How did Euclid's work influence mathematics?
Link to this answer
Share this credible answer with others. Simply paste this code into your blog or Web page:
Although Euclid's system no longer satisfies modern requirements of logical rigor, its importance in influencing the direction and method of the development of mathematics is undisputed. One consequence of the critical examination of Euclid's system was the discovery in the early 19th cent. that his fifth postulate, equivalent to the statement that one and only one line parallel to a given line can be drawn through a point external to the line, can not be proved from the other postulates; on the contrary, by substituting a different postulate for this parallel postulate two different self-consistent forms of non-Euclidean geometry were deduced, one by Nikolai I. Lobachevsky (1826) and independently by János Bolyai (1832) and another by Bernhard Riemann (1854).
|
Answer verified with
|
Related research articles
HighBeam gives you access to newspaper, magazine, and trade journal articles plus press releases, facts, information, and biographies from thousands of sources.