"friendly numbers"/"amicable numbers"
friendly numbers are
pairs of
numbers such that each number is the
sum of the
divisors of the other number.
the "
pythagoreans" made the extraordinary discovery that 220 and 284
are friendly numbers.
the divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, and the sum of
all these is 284.
on the other hand the divisors of 284 are 1, 2, 4, 71, 142, and the sum of these
is 220.
the pair is said to be
symbolic of
friendship.
Martin Gardners book "
mathematical magic show" tells of
talismans sold
in the
middle ages which were inscribed with these numbers on the grounds that
wearing the
charms would
promote love.
an arab
numerologist documents the practice of carving 220 on one fruit and 284
on another, and then eating the first one and offering the second one to a lover
as a form of mathematical
aphrodisiac.
taken from "fermats last theorem" by Simon Singh
so now you know what to do if quoting pi to 100 decimals fails to allure the
object of your affections.