Question

Describe Non-Euclidean Geometry and show a visual example.

Answer #1

what role did the fifth postulate play in the development of
non-Euclidean Geometry?

(Euclidean and Non Euclidean geometry)
Consider the following statements:
Given a line l and a point P not on the line:
There exists at least one line through P which is
perpendicular to l.
There exists at most one line through P which is
perpendicular to l.
There exists exactly one line through P which is
perpendicular to l.
Prove each statement or give a
counter-example E2 (Euclidean Plane), H2 ,
(Hyperbolic Plane)and the sphere S2 (Spherical
Plane)
( Consider...

Non Euclidean Geometry
Show that if z=x+yi with y>0, then |U(z)|<1,
where U(z)= (iz+1)/(z+i)

Write an essay comparing Euclidean Geometry with
Hyperbolic Geometry?

NON EUCLIDEAN GEOMETRY
Prove the following:
Claim: Let AD the altitude of a triangle
▵ABC. If BC is longer than or equal to AB and AC, then
D is the interior of BC.
What happens if BC is not the longest side? Is D still always in
the interior of BC? When is D in the interior?

Use postulates (axioms) to explain how Projective geometry
differs from Euclidean geometry

prove that the product of a rotation and a translation is a
rotation
Euclidean Geometry and Transformatons

What methodological techniques inherited from Euclidean geometry
had to be ignored in order to apply algebra to geometry?

State, without proofs all theorems of Euclidean geometry that
permit to construct a straight line on a given point and
perpendicular to a given straight line in the Poincare disk Model
of the Hyperbolic geometry.

In topology, how do the intrinsic geometry differ among a
Euclidean plane, a flat torus, a Klein bottle, and a sphere?

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