Trisecting an Angle Using the Cycloid of Ceva
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The cycloid of Ceva has the polar equation . To trisect the angle
, construct a line parallel to the polar axis (the positive
axis). Let
be the point of intersection of the cycloid and the line. Then the angle
is one-third of the angle
. Proof: let angle
be
and let the point
on the
axis be such that
. Let
be the orthogonal projection of
on the line
. The angle
, so
. Since
,
,
. So angle
equals
, but
.
Contributed by: Izidor Hafner (October 2013)
Open content licensed under CC BY-NC-SA
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