Tag Archives: integral

Irrationality of pi: the integral that wasn't

And now for the punchline! Today we’ll show that, for large enough values of , completing the proof of the irrationality of . First, let’s show that is positive when . We know that is positive for . But I … Continue reading

Posted in algebra, calculus, convergence, famous numbers, proof, trig | Tagged , , , , | 8 Comments

Irrationality of pi: the impossible integral

We’re getting close! Last time, we defined a new function and showed that and are both integers, and that . So, consider the following: The first step uses the product rule for differentiation (recalling that and ); the last step … Continue reading

Posted in famous numbers, proof | Tagged , , , , , | 4 Comments