Johann Heinrich Lambert

Johann Heinrich Lambert

name = Johann Heinrich Lambert

image_width = 200px
caption = Johann Heinrich Lambert (1728-1777)
birth_date = 26 August, 1728
birth_place = Mülhausen, Alsace, France
death_date = 25 September, 1777
death_place = Berlin, Prussia
residence = Germany
nationality = German
field = Mathematician, physicist and astronomer
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known_for = Irrationality of π

Lambert-Beer-Bouguer Law
prizes =
religion = Huguenot
footnotes =

Johann Heinrich Lambert (August 26, 1728 – September 25 1777), was a Swiss mathematician, physicist and astronomer.

He was born in Mülhausen (now Mulhouse, Alsace, France). His father was a poor tailor, so Johann had to struggle to gain an education. He first worked as a clerk in an ironworks, then gained a position in a newspaper office. The editor recommended him as a private tutor to a family, which gave him access to a good library and provided enough leisure time in which to explore it. In 1759 he moved to Augsburg, then in 1763 he dwelled in Berlin. In the final decade of his life he gained the sponsorship of Frederick II of Prussia, and passed the rest of his life in reasonable comfort. He died in Berlin, Prussia (today Germany).

Lambert studied light intensity and was the first to introduce hyperbolic functions into trigonometry. Also, he made conjectures regarding non-Euclidean space. Lambert is credited with the first proof that π is irrational in 1761cite web
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title =Lambert Azimuthal Equal Area
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accessdate = 2007-03-30
] and of several map projections in 1772 such as the Lambert cylindrical equal-area projectioncite web
last =Mulcahy
first =Karen
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title =Cylindrical Projections
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publisher = City University of New York
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] cite web| last =Lambert| first =Johann Heinrich| authorlink =| coauthors =| title =Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten. Von J. H. Lambert (1772.) Hrsg. von A. Wangerin. Mit 21 Textfiguren. | work =| publisher =W. Engelmann, reprint 1894| date =1772| url = |format =xml| doi =| accessdate =2007-04-10 ] . Lambert also devised theorems regarding conic sections that made the calculation of the orbits of comets simpler. The first practical hygrometer and photometer were invented by Lambert. In 1760, he published a book on light reflection in Latin, in which the word albedo was introduced. In 1761, he hypothesized that the stars near the sun were part of a group which travelled together through the Milky Way, and that there were many such groupings (star systems) throughout the galaxy. The former was later confirmed by Sir William Herschel. Lambert wrote a classic work on perspective and also contributed to geometrical optics.

In his "New Organon", Lambert studied the rules for distinguishing subjective from objective appearances. This involved him with the science of optics. The Lambert-Beer law describes the way in which light is absorbed. In his "Cosmological Letters on the Arrangement of the Universe", he coined the word "phenomenology." This signified the study of the way that objects appear to the human mind.

Lambert also developed a theory of the generation of the universe that was similar to the nebular hypothesis that Immanuel Kant had recently published.Lambert had read Kant's "The Only Possible Argument in Support of a Demonstration of the Existence of God". In it, Kant had briefly summarized his theory of the origin of the planets from a gassy cloud. Kant's purpose was to illustrate God's wisdom and purposiveness and in this way to support his existence. Originally, Kant had published an extended version of this theory in his "Universal Natural History and Theory of the Heavens". Lambert was struck by the account that he read in Kant's summary and began a correspondence with the philosopher regarding this theory. Shortly afterward, Lambert published his own version of the nebular hypothesis of the origin of the solar system.

Lambert devised a formula for the relationship between the angles and the area of hyperbolic triangles. These are triangles drawn on a concave surface, as on a saddle, instead of the usual flat Euclidean surface. Lambert showed that the angles cannot add up to π (radians), or 180°. The amount of shortfall, called defect, is proportional to the area. The larger the triangle's area, the smaller the sum of the angles and hence the larger the defect CΔ = π — (α + β + γ). That is, the area of a hyperbolic triangle (multiplied by a constant C) is equal to π (in radians), or 180°, minus the sum of the angles α, β, and γ. Here C denotes, in the present sense, the negative of the curvature of the surface (taking the negative is necessary as the curvature of a saddle surface is defined to be negative in the first place). As the triangle gets larger or smaller, the angles change in a way that forbids the existence of similar hyperbolic triangles, as only triangles that have the same angles will have the same area. Hence, instead of expressing the area of the triangle in terms of the lengths of its sides, as in Euclid's geometry, the area of Lambert's hyperbolic triangle can be expressed in terms of its angles.



*"A Short Account of the History of Mathematics", W. W. Rouse Ball, 1908.
*"Asimov's Biographical Encyclopedia of Science and Technology", Isaac Asimov, Doubleday & Co., Inc., 1972, ISBN 0-385-17771-2.

See also

* Beer-Lambert law (Lambert-Beer law, Beer-Lambert-Bouguer law)
* lambert (unit)
* Lambert quadrilateral
* Lambert's cosine law
* Lambertian reflectance
* Lambert cylindrical equal-area projection
* Lambert series, of importance in number theory.
* Lambert's trinomial equation
* Lambert's W function
* π

External links

*MacTutor Biography|id=Lambert
* [ Entry from "A Short Account of the History of Mathematics"] .
* [ Britannica]
* [ NNDB]
* [ Rouse Ball]
* [,_Jean-Henri.html fascimiles of publications at] Université Louis Pasteur

NAME= Lambert, Johann Heinrich
SHORT DESCRIPTION= German Mathematician, physicist and astronomer
DATE OF BIRTH= 26 August, 1728
PLACE OF BIRTH= Mülhausen, Alsace, France
DATE OF DEATH= 25 September, 1777
PLACE OF DEATH= Berlin, Prussia

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