>>12497502No, you fucking dipshit, I'm proposing some of the idiots who think they're hot stuff like the hordes of undergrads on /mg/ to actually engage their brains and think.
This shit isn't that hard. We know that
which you can check by comparing and and you'll easily see falls in the range of validity.
Now
so it remains to show that
which is easy. You can do this in many ways. For example, use Jordan's lemma to show that
, remember that the denominator is greater than unity (here we only use the fact that positive numbers have positive square roots - not a calculation) so we're now done if we can convince ourselves that
or in other words, that
Again, we don't want to perform a calculation, but by drawing some pretty simple diagrams you can convince yourself that the ratio of the circumference to diameter in a circle is less than 8.
Or, draw a square of side length 2, and inscribe the unit circle to show that
This completes the proof.
