id: 05638598
dt: j
an: 2009f.00051
au: Eide, Morten
ti: Abel, the elliptic functions, and lemniscates. (Abel, de elliptiske
funksjoner, og lemniskaten.)
so: Normat. 57, No. 1, 1-9 (2009).
py: 2009
pu: Nationellt Centrum för Matematikutbildning (NCM), Göteborgs Universitet,
Göteborg
la: NO
cc: A30 I80 G90
ut: elliptic functions; geometric constructions; constructions with rules and
compasses; arclength of the lemniscate
ci:
li:
ab: Summary: Abel discovered that if $p=2^n+1$ is a prime, a lemniscate can be
divided into $p$ parts of equal lengths, using ruler and compass. This
result is explored from an elementary point of view, introducing the
lemniscate, the integral expression for its arclength and from that its
connection to elliptic functions, and concluding by considering the
most elementary cases $p=2,3$ using explicit formulas for the doubling
and tripling of arguments for elliptic functions.
rv: