144 Normat 55:3, 144 (2007)

Summary in English

Henrik Kragh Sørensen and Hel-

ge S.Kragh, Longomontanus og cirk-

lens kvadratur (Danish).

Longomontanus was a Dane living in

the ﬁrst half of the 17th century. He

is mostly known as an astronomer and

a disciple of Tycho Brahe, but he al-

so dabbled in mathematics, being ob-

sessed with the classical problem of

the quadrature of the circle. He pub-

lished a lot which was mercifully neg-

lected by the international community

until it came under scathing criticism

of John Pell. In the paper his numerolo-

gical musings in astronomy are related

to his quadratures, some of his proofs

are discussed along with Pells refutation

of them, leading to a general analysis of

the practice of mathematics at the time.

Eggert Briem, Approximation i ende-

lig dimensionale rum (Danish).

The well-known Stone-Weierstrass

claims that any real continuos function

on a compact subset of R

n

can be uni-

formly approximated by the elements of

an algebra which contains the constant

functions and separates points. A parti-

cular case is that of polynomials. In the

complex valued case one also need to

add the condition of being closed under

complex conjugation, as uniform con-

vergences of polynomials are analytic.

In the article a weakening of the multi-

plicative condition of the set of approxi-

mating functions is being discussed.

Juliusz Brzezinski , Komposition av

kvadratiska former - från Gauss till

Bhargava (Swedish).

The young Indian mathematician Bhar-

gava recently presented a new way

of looking at Gauss classical com-

position of integral quadratic binary

forms, which has opened up the pos-

sibility of generalizing it systematically

with applications to class-ﬁeld theory.

The article is an introduction to the

works of Bhargava. In it the reader can

learn about Gauss classical work, and

in particular the correspondence betwe-

en such forms and ideals in quadratic

rings, which explains why it all should

work. In the context of Bhargava tri-

linear maps can be associated with ’cu-

bical’ matrices which are being treated

systematically.

Ulf Persson, SO(4) och S

3

(Swedish).

The 3-dimensional sphere can be

thought of as a union of two solid to-

ri glued along their boundaries. Those

come from torus-ﬁbrations, and this

short note explores some elementary

facts of how SO(4) operates on them

with connections to Hopf ﬁbrations and

quaternionic multiplication.

Rättelse Normat 2007:2

Selmer blev mycket riktigt 86 år. Han

föddes 1920 och dog därmed 2006, och

inget annat år, som det tyvärr råka-

de stå i överskriften till Tverbergs runa

över Selmer i förra numret. Denna fadäs

beklagas djupt av huvudredaktören som

ensam bär det fullständiga ansvaret.

Ulf Persson