2012 USAJMO Problems/Problem 4
Problem
Let be an irrational number with
, and draw a circle in the plane whose circumference has length 1. Given any integer
, define a sequence of points
,
,
,
as follows. First select any point
on the circle, and for
define
as the point on the circle for which the length of arc
is
, when travelling counterclockwise around the circle from
to
. Supose that
and
are the nearest adjacent points on either side of
. Prove that
.
Solution
See Also
2012 USAJMO (Problems • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAJMO Problems and Solutions |