What happens to parallel lines in Lobachevsky geometry? Detailed answer

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What happens to parallel lines in Lobachevsky geometry? Detailed answer

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What happens to parallel lines in Lobachevsky geometry?

According to popular belief, in Lobachevsky geometry, parallel lines intersect. In fact, they cannot intersect in any geometry by virtue of the very definition of parallelism. The main difference between Lobachevsky's geometry and Euclidean geometry is that through a point not lying on a given line, one can draw not one, but at least two straight lines that do not intersect it and are in the same plane.

Authors: Jimmy Wales, Larry Sanger

Random interesting fact from the Great Encyclopedia:

What is a neutron star?

Neutron stars are formed as a result of the gravitational collapse of stars with a mass 1,5-2,5 times the mass of the Sun (if the mass of the star is greater, a black hole appears).

Inside a neutron star, free electrons and protons neutralize each other, forming neutrons and neutrinos, which stops the collapse. This process of "neutronization" continues until the main part of the star consists of neutrons.

The density of a neutron star is approximately a quintillion (billion billion) kilograms per cubic meter, which is greater than the density of an atomic nucleus. One cubic centimeter of neutron star matter would weigh about a billion tons on Earth.

It is precisely because of their enormous density that neutron stars are extremely compact: with a mass of about two solar masses, a neutron star has a radius of about 10 kilometers.

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