| |
| Work – Pioneering Even Today |
| |
Carl Friedrich Gauss decided finally to take a mathematical approach when, as a student in 1796, he proved that the regular 17-gon can be constructed by using only a ruler and compass. This was the first advance in this field in two millennia. In 1799 he earned his doctorate at the University of Helmstedt in absentia and without any viva voce examination simply on the basis of the first exact proof of the fundamental theorem of algebra.
 |  |
| According to Gauss, the cosine of the nth part of 360° can be expressed by rational calculation operations and square roots if n is a prime number in accordance with n = 2m +1. | The shaded area indicates the probability that an error or an observation falls into the interval from a to b. |
| |
In 1801 Gauss published his major mathematical work:
”Disquisitiones Arithmeticae”. In this he investigated above all the number theory, the theory of congruency, the theory of square forms and the theory of division of a circle into equal arcs, for which he provided ample proof. In the theory of division of the circle he introduced the general solution for the constructability by ruler and compass of regular polygons.
Alongside the many still valid innovations in pure mathematics (error theory, theory of elliptical functions, theory of surfaces, prime number theory, representation of complex numbers, theory of powers), Gauss also achieved significant practical advances in other areas.
Modern computer technology, for example, would be nowhere without his algorithms for software. Very important, too, are the Gaussian quadrature methods for the numerical calculation of unidimensional or multidimensional integrals, and the Gaussian method of elimination for resolving linear equation systems. A practical tool is the adjustment calculation which makes it possible to obtain the best approximate values from aberrant measured values and thus specify the accuracy.
Return to the top of the page | |
|