It’s no wonder to me that Nikolai is the name of both a mathematician, and a vodka. After reading some of the work of Nikolai Lobachevski, I understand why someone would need a glass, or four, of Nikolai to relax. Among other accomplishments, Lobachevski’s greatest work was discovering hyperbolic geometry, also known as Lobachevskian geometry. During the time of this discovery, many other mathematicians were trying to prove Euclid’s fifth postulate, the parallel line postulate, from other axioms. Lobachevski, however, took a different approach to this geometry. Instead of proving the existence of the parallel line postulate, Lobachevski found a geometry in which the parallel postulate was not true, which is where we get hyperbolic geometry. This geometry goes against everything that most people believe to be true about geometry. That is because most people, if they are familiar with any type of geometry, are only familiar with Euclidean geometry. Hyperbolic geometry offers an entirely different set of axioms and theorems. The most shocking of these is that of parallel lines. In hyperbolic geometry, there exists more than one line through any given point such that the lines are parallel to another line not contained by the point. Another consequence of hyperbolic geometry was that every triangle has an angle sum measure less than 180 . These discoveries paved the road for other types of geometries, such as differentiable geometry. As E. T. Bell stated “the boldness of his challenge and his successful outcome have inspired mathematicians and scientists in general to challenge other `axioms’ or `accepted truths’”. Nikolai Lobachevski has been referred to as the Copernicus of Geometry for his work in this discipline of math. Along with his work in hyperbolic geometry, Lobachevski was also known to have worked with physics and analysis and is thought to have been the first to make a distinction between continuous and differentiable curves.

Funny opening.

ReplyDeleteclear: purpose is to write about Lobachevsky and his math, emphasizing NE geom. But you need to break up into paragraphs and have topics for the paragraph.

coherent: +

complete, content: if the point is the geometry, explain a little more. If it's the history, talk about the effect on mathematics.

consolidated: summary or synthesize. What did you communicate, OR so what does it matter, OR what is next?