Skip to content

Commit

Permalink
Limit the range of values taken by $\theta$.
Browse files Browse the repository at this point in the history
  • Loading branch information
l0stman committed Aug 6, 2012
1 parent dbbc48b commit 6eec9a2
Showing 1 changed file with 6 additions and 6 deletions.
12 changes: 6 additions & 6 deletions chap6/6.4/6.4.tex
Expand Up @@ -100,12 +100,12 @@
will cause a division overflow most of the time.

\newpar{8} Let $n$ be a positive integer and $\theta$ an irrational
positive real. We choose a point of origin noted $0$ on a circle
whose circumference is $1$. We then move clockwise on the circle and
place the points whose distance from $0$ is $i\theta$ (we refer to
this point as $i$), for $i$ varying between $0$ and $n$. Note that if
$\alpha$ is irrational then $\lceil \alpha\rceil = 1+\lfloor
\alpha\rfloor$, thus
positive real between $0$ and $1$. We choose a point of origin noted
$0$ on a circle whose circumference is $1$. We then move clockwise on
the circle and place the points whose distance from $0$ is $i\theta$
(we refer to this point as $i$), for $i$ varying between $0$ and $n$.
Note that if $\alpha$ is irrational then $\lceil \alpha\rceil =
1+\lfloor \alpha\rfloor$, thus

\[ \{-\alpha\} = - \alpha - \lfloor -\alpha\rfloor= - \alpha + \lceil \alpha
\rceil = 1 - \{\alpha\}.\]
Expand Down

0 comments on commit 6eec9a2

Please sign in to comment.