144 Normat 56:3, 144 (2008)

Summary in English

Nils A. Baas and Christian F.

Skau, The Selberg interviewt III - The

Riemann hypotheis and the trace for-

mula (Norwegian).

This is the third part of the interview

with Selberg. This is more mathemat-

ical than the previous parts, discussing

the signiﬁcance of the Riemann hypoth-

esis, and explicitly writing out the trace

formula. Selberg acknowledges that the

latter is probably his most important

contribution, at least the one with the

greatest number of applications. He also

reveals some of the ideas he has had in

the last decades to prove the Riemann

hypothesis.

Patrik Lundström, Pythagorean

triplets in six diﬀerent ways (Swedish).

Six diﬀerent ways of parametrising

Pythagorean triplets are presented,

from the elementary arguments sup-

plied by the Greek, via trigonometry

to Gaussian integers and applications of

Hilbers 90th theorem.

Hans G.Killingbergtrø, Parallel ax-

ial helixes in the double winding surface

(Norwegian).

The contour of the shade caused by par-

allel light-rays falling on a winding sur-

face forms a helix, cut out by an excen-

tric cylinder containing the axis of the

surface. The presence of such helixes, as

opposed to the obvious concentric ones,

cut out by cylinders whose central axi

coincide with that of te surface, seems

not to have been pointed out previously

in the literature.

Morten Eide Tangent Circles and

tetracyclic coordinates (Norwegian).

A natural angular distance between cir-

cles is introduced, leading to a repre-

sentation of circles as vectors in a 4-

dimensional space (tetracyclic), going

back to Darboux (and Cliﬀord). This is

applied to prove the so called Arbelos

theorem, as well as the theorem of Pap-

pus and to give relations between the

radi of the eight circles tangent to three

given ones.

Ulf Persson Periodic decimal expan-

sions (Swedish).

Some elementary but striking properties

of periodic expansions of fractions with

periods of maximal length are discussed,

such as the almost equidistribution of

digits and combinations thereof.