Johann Heinrich Lambert

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

Biography:

Johann Heinrich (or John Henry) Lambert was the son of Lukas Lambert, a tailor, and Elisabeth Schmerber. He had two sisters and four brothers. The family lived poorly and as a result Johann was forced to leave school at the age of 12 to pursue training as a tailor. However, it was a younger brother who would go on to become the tailor in the family while Johann would independently pursue interests in literature, the Latin and French languages, calculus and elementary sciences. During this same time Johann became interested in astronomy as well.

Edited Timeline

1743 ? accepted a position as a bookkeeper for an ironworks company.
1744 ? observed the comet of 1744 (Klinkenberg-De Cheseauz) and attempted to calculate its orbit.
1745 ? went to Basel, Switzerland and got a job as scientific writer for Professor Johann Rudolf Jselin, where he found more time for his private studies of math, sciences and newly, philosophy.
1748 ? on the recommendation of his editor, Johann accepts the position of teacher in the house of Graf in Chur, Switzerland, where he stayed for eight years. During this time Johann had access to an extensive library with sufficient leisure time to pursue his interests allowing for the foundation of his later scientific and philosophical works.
1761 ? published Eigenschaften über Kometenbahnen, a geometrical method to determine cometary orbits
1759 ? appointed to the Chur-Bavarian Academy of Sciences
1765 ? appointed to the Berlin Academy of Sciences by the King of Prussia.
1765 ? found a proof for the irrationality of the numbers Pi and e.
1775 ? caught an illness but refused medical attention. Despite increasing health problems, he completes his Pyrometrie, a treatise of the theory of heat.
1786 ? his discussion of Newtonian physics in the language of differential calculus (Vis Viva, 1783) and his investigations on parallels, a predecessor theory of non-Euclidean geometry (Theorie der Parallellinien, 1786) was published only posthumously.

For a more complete account please visit the following website:

http://www.seds.org/~spider/spider/Misc/lambert.html

Contributions to Mathematics in General:

Johann Lambert is best known for his work on π. Euler had already established in 1737 that e and e? are irrational. Lambert was the first to provide a rigorous proof that π is irrational.

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

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

Vis Viva expressed Newton?s second law of motion in the notation of differential calculus.

Lambert is also responsible for many innovations in the study of heat and light as well as working on the theory of probability.

Contributions to Geometry:

Lambert made the first systematic development of hyperbolic functions.

Lambert studied quadrilaterals having at least three right angles, which are now named after him. A Lambert quadrilateral can be "doubled" (by reflecting it across an included side of two right angles) to obtain a Saccheri quadralateral.

Like Saccheri, Lambert disproved the obtuse angle hypothesis and studied the implications of the "inimical" acute angle hypothesis. He observed that it implied that similar triangles must then be congruent, which in turn implied the existence of an absolute unit of length.

In 1766 Lambert wrote Theorie der Parallellinien which was the study of the parallel postulate. By assuming the parallel postulate was false, he managed to declare 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.

In his paper on trigonometry, read in 1768, he developed Demoivre?s theorems on the trigonometry of complex variables, and introduced the hyperbolic sine and cosine denoted by the symbols sinh(x), cosh(x).

For a more complete account please visit the following websites:

http://www.maths.tcd.ie/pub/HistMath/People/Lambert/RouseBall/RB_Lambert.html

http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Lambert.html