Johann Heinrich Lambert
Encyclopedia
Johann Heinrich Lambert (August 26, 1728 – September 25, 1777) was a Swiss
mathematician
, physicist
, philosopher and astronomer
.
Asteroid
187 Lamberta
was named in his honour.
(now in Alsace
, France
), at that time an exclave of Switzerland. Leaving school he continued to study in his free time whilst undertaking a series of jobs. These included assistant to his father (a tailor), a clerk at a nearby iron works, a private tutor, secretary to the editor of Basler Zeitung and, at the age of 20, private tutor to the sons of Count Salis in Chur
. Travelling Europe with his charges (1756–1758) allowed him to meet established mathematicians in the German states, The Netherlands, France and the Italian states. On his return to Chur he published his first books (on optics and cosmology) and began to seek an academic post. After a few short posts he was rewarded (1764) by an invitation from Euler
to a position at the Prussian Academy of Sciences in Berlin, where he gained the sponsorship of Frederick II
of Prussia
. In this stimulating, and financially stable, environment he worked prodigiously until his death in 1777.
s into trigonometry
. Also, he made conjectures regarding non-Euclidean space. Lambert is credited with the first proof that π is irrational (although it is speculated that Aryabhata was the first to hint at that, in 500 CE). Lambert also devised theorems regarding conic section
s that made the calculation of the orbit
s of comet
s simpler.
Lambert devised a formula for the relationship between the angles and the area of hyperbolic triangle
s. 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 (radian
s), 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.
s. In particular he was the first to discuss the properties of conformality and equal area
preservation and to point out that they were mutually exclusive.
(Snyder 1993 p77). In 1772 Lambert published
seven new map projections under the title Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten, (Notes and Comments on the Composition of Terrestrial and Celestial MapsTobler, Waldo R, Notes and Comments on the Composition of Terrestrial and Celestial Maps, 1972. University of Michigan Press. This is a translation Lambert's paper.). Lambert did not give names to any of his projections but they are now known as:
The first three of these are of great importance. Further details may be found at map projections and in several texts.
. In 1760, he published a book on light reflection, the Photometria, in which he formulated the law of light absorption—the Beer–Lambert law). Lambert also wrote a classic work on perspective
and also contributed to geometrical optics
. The photometric unit lambert is named in recognition of his work in establishing the study of photometry
.
from objective
appearances. This connects with his work in the science
of optics
. In 1765 he began corresponding with Immanuel Kant
who intended to dedicate him the Critique of Pure Reason
but the work was delayed, appearing after his death.
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 system
s) throughout the galaxy
. The former was later confirmed by Sir William Herschel
.
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
, philosopher and astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
.
Asteroid
Asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
187 Lamberta
187 Lamberta
187 Lamberta is a large and very dark main-belt asteroid. It has a composition of primitive carbonaceous materials.It was discovered by J. Coggia on April 11, 1878. It was the second of his five asteroid discoveries. It is named after the astronomer Johann Heinrich Lambert....
was named in his honour.
Biography
Lambert was born in 1728 in the city of MulhouseMulhouse
Mulhouse |mill]] hamlet) is a city and commune in eastern France, close to the Swiss and German borders. With a population of 110,514 and 278,206 inhabitants in the metropolitan area in 2006, it is the largest city in the Haut-Rhin département, and the second largest in the Alsace region after...
(now in Alsace
Alsace
Alsace is the fifth-smallest of the 27 regions of France in land area , and the smallest in metropolitan France. It is also the seventh-most densely populated region in France and third most densely populated region in metropolitan France, with ca. 220 inhabitants per km²...
, France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
), at that time an exclave of Switzerland. Leaving school he continued to study in his free time whilst undertaking a series of jobs. These included assistant to his father (a tailor), a clerk at a nearby iron works, a private tutor, secretary to the editor of Basler Zeitung and, at the age of 20, private tutor to the sons of Count Salis in Chur
Chur
Chur or Coire is the capital of the Swiss canton of Graubünden and lies in the northern part of the canton.-History:The name "chur" derives perhaps from the Celtic kora or koria, meaning "tribe", or from the Latin curia....
. Travelling Europe with his charges (1756–1758) allowed him to meet established mathematicians in the German states, The Netherlands, France and the Italian states. On his return to Chur he published his first books (on optics and cosmology) and began to seek an academic post. After a few short posts he was rewarded (1764) by an invitation from Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
to a position at the Prussian Academy of Sciences in Berlin, where he gained the sponsorship of Frederick II
Frederick II of Prussia
Frederick II was a King in Prussia and a King of Prussia from the Hohenzollern dynasty. In his role as a prince-elector of the Holy Roman Empire, he was also Elector of Brandenburg. He was in personal union the sovereign prince of the Principality of Neuchâtel...
of Prussia
Prussia
Prussia was a German kingdom and historic state originating out of the Duchy of Prussia and the Margraviate of Brandenburg. For centuries, the House of Hohenzollern ruled Prussia, successfully expanding its size by way of an unusually well-organized and effective army. Prussia shaped the history...
