidean geometry, parallels never meet. In other geometry, such as spherical geometry, this is not true.
Are the rules of parallel and perpendicular lines different in spherical geometry than in Euclidean geometry?
yes
Is it true that in the nineteenth century Euclidean geometry was disproved by spherical geometry which was in turn disproved by hyperbolic geometry?
False.
In the nineteenth century Euclidean geometry was disproved by spherical geometry which was in turn disproved by hyperbolic geometry.g?
No. Spherical geometry did not disprove Euclidean geometry but demonstrated that more than one geometries were possible. Different circumstances required different geometries. Similarly hyperbolic geometry did not disprove either of the others.
Riemann's Negation created what famous form of non-Euclidean geometry?
Spherical
What is the difference between Euclidean Geometry and non-Euclidean Geometry?
In Euclidean geometry parallel lines are always the same distance apart. In non-Euclidean geometry parallel lines are not what we think of a parallel. They curve away from or toward each other. Said another way, in Euclidean geometry parallel lines can never cross. In non-Euclidean geometry they can.
Did Lobachevsky negation created spherical geometry?
Lobachevsky's work did not create spherical geometry; rather, he is known for developing hyperbolic geometry, which deviates from Euclidean principles. Spherical geometry, on the other hand, is based on the properties of figures on the surface of a sphere and includes concepts such as great circles and the sum of angles in a triangle exceeding 180 degrees. Both geometries are non-Euclidean, but they arise from different fundamental assumptions about space. Lobachevsky's contributions helped to expand the understanding of non-Euclidean geometries, including both hyperbolic and spherical forms.
Does a line go on forever in both directions?
In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.
