MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

164 Biographical Vignettes
sität Braunschweig), which he attended from 1792 to 1795, and to the University
of Göttingen from 1795 to 1798. His first great breakthrough came in 1796
when he showed that any regular polygon with a number of sides which is a
Fermat prime can be constructed by compass and straightedge. This achievement
led Gauss to choose Mathematics, which he termed the Queen of the
Sciences, as his life’s vocation. Gauss was so enthused by this discovery that
he requested that a regular heptadecagon (17 sided polygon) be inscribed on his
tombstone, a request that was not fulfilled because of the technical challenge
which it posed. He returned to Braunschweig in 1798 without a degree but received
his doctorate in abstentia from the University of Helmstedt in 1799 with
a dissertation on the Fundamental Theorem of Algebra under the nominal supervision
of J. F. Pfaff. With the Duke’s stipend to support him, he published,
in 1801, his magnum opus Disquisitiones Arithmeticae, a work which he had
completed in 1798 at age 21. Disquisitiones Arithmeticae summarized previous
work in a systematic way, resolved some of the most difficult outstanding
questions, and formulated concepts and questions that set the pattern of research
for a century and that still have significance today. It is here that he
introduced modular arithmetic and proved the law of quadratic reciprocity as
well as appended his work on constructions with compass and straightedge.
In this same year, 1801, he predicted the orbit of Ceres with great accuracy
using the method of least squares, a feat which brought him wide recognition.
With the Duke’s death, he left Braunschweig in 1807 to take up the position of
director of the Göttingen observatory, a post which he held for the rest of his
life. In 1809, he published Theoria motus corporum coelestium, his two volume
treatise on the motion of celestial bodies. His involvement with the geodetic
survey of the state of Hanover (when he invented the heliotrope) led to his
interest in differential geometry. Here, he contributed the notion of Gaussian
curvature and the Theorema Egregium which informally states that the curvature
of a surface can be determined entirely by measuring angles and distances
on the surface, i.e. curvature of a two-dimensional surface does not depend
on how the surface is embedded in three-dimensional space. With Wilhelm
Weber, he investigated terrestrial magnetism, discovered the laws of electric
circuits, developed potential theory and invented the electromechanical telegraph.
His work for the Göttingen University widows’ fund is considered part
of the foundation of actuarial science. Property 38 describes the equilateral
triangle in the Gauss plane and Property 39 states Gauss’ Theorem on Triangular
Numbers. Although not enamored with teaching, he counted amongst
his students such luminaries as Bessel, Dedekind and Riemann. The CGS unit
of magnetic induction is named for him and his image was featured on the
German Deutschmark as well as on three stamps. Gauss was not a prolific
writer, which is reflected in his motto Pauca sed matura (“Few, but ripe”).
What he did publish may best be described as terse, in keeping with his belief