Originally posted by fearlessleader
if pie is irratinal, and it is equal to the diamiter/cercumfrence, then either the cercumphrence or the diamiter or both must always be irratinal as well. so how dose one calculate pie?
well, first of all, it's spelled pi
, not as the confection; the "perimeter" of the circle is "circumference"; and the type of number is "irratio
that said, very few occasions demand the preceise measurement of both
diamerter and circumference. if you construct a circle using a compass, usually the diameter will be rational, though of course this will be in doubt since it is impossible to make it exact. the circumference will then be the irrational part.
the case of needing the circumfrerence
only is less common.
of course, there is nothing that says that both
components can't be irrational. e. g.
, construct a square of side length 1, and circumscribe a circle. the diameter of said circle is thus sqrt(2) and circumference is pi
*sqrt(2), both of which are irrational quantities, though of different classes (sqrt(2) is algebraic, pi
(both by itself and times that) is transcendental).
it would be a more difficult, and possibly not even feasible, problem to construct a circle in which both
diameter and circumference are transcendental numbers.
in any event, i think i'm going in circles so will end this discussion.