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Johann Heinrich Lambert
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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.
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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 dwelt 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 p is irrational in 1761 and of several map projections in 1772 such as the Lambert cylindrical equal-area projection. 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 his main philosophical work, "New Organon" (1764), Lambert studied the rules for distinguishing subjective from objective appearances. This connects with his work in the science of optics. In 1760, he published a book on light reflection in Latin, the Photometria, in which the word albedo was introduced and the Lambert-Beer law was formulated that describes the way in which light is absorbed. Lambert also wrote a classic work on perspective and also contributed to geometrical optics.
Lambert also developed a theory of the generation of the universe that was similar to the nebular hypothesis that Thomas Wright and Immanuel Kant had (independently) developed. Wright published his account in "An Original Theory or New Hypothesis of the Universe" (1750), Kant in "Allgemeine Naturgeschichte und Theorie des Himmels", published anonymously in 1755. Shortly afterward, Lambert published his own version of the nebular hypothesis of the origin of the solar system in "Cosmologische Briefe über die Einrichtung des Weltbaues" (1761). Lambert 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 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 p (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 C? = p — (a + ß + ?). That is, the area of a hyperbolic triangle (multiplied by a constant C) is equal to p (in radians), or 180°, minus the sum of the angles a, ß, and ?. 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.
See also
External links
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- Université Louis Pasteur
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