Caspar Wessel
Encyclopedia
Caspar Wessel was a Norwegian
-Danish
mathematician
and cartographer
. In 1799, Wessel was the first person to describe the complex numbers. He was the younger brother of poet and playwright Johan Herman Wessel
.
, Akershus
, Norway. In 1763, having completed secondary school, he went to Denmark for further studies. He attended the University of Copenhagen
and acquired the degree of candidatus juris in 1778. From 1794, however, he was employed as a surveyor
(from 1798 as Royal inspector of Surveying).
It was the mathematical aspect of surveying that led him to exploring the geometrical significance of complex number
s. His fundamental paper, Om directionens analytiske betegning, was published in 1799 by the Royal Danish Academy of Sciences and Letters
. Since it was in Danish, it passed almost unnoticed, and the same results were later independently rediscovered by Argand
in 1806 and Gauss
in 1831.
One of the more prominent ideas presented in "On the Analytical Representation of Direction" was that of vectors. Even though this was not Wessel's main intention with the publication, he felt that a geometrical concept of numbers, with length and direction, was needed. Wessel's approach on addition was: "Two straight lines are added if we unite them in such a way that the second line begins where the first one ends and then pass a straight line from the first to the last point of the united lines. This line is the sum of the united lines". This is the same idea as used today when summing vectors.
Wessel's priority to the idea of a complex number as a point in the complex plane
is today universally recognised. His paper was re-issued in French translation in 1899, and in English in 1999 as On the analytic representation of direction (ed. J. Lützen et al.).
Wessel's elder brother Johan Herman Wessel
was a major name in Danish-Norwegian literature.
Norway
Norway , officially the Kingdom of Norway, is a Nordic unitary constitutional monarchy whose territory comprises the western portion of the Scandinavian Peninsula, Jan Mayen, and the Arctic archipelago of Svalbard and Bouvet Island. Norway has a total area of and a population of about 4.9 million...
-Danish
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
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....
and cartographer
Cartography
Cartography is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively.The fundamental problems of traditional cartography are to:*Set the map's...
. In 1799, Wessel was the first person to describe the complex numbers. He was the younger brother of poet and playwright Johan Herman Wessel
Johan Herman Wessel
thumb|Johan Herman WesselJohan Herman Wessel was a Norwegian-Danish poet. Some of his satirical poems are still popular.-Biography:...
.
Biography
Wessel was born in Jonsrud, VestbyVestby
Vestby is a municipality in Akershus county, Norway. It is part of the Follo traditional region. The administrative centre of the municipality is the village of Vestby.-Name:...
, Akershus
Akershus
- Geography :The county is conventionally divided into the traditional districts Follo and Romerike, which fill the vast part of the county, as well as the small exclave west of Oslo that consists of Asker and Bærum...
, Norway. In 1763, having completed secondary school, he went to Denmark for further studies. He attended the University of Copenhagen
University of Copenhagen
The University of Copenhagen is the oldest and largest university and research institution in Denmark. Founded in 1479, it has more than 37,000 students, the majority of whom are female , and more than 7,000 employees. The university has several campuses located in and around Copenhagen, with the...
and acquired the degree of candidatus juris in 1778. From 1794, however, he was employed as a surveyor
Surveying
See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...
(from 1798 as Royal inspector of Surveying).
It was the mathematical aspect of surveying that led him to exploring the geometrical significance of complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
s. His fundamental paper, Om directionens analytiske betegning, was published in 1799 by the Royal Danish Academy of Sciences and Letters
Royal Danish Academy of Sciences and Letters
Royal Danish Academy of Sciences and Letters is a Danish non-governmental science Academy, founded 13 November 1742 by permission of the King Christian VI, as a historical Collegium Antiquitatum...
. Since it was in Danish, it passed almost unnoticed, and the same results were later independently rediscovered by Argand
Jean-Robert Argand
Jean-Robert Argand was a gifted amateur mathematician. In 1806, while managing a bookstore in Paris, he published the idea of geometrical interpretation of complex numbers known as the Argand diagram.-Life:...
in 1806 and Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
in 1831.
One of the more prominent ideas presented in "On the Analytical Representation of Direction" was that of vectors. Even though this was not Wessel's main intention with the publication, he felt that a geometrical concept of numbers, with length and direction, was needed. Wessel's approach on addition was: "Two straight lines are added if we unite them in such a way that the second line begins where the first one ends and then pass a straight line from the first to the last point of the united lines. This line is the sum of the united lines". This is the same idea as used today when summing vectors.
Wessel's priority to the idea of a complex number as a point in the complex plane
Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis...
is today universally recognised. His paper was re-issued in French translation in 1899, and in English in 1999 as On the analytic representation of direction (ed. J. Lützen et al.).
Wessel's elder brother Johan Herman Wessel
Johan Herman Wessel
thumb|Johan Herman WesselJohan Herman Wessel was a Norwegian-Danish poet. Some of his satirical poems are still popular.-Biography:...
was a major name in Danish-Norwegian literature.