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Euclidean geometry is the traditional geometry: it is the geometry of a plane surface, as developed by Euclid. Among other things, it is based on Euclid's parallel postulate which said (in effect) that given a line and a point outside that line there could only be one line through that point that was parallel to the given line. It has since been discovered that both alternatives to that postulate - that there are many such lines possible and that there are none - give rise to consistent geometries. These are non-Euclidean geometries.
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What is a characteristic of 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.
What is equiform geometry?
The geometry of similarity in the Euclidean plane or Euclidean space.
Both Euclidean and non-Euclidean geometry have been accepted as valid types of geometry?
true
What are the names of Non Euclidean Geometries?
There are two non-Euclidean geometries: hyperbolic geometry and ellptic geometry.
Give a brief history of euclidean geometry?
Euclid developed Euclidean geometry around 300 BC. I cannot get much briefer than that.
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.
What is a characteristic of 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.
What is a characteristic of non-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.
What are the similarities in non euclidean and euclidean geometry?
both the geometry are not related to the modern geometry
What is equiform geometry?
The geometry of similarity in the Euclidean plane or Euclidean space.
What are the names of Non-Euclidean Geometries?
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.
Famous geometers and their contributions in geometry?
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
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.
Different types of geometry?
Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few
Does the Pythagorean theorem work with Euclidean and Hyperbolic geometry?
It works in Euclidean geometry, but not in hyperbolic.
The study of Euclidean geometry has led to the development and acceptance of other non-Euclidean types of geometry?
true
Both Euclidean and non-Euclidean geometry have been accepted as valid types of geometry?
true
