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The main different ideas are based on Euclid's fifth postulates, more commonly known as the parallel postulate. Unlike his other postulates which are simple and self-evident, the parallel postulate is not.
Along with the other postulates, the Fifth postulate is equivalent to the assertion that given a straight line and a point not on that line, there is exactly one line which goes through the given point and is parallel to the given line. A consistent geometry can be developed from these axioms.
However, it is also possible to develop wholly consistent geometries with either of the two alternatives to the parallel postulate. One is that no such parallel lines exist and this gives rise to affine or projective geometries. The other is that there are more than one parallel lines and this gives rise to elliptic geometry.
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Who discovered geometry and used geometry?
The branch of mathematics we know as geometry was not "discovered" by any one person. Rather, it was developed by different philosophers and mathematicians across many hundreds of years or even thousands of years. We know geometry was studied by the ancient Greeks, and there is evidence that other ancient cultures had investigators who worked with geometric ideas. It is not difficult to look around in the world and see geometric ideas. They can be found in natural things, like the shapes and arrangements of flower petals, to cite one example. The builders of many structures in the ancient world obviously mastered geometry and the physics (mechanical engineering) of structures. Today we can find no architects that lack an appreciation of geometric ideas; there is a geometry apparent in things we build, both large and small. And the ideas of geometry are an essential part of study for matriculating teenagers because of the wide applications in which geometry plays a part.
What is line of geometry?
There are many different lines in geometry
What are the different types of symmetry in geometry?
The different types of symmetry in geometry are symmetrical and asymmetrical.
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.
Are the rules of parallel and perpendicular lines different in spherical geometry than in Euclidean geometry?
yes
