Q: What is a characteristic of Euclidean geometry?

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The geometry of similarity in the Euclidean plane or Euclidean space.

true

There are two non-Euclidean geometries: hyperbolic geometry and ellptic geometry.

Euclid developed Euclidean geometry around 300 BC. I cannot get much briefer than that.

not in euclidean geometry (I don't know about non-euclidean).

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One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.

In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.

both the geometry are not related to the modern geometry

The geometry of similarity in the Euclidean plane or Euclidean space.

Archimedes - Euclidean geometry Pierre Ossian Bonnet - differential geometry Brahmagupta - Euclidean geometry, cyclic quadrilaterals Raoul Bricard - descriptive geometry Henri Brocard - Brocard points.. Giovanni Ceva - Euclidean geometry Shiing-Shen Chern - differential geometry René Descartes - invented the methodology analytic geometry Joseph Diaz Gergonne - projective geometry; Gergonne point Girard Desargues - projective geometry; Desargues' theorem Eratosthenes - Euclidean geometry Euclid - Elements, Euclidean geometry Leonhard Euler - Euler's Law Katyayana - Euclidean geometry Nikolai Ivanovich Lobachevsky - non-Euclidean geometry Omar Khayyam - algebraic geometry, conic sections Blaise Pascal - projective geometry Pappus of Alexandria - Euclidean geometry, projective geometry Pythagoras - Euclidean geometry Bernhard Riemann - non-Euclidean geometry Giovanni Gerolamo Saccheri - non-Euclidean geometry Oswald Veblen - projective geometry, differential 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.

Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few

It works in Euclidean geometry, but not in hyperbolic.

true

true

There are two non-Euclidean geometries: hyperbolic geometry and ellptic geometry.

Geometry that is not on a plane, like spherical geometry