144 Normat 60:3, 144 (2012)

Summary in English

Johan Carl-Erik Stén, Anders Johan

Lexell som matematiker (Swedish)

A short presentation of the Swedish

Mathematician Lexell (1740-1784)

which can be seen as a trailer to the

full biography written by the author.

The name of Lexell is now essentially

unknown but in his time he was a very

respected mathematician who worked

closely with Euler during the second

and ﬁnal period of the latter at the

Academy at St-Petersburg. In fact Lex-

ell was an eye-witness to Euler’s death,

and his report thereof in the form of

a private letter is added as an appen-

dix. Lexell was precocious and showed

his mathematical skill by his solutions

of some non-linear ordinary diﬀerential

equations, a work which impressed Eu-

ler. As a further example of his technical

skill was his expression of the integral

⁄

dx

(1 + x)(2x

2

≠ 1)

1

4

in elementary functions. He was also in-

volved in applied mathematics, notab-

ly the determination of the solar paral-

lax in connection with the Venus pas-

sage 1769 and was a pioneer treating

observational data statistically, thereby

obtaining a very good approximation of

that parallax. However, his main contri-

butions concern spherical geometry, an

example of which is that the locus of

the moving vertex of spherical triang-

les with ﬁxed base and area is a small

circle.

Christoph Kirfel, Dypdykk i ufornuf-

ten, irrasjonale tall og det som verre

er(Norwegian).

This is a presentation of irrational num-

bers starting from the most elementary

level suitable for elementary school, to

the construction of transcendental num-

bers in the spirit of Liouville and the

proof of the irrationality of e and that

of some trigonometric values.

Ulf Persson, Lexell’s theorem

A short presentation of a simple proof

of Lexell’s theorem.