. In this stimulating, and financially stable, environment he worked prodigiously until his death in 1777.
Mathematics
Lambert was the first to introduce hyperbolic functionHyperbolic function
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh" , and the hyperbolic cosine "cosh" , from which are derived the hyperbolic tangent "tanh" and so on.Just as the points form a...
s into trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
. Also, he made conjectures regarding non-Euclidean space. Lambert is credited with the first proof that π is irrational (although it is speculated that Aryabhata was the first to hint at that, in 500 CE). Lambert also devised theorems regarding conic section
Conic section
In mathematics, a conic section is a curve obtained by intersecting a cone with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2...
s that made the calculation of the orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
s of comet
Comet
A comet is an icy small Solar System body that, when close enough to the Sun, displays a visible coma and sometimes also a tail. These phenomena are both due to the effects of solar radiation and the solar wind upon the nucleus of the comet...
s simpler.
Lambert devised a formula for the relationship between the angles and the area of hyperbolic triangle
Hyperbolic triangle
In mathematics, the term hyperbolic triangle has more than one meaning.-Hyperbolic geometry:In hyperbolic geometry, a hyperbolic triangle is a figure in the hyperbolic plane, analogous to a triangle in Euclidean geometry, consisting of three sides and three angles...
s. These are triangles drawn on a concave surface, as on a saddle
Saddle
A saddle is a supportive structure for a rider or other load, fastened to an animal's back by a girth. The most common type is the equestrian saddle designed for a horse, but specialized saddles have been created for camels and other creatures...
, instead of the usual flat Euclidean surface. Lambert showed that the angles cannot add up to π (radian
Radian
Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...
s), 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
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
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.
Map projection
Lambert was the first mathematician to address the general properties of map projectionMap projection
A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...
s. In particular he was the first to discuss the properties of conformality and equal area
preservation and to point out that they were mutually exclusive.
(Snyder 1993 p77). In 1772 Lambert published
seven new map projections under the title Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten, (Notes and Comments on the Composition of Terrestrial and Celestial MapsTobler, Waldo R, Notes and Comments on the Composition of Terrestrial and Celestial Maps, 1972. University of Michigan Press. This is a translation Lambert's paper.). Lambert did not give names to any of his projections but they are now known as:
- Lambert conformal conicLambert conformal conic projectionA Lambert conformal conic projection is a conic map projection, which is often used for aeronautical charts. In essence, the projection superimposes a cone over the sphere of the Earth, with two reference parallels secant to the globe and intersecting it. This minimizes distortion from projecting...
- Transverse MercatorTransverse Mercator projectionThe transverse Mercator map projection is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the UTM...
- Lambert azimuthal equal areaLambert azimuthal equal-area projectionThe Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk . It accurately represents area in all regions of the sphere, but it does not accurately represent angles...
- Lagrange projection
- Lambert cylindrical equal areaLambert cylindrical equal-area projectionIn cartography, the Lambert cylindrical equal-area projection, or Lambert cylindrical projection, is acylindrical, equal area map projection...
- Transverse cylindrical equal area
- Lambert conical equal area
The first three of these are of great importance. Further details may be found at map projections and in several texts.
Physics
Lambert invented the first practical hygrometerHygrometer
A hygrometer is an instrument used for measuring the moisture content in the environmental air, or humidity. Most measurement devices usually rely on measurements of some other quantity such as temperature, pressure, mass or a mechanical or electrical change in a substance as moisture is absorbed...
. In 1760, he published a book on light reflection, the Photometria, in which he formulated the law of light absorption—the Beer–Lambert law). Lambert also wrote a classic work on perspective
Perspective (visual)
Perspective, in context of vision and visual perception, is the way in which objects appear to the eye based on their spatial attributes; or their dimensions and the position of the eye relative to the objects...
and also contributed to geometrical optics
Geometrical optics
Geometrical optics, or ray optics, describes light propagation in terms of "rays". The "ray" in geometric optics is an abstraction, or "instrument", which can be used to approximately model how light will propagate. Light rays are defined to propagate in a rectilinear path as far as they travel in...
. The photometric unit lambert is named in recognition of his work in establishing the study of photometry
Photometry (optics)
Photometry is the science of the measurement of light, in terms of its perceived brightness to the human eye. It is distinct from radiometry, which is the science of measurement of radiant energy in terms of absolute power; rather, in photometry, the radiant power at each wavelength is weighted by...
.
