188 Normat 52:4, 188 (2004)

Summary in English

Jöran Friberg, Mathematical cunei-

form texts in the Norwegian Schøyen

collection. (Swedish.) The author is

a leading scholar of Babylonian and

Sumerian mathematical texts. Here he

gives examples of cuneiform mathemat-

ical clay tablets from the Schøyen collec-

tion. Some of the texts are elementary

calculation exercises by school pupils.

And there are multiplication tables, ta-

bles of squares and of reciprocals and

so forth, in the sexagesimal system

used in Babylonia. But more advanced

problems and methods of solution are

also found in these mathematical texts.

There is a geometrical problem where

the three-dimensional Pythagorean rule

came into play, long before Pythagoras

lived. And there is a calculation of the

weight of a regular icosahedron made

from copper plate of a speciﬁed thick-

ness.

Claus Jensen, Perspective boxes and

mathematics. (Danish.) A perspective

box is a wooden box with a scene

painted on some of the interior sides

using the laws of p erspective. Light is

admitted through an aperture, and the

scene is p e rused through a peephole. To

obtain a lifelike view through the peep-

hole, it is necessary to combine several

central projections onto diﬀerent pro-

jection planes on the interior sides of

the box. From the p e riod of enthusiasm

for perspective boxes in the late seven-

teenth century, only six boxes have sur-

vived. The author describes these six,

and gives a more detailed analysis of the

perspective box made by Samuel van

Ho ogs traten, wh ich is to day in the Na-

tional Gallery in London.

Kent Holing, A quartic equation and

its Galois group. (Norwegian.) The au-

thor discusses the Galois group of the

quartic equation related to the well

known ladder box problem. In the spe-

cial case of the square box problem a

complete analysis of the Galois group

is given, using elementary results from

number theory. A complete analysis of

the Galois group in the general case

is n ot available. However, in the gen-

eral case all possible Galois groups are

achievable, with one exception. It is

proven that Z

4

is never achievable. Sev-

eral examples are hard to ﬁnd such as

A

4

. The examples of A

4

are constructed

using the theory of elliptic curves. Also,

several examples producing the trivial

group are given.

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