id: 06123513
dt: j
an: 2013c.00063
au: Nielsen, Frank
ti: Rømer’s cog wheel.
so: Normat 58, No. 3, 97-108, 144 (2010).
py: 2010
pu: Nationellt Centrum för Matematikutbildning (NCM), Göteborgs Universitet,
Göteborg
la: DA
cc: A30
ut:
ci:
li:
ab: Summary: The Danish scientist Rømer, known for his determination of the
velocity of light, was a correspondent of Newton, Leibniz and Huygens.
He made an invention of cogwheels, allowing both wheels to rotate at
constant angular velocities as they engaged with each others teeth. It
was based on epi- and hypocycles, i.e. curves traced by a fixed point
on a circle rolling inside or outside a given circle. Unfortunately the
details were lost, but a reconstruction has later been found in the
collected works Huygens. Taking this as a point of departure, the
article explains the mathematics behind the construction, based on
beautiful geometric properties of the curves involved.
rv: