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Johann Lambert was a colleague of Euler and Lagrange at the Berlin Academy of Sciences.
In 1766 Lambert wrote Theorie der Parallellinien which was a study of the parallel postulate. By assuming that the parallel postulate was false, he managed to deduce a large number of non-euclidean results. He noticed that in this new geometry the sum of the angles of a triangle increases as its area decreases.
Lambert is best known, however, for his work on p. Euler had already established in 1737 that e and e2 are irrational. Lambert was the first to provide a rigorous proof that p is irrational.
In a paper presented to the Berlin Academy in 1768 Lambert showed that, if x is a nonzero rational number, then neither ex nor tan x can be rational. Since tan p/4 = 1 then p/4 must be irrational.
Lambert conjectured that e and p are transcendental. This was not proved for another century when Hermite proved that e is transcendental and Lindemann proved that p is transcendental.
Lambert also made the first systematic development of
hyperbolic functions. A few years earlier they had been studied by Vincenzo
Riccati. Lambert is also responsible for many innovations in the study of
heat and light as well as working on the theory of probability.
Texto original por: J J O'Connor and E F Robertson
Click on this link to see a list of the Glossary entries for this page
| List of References (22 books/articles) | Some Quotations (2)
|
| A Poster of Johann H Lambert | Mathematicians born in the same country |
| Some pages from publications | Title page of Freye perspective (1774) A page from Theorie der parallelinien (1895) |
| Cross-references to History Topics | |
| Other references in MacTutor | Chronology: 1760 to 1780 |
| Honours awarded to Johann H
Lambert (Click a link below for the full list of mathematicians honoured in this way) | |
| Planetary features | Crater T Mayer on Mars |
| Other Web sites | |
| JOC/EFR December 1996 | School of
Mathematics and Statistics University of St Andrews, Scotland | 
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| The URL of this page
is: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Lambert.htm | ||