**Caspar Wessel** (June 8, 1745,
**Vestby**

Vestby – March 25, 1818, Copenhagen)
was a Norwegian–Danish mathematician and cartographer. In 1799,
Wessel was the first person to describe the geometrical interpretation
of complex numbers as points in the complex plane. He was the younger
brother of poet and playwright Johan Herman Wessel.
Biography[edit]
Wessel was born in Jonsrud, Vestby, Akershus,
**Norway**

Norway and was one of
thirteen children in a family. In 1763, having completed secondary
school at Oslo Cathedral School, he went to
**Denmark**

Denmark for further
studies. He attended the University of
**Copenhagen**

Copenhagen to study law, but
due to financial pressures, could only do so for a year. To survive,
he became an assistant land surveyor to his brother and they worked on
the Royal Danish Academy of Sciences and Letters' topographical survey
of Denmark. This was not enough, however, and he took on extra work as
a cartographer. He worked as a surveyor for the rest of his life,
stopping only for a sabbatical year in 1778 to finish his law
degree.[1] By 1798 had risen to the supervisory role of Royal
Inspector of Surveying.[2]
It was the mathematical aspect of surveying that led him to exploring
the geometrical significance of complex numbers. His fundamental
paper, Om directionens analytiske betegning, was presented in 1797 to
the Royal Danish Academy of Sciences and Letters.[3] Since it was in
Danish and published in a journal rarely read outside of Denmark, it
went unnoticed for nearly a century.[2] The same results were
independently rediscovered by Argand in 1806 and Gauss in 1831.[1]
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 1897,[4] and in English in 1999 as On the
analytic representation of direction (eds. Bodil & Lützen).[5]
In 1815, Wessel was made a knight of the
**Order of the Dannebrog**

Order of the Dannebrog for
his contributions to surveying.
References[edit]

^ a b O'Connor, John J.; Robertson, Edmund F. (October 2000), "Caspar
Wessel", MacTutor History of
**Mathematics**

Mathematics archive, University of St
Andrews .
^ a b Nahin, Paul J. (1998). An Imaginary Tale: The Story of

−
1

displaystyle sqrt -1

. Princeton University Press. pp. 48–49.
ISBN 978-0-691-14600-3.
^ Wessel, Caspar (1799). "Om Directionens analytiske Betegning, et
Forsog, anvendt fornemmelig til plane og sphæriske Polygoners
Oplosning" [On the analytic representation of direction, an effort
applied in particular to the determination of plane and spherical
polygons]. Nye Samling af det Kongelige Danske Videnskabernes Selskabs
Skrifter (in Danish). Copenhagen: Royal Danish Academy of Sciences and
Letters. 5: 469–518.
^ Wessel, Caspar (1799). Essai sur la représentation analytique de la
direction [Essay on the Analytic Representation of Direction] (in
French). Translated by Zeuthen, H. G. Copenhagen: Royal Danish Academy
of Sciences and Letters (published 1897). BNF 31640182t.
^ Wessel, Caspar (1797). Branner, Bodil; Lützen, Jesper, eds. On the
analytical representation of direction: an attempt applied chiefly to
solving plane and spherical polygons, 1797. Translated by Damhus,
Flemming. Copenhagen: C.A. Reitzels (published 1997).
ISBN 8778761581. OCLC 43346556.

Further reading[edit]

Brun, Viggo (1962). Regnekunsten i det gamle Norge (in Norwegian).
Oslo: Universitetsforlaget. pp. 97–111.
OCLC 492224079.

Authority control

WorldCat Identities
VIAF: 61663824
LCCN: n90627359
ISNI: 0000 0001 0979 2129
GND: 122240030
SUDOC: 058928901
BNF: cb12563002z (data)

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