Mathematics concepts and applications

¶ … theory on plate tectonics, the theory of Motion of heavenly bodies and several other theories that were developed during his lifetime.

Mathematicians Life and Works: Karl Gauss

There are many well-known mathematicians from history whose work is well-known and position widely recognised. However, there are also many lesser known mathematicians that have also made equally valuable contributions. Karl Friedrich Gauss is one of these, and as such is a worthwhile individual to study. Gauss developed many ideas and theories which are still in use today.

He is best known for his theory of plate tectonics and his work entitled "Theoria Motus Corporum Coelestium"; Theory of the Motion of Heavenly Bodies in 1809. With Wilhelm E. Weber; a physicist he also developed a theory concerning geomagnetism. Much of his work is still used today, including work in the fields of physics, astronomy, and his statistical theories are even used in software algorithms. In this we see man who has made large contributions to the world of mathematics and related disciplines (Schaaf, 1964).

If we look Karl Friedrich Gauss he was born in Brunswick, Germany in 1777 and died in 1855. His background was not one pf privilege, but his talent for mathematics was seen at a young age. In one story it is reported that mathematics and logic were displayed at an early age when if was asked to add up all the numbers from one to one hundred. Logically, he deduced that the order of the addition did not matter, as this would give the same results, and that it would be easier to do 1+99 and the 2 +98 and so on (Schaaf, 1964). This reduced the equation to (49x100) +50 +100. This resulted in a very fast computation with the answer of 5,050, when many peers would not be able to carry out the sum, or would take much longer to do so (Rassias, 1991, Schaaf, 1964).

It was when in his teens that he propounded the theory of least squares and also solved the problem of divided the circle into seventeen parts. It is also interesting to note that there were many other discoveries at this time, only discovered when his diaries were read. In 1792 Gauss entered Brunswick Collegium Carolinum, paid for with a stipend form the Duke of Brunswick- Wolfenbuotel, who had noticed his genius (Schaaf, 1964). The Duke was also to become a friend as well as benefactor.

When Gauss left the collage in 1795 he went to study at the Gotingen University. Where he learnt under Kaestner and made the acquaintance of Farkas Bolyai. He left in 1798, and although he had already made a major discovery; the make up of a regular 17-gon by ruler and compasses, a discovery that is not seen as amazing, and one of the most advanced discoveries since the Ancient Greeks (Rassias, 1991, Schaaf, 1964).

With a return to Brunswick in 1799 Gauss was to get his degree, but this was a doctorate, with the aid of the Duke, he submitted a dissertation to Pfaff at the University of Helmstedt. It was also around this time that Gauss was to become interested in astronomy (Schaaf, 1964).

His personal life was happy, and then in 1805 it became better, when he married Johanna Ostoff. In 1807 the Duke was killed fighting the Prussians, as a result he had to find a job. He obtained the position of director of the Gotingen observatory. This must have been a likable job as he was to remain in this position for the rest of his life until 1855 when he died. Tragedy was to strike again, only a year after taking up this post, when in 1808 his father dies, and then in 1809, whilst in childbirth, his wife dies, and the second son, who she was giving birth to, was also to die soon after. However, is work does not appear to have suffered in the long-term, but the short-term saw him take time off of work and devote himself to his three children (Schaaf, 1964).

In 1810 he remarried, there were another three children, but this is generally though to have been a marriage of convenience rather than a love match (Schaaf, 1964).

Some of his major works included work on how to calculate the orbit of the planets. In his work Theoria Motus Corporum Coelestium he examined and discussed the use of differential equations, conic sections and the elliptic orbits, and then in the next volume of this work he then showed how the orbit of a planet could be estimated and then the estmate could be further refined (Rassias, 1991). By 1817 he had made is contributions to astronomy, and despite continuing observations he did not add more to the theoretical framework of astronomy (Schaaf, 1964).

Gauss did look to other subjects, publishing a total of one hundred and fifty papers over his career, he contributed to many other areas. Papers included Methodus nova integralium valores per approximationem inveniendi which was a practical essay that concerned the use of approximate integration, a discussion of statistical estimators in Bestimmung der Genauigkeit der Beobachtungen and geodesic problems in Theoria attractionis corporum sphaeroidicorum ellipticorum homogeneorum methodus nova tractate (Schaaf, 1964).

During the 1820's the work of Gauss appeared to start taking him more in the direction of geodesy. This may have started when, in 1818, he was requested to undertake a geodesic survey of Hanover, to link up to the Danish grid that was already in existence. He took total charge, and made the measurements during the day, and in the evenings he would reduce them to the calculations. It was during this survey, and as a result of the survey needs, that he invented the heliotrope (Rassias, 1991). Unfortunately, in the survey there were erroneous base lines used (Rassias, 1991).