What are the two main branches of Non-Euclidean Geometry What is the.pdf

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What are the major differences between foreign bonds and Eurobonds? Why do some US companies prefer to issue Eurobonds to raise US dollars from foreign markets? Solution A Eurobond is long term bond issued and sold by the compnies outside the country in which it is dominated. If US company issued a bond in dollar and selling it to Japanese investors in Japan then it is know as Eurobond. Foreign is also sold in the other courtry but it is issued in that country currency as well that\'s a difference from Eurobond. US company selling and issuing a bond in Yen for Japanese investors. US companies issue Eurobonds because in that way US companies can hedge its currency risk..

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What are the two main branches of Non-Euclidean Geometry? What is the primary difference
between them? Describe the historical development of Non-Euclidean Geometry, include work
done by Lobachevsky, Playfair and Riemann.
Solution
Two main branches of Non-Euclidean Geometry-
a. Hyperbolic Geometry
b. Elliptical Geometry
Primary difference-
In hyperbolic geometry, the lines "curve away" from each other while in elliptical geometry,
the "lines curve" towards each other.
History-
Non-Euclidean geometries were not widely accepted until the 19th century. The discovery of
non-euclidean geometry began when Euclid's work "Element" was written. Euclid began with
a limited number of assumptions and sought to prove all the other results in the work.The most
notorious of the postulates is often referred to as "Euclid's Fifth Postulate" which tells about
hyperbolic and elliptical geometry.
Lobachevsky booklet explains that-
All straight lines which in a plane go out from a point can, with reference to a given straight line
in the same plane, be divided into two classes - into cutting and non-cutting. The boundary lines
of the one and the other class of those lines will be called parallel to the given line.
Playfair explaination-
Given a line and a point not on the line, it is possible to draw exactly one line through the given
point parallel to the line.
Riemann gave theory of spherical geometry. In the Riemann type of spherical geometry, lines
have no (or more precisely two imaginary) infinitely distant points.

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