Lambert

Johann Heinrich Lambert

Born: 26 Aug 1728 in Mülhausen, Alsace, France
Died: 25 Sept 1777 in Berlin, Prussia (now Germany)

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Lambert was the first to provide a rigorous proof that Pi is irrational.

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 pi. Euler had already established in 1737 that e and e^2 are irrational. Lambert was the first to provide a rigorous proof that pi is irrational.

In a paper presented to the Berlin Academy in 1768 Lambert showed that, if x is a nonzero rational number, then neither e^x nor tan x can be rational. Since tan pi/4 = 1 then pi/4 must be irrational.

Lambert conjectured that e and pi are transcendental. This was not proved for another century when Hermite proved that e is transcendental and Lindemann proved that pi is transcendental.

Lambert also made the first systematic development of hyperbolic functions. A few years earlier they had been studied by Vicenzo Riccati. Lambert is also responsible for many innovations in the study of heat and light as well as working on the theory of probability.

References elsewhere in this archive:

Tell me about Lambert's work on non-Euclidean geometry

References:

  1. Dictionary of Scientific Biography
  2. Biography in Encyclopaedia Britannica
  3. M Steck, Bibliographia Lambertiana (Hildesheim, 1970).
  4. O B Sheynim, J H Lambert's Work on Probability, Archive for History of Exact Sciences 7 (1971), 244-256.
  5. J J Gray and L Tilling, Johann Heinrich Lambert, mathematician and scientist 1728-1777, Historia Mathematica 5 (1978), 13-41.
  6. R Laurent, La place de J-H. Lambert (1728-1777) dans l'histoire de la perspective (Paris, 1987).
  7. R Jaquel, Le savant et philosophe mulhousien Jean-Henri Lambert (1728-1777) : etudes critiques et documentaires (Paris, 1977). 
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