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.

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.

both the geometry are not related to the modern 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.

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

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

The 2 types of non-Euclidean geometries are hyperbolic geometry and ellptic geometry.

Geometry that is not on a plane, like spherical geometry

true

true

Geometry that is not on a plane, like spherical geometry

Answer The two commonly mentioned non-Euclidean geometries are hyperbolic geometry and elliptic geometry. If one takes "non-Euclidean geometry" to mean a geometry satisfying all of Euclid's postulates but the parallel postulate, these are the two possible geometries.

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

Richard L. Faber has written:

'Applied calculus' -- subject(s): Calculus

'Foundations of Euclidean and non-Euclidean geometry' -- subject(s): Geometry, Geometry, Non-Euclidean

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

elliptic - a kind of non-Euclidean geometry.

Harold Eichholtz Wolfe has written:

'Introduction to non-Euclidean geometry' -- subject(s): Geometry, Non-Euclidean, History

In Euclidean geometry, yes.

In Euclidean geometry, yes.

In Euclidean geometry, yes.

In Euclidean geometry, yes.

Euclid's parallel axiom is false in non-Euclidean geometry because non-Euclidean geometry occurs within a different theory of space. There may be one absolute occurrence in non-Euclidean space where Euclid's parallel axiom is valid. Possibly as some form of infinity.

YES

False

Marvin J. Greenberg has written:

'Euclidean and non-Euclidean geometries' -- subject(s): Geometry, Geometry, Non-Euclidean, History

'Lectures on algebraic topology' -- subject(s): Algebraic topology

Non-Euclidean geometry is most practical when used for calculations in three dimensions, as opposed to only two. For example, planning the fastest route for an airplane or a ship to travel across the world requires non-Euclidean geometry, because the Earth is a sphere.

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

Janos Bolyai! and john playfair i think

more than

Spherical

He was famous for inventing the idea of Non-Euclidean geometry.

more than

more than

more than

False

No. Non-Euclidean geometries usually start with the axiom that Euclid's parallel postulate is not true. This postulate can be shown to be equivalent to the statement that the internal angles of a traingle sum to 180 degrees. Thus, non-Euclidean geometries are based on the proposition that is equivalent to saying that the angles do not add up to 180 degrees.

more than

Any number you like.

It works in Euclidean geometry, but not in hyperbolic.

In basic Euclidean geometry no, the sum of the angles always equals 180 degrees exactly.

In non-Euclidean geometry it can exceed 180 degrees.

In Euclidean geometry, parallel lines never intersect.

They go this way forever and never intersect but watch this typing.

_______________

_______________

In non-Euclidean geometry, they intersect when the faces are uneven.

Assuming you are referring to a triangle. In Euclidean, or plane geometry, always to 180 degrees. In non-Euclidean geometry either more or less than 180 degrees.

false

greeks

In Euclidian geometry it's a point. In non-Euclidean geometry all bets are off.

Pi is only constant in Euclidean Geometry, it is not the same in other Geometries. In the non-Euclidean geometry that Relativity theory uses the difference between PiE and PiNE is extremely small, approaching zero.

Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria.

euclidean

euclidean

No.

Richard D. Anderson has written:

'Concepts of informal geometry' -- subject(s): Geometry, Geometry, Non-Euclidean, Mathematics, Study and teaching

In Euclidean geometry, a triangle must be one of these: acute, obtuse, or right. Maybe there is a non-Euclideangeometry for which some obtuse triangles can contain a right angle, but it doesn't happen in Euclidean geometry.