Normat – Abstracts 3/2005

 

Uffe Thomas Jankvist and Neslihan Saglanmak
What did they seek and what did they find? Combinatoric solutions for algebraic equations - from Cardano to Cauchy - Part 2 (in Danish)
A history of algebraic equation solving before Gauss, Abel and Galois, more specifically in the period from 1545 to 1815. In this second and concluding part of the article the authors, in their search for usage of combinatorics, permutations and invariance considerations in algebraic equation solving, survey the methods of Lagrange, Ruffini and Cauchy. The authors point to three different approaches to algebraic equation solving; (1) symmetric functions of roots, (2) substitutions, change of variabels and elimination, and (3) the use of n-th roots of unity and Lagrange resolvents. The authors conclude that the work on algebraic equation solving in the period from 1546 to 1770 has been noticably important for the later so astonishing contributions of Abel and Galois.

Hans Georg Killingbergtrø
A generalization from Pascal's Hexagon Theorem to (4n + 2)-gons (in Norwegian)
A classic theorem of Pascal states that opposing sides of a hexagon inscribed in a conic section meet in three collinear points. The author reformulates this result, and generalizes it to (4n+2)-gons.

Lars Kristiansen
The countable and the over-countable (in Norwegian)
The paper gives a nontechnical introduction to the Continuum Hypothesis and some related mathematical concepts, such as uncountable sets and diagonalization. Particular emphasis is placed on making the exposition readable by a broad audience.

Leif Andersen and Vagn Lundsgaard Hansen

Mathematics in a Nautilus Shell (in Danish)
With an equiangular (logarithmic) spiral as the point of departure, the authors design a mathematical model of a Nautilus shell. They establish a close connection in the model between the characteristic angle in the underlying equiangular spiral and the golden angle.