Last Updated：2025/12/30
Sentence
If
aₙ
and
bₙ
denote
the
perimeters
of
inscribed
and
circumscribed
regular
n-gons,
respectively,
along
some
circle
then
the
harmonic
mean
and
geometric
mean
of
those
two
perimeters
yield
the
perimeters
of
the
inscribed
and
circumscribed
regular
2n-gons,
respectively,
along
that
same
circle.
(This
is
Archimedes'
Recurrence
Formula.)
Quizzes for review
If aₙ and bₙ denote the perimeters of inscribed and circumscribed regular n-gons, respectively, along some circle then the harmonic mean and geometric mean of those two perimeters yield the perimeters of the inscribed and circumscribed regular 2n-gons, respectively, along that same circle. (This is Archimedes' Recurrence Formula.)
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