Philosophy
In his main philosophical work, New Organon (1764), Lambert studied the rules for distinguishing subjectiveSubjectivity
Subjectivity refers to the subject and his or her perspective, feelings, beliefs, and desires. In philosophy, the term is usually contrasted with objectivity.-Qualia:...
from objective
Objectivity (science)
Objectivity in science is a value that informs how science is practiced and how scientific truths are created. It is the idea that scientists, in attempting to uncover truths about the natural world, must aspire to eliminate personal biases, a priori commitments, emotional involvement, etc...
appearances. This connects with his work in the science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
of optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
. In 1765 he began corresponding with Immanuel Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....
who intended to dedicate him the Critique of Pure Reason
Critique of Pure Reason
The Critique of Pure Reason by Immanuel Kant, first published in 1781, second edition 1787, is considered one of the most influential works in the history of philosophy. Also referred to as Kant's "first critique," it was followed by the Critique of Practical Reason and the Critique of Judgement...
but the work was delayed, appearing after his death.
Astronomy
Lambert also developed a theory of the generation of the universeUniverse
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
that was similar to the nebular hypothesis that Thomas Wright
Thomas Wright (astronomer)
Thomas Wright was an English astronomer, mathematician, instrument maker, architect and garden designer. He was the first to describe the shape of the Milky Way and speculate that faint nebulae were distant galaxies....
and Immanuel Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....
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
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
in Cosmologische Briefe über die Einrichtung des Weltbaues (1761). Lambert hypothesized that the stars near the sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
were part of a group which travelled together through the Milky Way
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...
, and that there were many such groupings (star system
Star system
A star system or stellar system is a small number of stars which orbit each other, bound by gravitational attraction. A large number of stars bound by gravitation is generally called a star cluster or galaxy, although, broadly speaking, they are also star systems.-Binary star systems:A stellar...
s) throughout the galaxy
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
. The former was later confirmed by Sir William Herschel
William Herschel
Sir Frederick William Herschel, KH, FRS, German: Friedrich Wilhelm Herschel was a German-born British astronomer, technical expert, and composer. Born in Hanover, Wilhelm first followed his father into the Military Band of Hanover, but emigrated to Britain at age 19...
.
Logic
Johann-Heinrich Lambert is the author of a treatise on logic, which he called Neues Organon, that is to say, the New Organon. The most recent edition of this work named after Aristotle's Organon was issued in 1990 by the Akademie-Verlag of Berlin. To say nothing of the fact that in it one has the first appearance of the term phenomenology, one can find therein a very pedagogical presentation of the various kinds of syllogism. In A System of Logic Ratiocinative and Inductive, John-Stuart Mill expresses his admiration for Johann Heinrich Lambert.See also
- Beer-Lambert lawBeer-Lambert lawIn optics, the Beer–Lambert law, also known as Beer's law or the Lambert–Beer law or the Beer–Lambert–Bouguer law relates the absorption of light to the properties of the material through which the light is travelling.-Equations:The law states that there is a logarithmic dependence between the...
(Lambert-Beer law, Beer-Lambert-Bouguer law) - lambert (unit)Lambert (unit)The lambert is a non-SI unit of luminance named for Johann Heinrich Lambert , a Swiss mathematician, physicist and astronomer. A related unit of luminance, the foot-lambert, is used in the lighting, cinema and flight simulation industries...
- Lambert quadrilateralLambert quadrilateralIn geometry, a Lambert quadrilateral,named after Johann Heinrich Lambert,is a quadrilateral three of whose angles are right angles. Historically, the fourth angle of a Lambert quadrilateral was of considerable interest since if it could be shown to be a right angle, then the Euclidean parallel...
- Lambert's cosine lawLambert's cosine lawIn optics, Lambert's cosine law says that the radiant intensity observed from a Lambertian surface or a Lambertian radiator is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal. A Lambertian surface is also known as an ideal diffusely...
- Lambertian reflectanceLambertian reflectanceIf a surface exhibits Lambertian reflectance, light falling on it is scattered such that the apparent brightness of the surface to an observer is the same regardless of the observer's angle of view. More technically, the surface luminance is isotropic...
- Lambert cylindrical equal-area projectionLambert cylindrical equal-area projectionIn cartography, the Lambert cylindrical equal-area projection, or Lambert cylindrical projection, is acylindrical, equal area map projection...
- Lambert conformal conic projectionLambert conformal conic projectionA Lambert conformal conic projection is a conic map projection, which is often used for aeronautical charts. In essence, the projection superimposes a cone over the sphere of the Earth, with two reference parallels secant to the globe and intersecting it. This minimizes distortion from projecting...
- Lambert azimuthal equal-area projectionLambert azimuthal equal-area projectionThe Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk . It accurately represents area in all regions of the sphere, but it does not accurately represent angles...
- Lambert series, of importance in number theory.
- Lambert's trinomial equation
- Lambert's W function
- πPi' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
External links
- Johann Heinrich Lambert (1728-1777): Collected Works - Sämtliche Werke Online
- Entry from "A Short Account of the History of Mathematics".
- Britannica
- NNDB
- Rouse Ball
- fascimiles of publications at Université Louis Pasteur
- Sarah Lowengard "Number, Order, Form: Color Systems and Systematization" and Johann Heinrich Lambert The Creation of Color in Eighteenth-Century Europe (New York: Columbia University Press, 2006)