188 Normat 51:4, 188 (2003)

Summary in English

Signe Holm Knudtzon and Johan

F. Aarnes, Morley’s heart – playing

with a geometric theorem – part 1. (Nor-

wegian.) The article starts by presenting

simple geometric proofs of Morley’s fa-

mous theorem and its natural general-

terion, it is shown that six of the ver-

tices of these equilaterals are located on

a conic.

Martin Brundin, Continuity really

does not imply differentiability.

(Swedish.) Using elementary calculus,

the author gives an example of an ev-

erywhere continu ous but nowhere dif-

ferentiable function. A similar example

was given by van der Waerden in 1930.

of them known for years but presented

in an intelligible way. Eulers results on

both even and odd perfect numbers are

given. The author then shows that the

number of different prime divisors of an

odd perfect number has to be at least 4

and thus there cannot be small odd per-

fect numb ers (below 1 000 000). Then he

shows that – roughly speaking – the ex-

means of results on geometric series and

prime factors in those s eries. Some up-

ond least prime in a perfect number

are given. Kanold and Pomerance’s re-

sult – there is only a finite number of

perfect numbers having a given num-

ber of prime devisors – is mentioned.

Finally the factor-chain method is ex-

plained by an example. A list of known

results about perfect number concludes

the article.

Peter Lindqvist, Euler’s Beta func-

tion and the Schwarz–Christoffel for-

mula for a triangle. (Swedish.) The au-

for the Beta function. The proof pro-

ceeds via the conformal mapping of a

half plane onto a triangle.