56 Normat 52:1, 56 (2004)
Summary in English
Audun Holme, Arabic mathematics
(Norwegian.) This is the first of two
articles on Arabic mathematics. The
Arabs have not received proper credit
in the Western version of the History of
Mathematics; many of their important
discoveries were attributed to West-
ern mathematicians like Fermat, Pas-
cal or Descartes. The author starts out
with the House of Wisdom in Bagh-
dad, one of the eminent centres of cul-
ture and learning rivaling the ancient
academies in Athens and in Alexan-
dria. Al-Khwarizmi, the father of al-
gebra, worked there. After describing
some central themes from the work of
this great mathematician, the author
discusses the life and work of several
other eminent Arab mathematicians of
the Middle Ages, ending with the re-
markable poet and scholar Omar al-
Khayyami, who worked on cubic equa-
tions.
D. Laksov, Discrete mathematics does
not exist (Norwegian.) The author ar-
gues that there is no such thing as dis-
crete mathematics. He gives examples
showing that even on finite sets and
the integers there are n atural and use-
ful concepts of distance. He also points
out that much of the mathematics that
is erroneously termed discrete consist
of simple arguments that require no
knowledge of mathematics. Most of the
much ballyho oed applications of this
kind of mathematics consist of naive re-
formulations of mathematical ideas in
the language of everyday life. Several
examples illustrate this point.
Signe Holm Knudtzon and Johan
F. Aarnes, Morley’s heart – playing
with a geometric theorem – part 2. (Nor-
wegian.) If we are given an equilat-
eral triangle abc, and specify three ar-
bitrary angles , , , whose sum is
equal to 180 degrees, we may construct
a triangle ABC which by trisection of
each of its angles produces the equilat-
eral abc. This is essentially Morley’s tri-
sector theorem, and was discussed in
part one of this article. In this sec-
ond part the authors consider the fol-
lowing problem. If we vary the angles
, , , keeping abc fixed, the triangle
ABC will change its shape and posi-
tion, and so will its incenter, i.e., the
center of the inscribed circle of ABC .
The incenters will occupy a region in-
side abc, and the authors show that the
boundary of this region is made up of
three branches of hyperbolas. They also
consider the same problem for the in-
centers of the equilateral triangles ob-
tained by trisecting one angle internally
and two angles externally. An interac-
tive version of this article may be found
on http://shk.ans.hive.no/.
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