Then apply some trigonometric identities to obtain the polynomial relations. This problem has been solved! 5 points Odd multiples of pi by 2 Ask for details ; Follow Report by Abhishek11161 14.12.2019 Log in to add a comment What do you need to … For discussion of the general topic, and further links, please see this Wikipedia entry.

A topological result (cf. In the spirit of experimental mathematics, I did a calculation of the quantity $|q\epsilon|$ for the first $100$ rational approximations for $\pi$ up to $10^{-n}$ accuracy, and it looks like it in fact decreases exponentially: So if this trend continues, you can indeed approximate $\pi$ by large enough integers.

Again, this same trick (dividing the imaginary part by ) works for the tangent of any rational multiple of . Oh, try this "what is the largest prime smaller than 5000?" If running it up to n = 1000 is cool, what about n = 10,000? I think not. 0. Here is my plan.

Ad Choices. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Pi Day is over. Another way to prevent getting this page in the future is to use Privacy Pass. What about 14/3. They are members of the infinite set of numbers of the form (2*pi)*k where k is an integer. Essentially it is a calculator that uses google and Wolfram Alpha.

8.

Coincidence? You may need to download version 2.0 now from the Chrome Web Store.

Asking for help, clarification, or responding to other answers. Note: Without rigorous proof, we can see that this is true, since the angles which match the equation are all in the first and third quadrant, and all have reference triangles of . Best Answer. Use our site without ad tracking and without advertising for I admit that I'm probably out of my depth with this question, but I can't help but feel curious. MathWorks is the leading developer of mathematical computing software for engineers and scientists. By the inequality, the difference between $\sin(\frac{3}{2}M)$ and $1$ -- or $\sin(\frac{1}{2}M)$ and $1$, whichever -- would be at most $\frac{3}{2} \epsilon$. Anyway, back to Pi Day.

Should you consider anything before you answer a question?

Coffee stains and the Simpsons in your LaTeX document, Playing the probabilities in Settlers of Catan, E-Z Pass, speeding tickets, and the mean value theorem. Isn't it better than writing 3.14? Really, I can see where they are coming from. Boom. But the following trigonometric argument is too nice to skip.

If $\pi = \frac{p}{q} + \epsilon$, then $q\pi - q\epsilon = p$; thus, the size of $q$ becomes important to the accuracy, since the $\epsilon$ we were considering above is $q\epsilon$ in these terms. Government conspiracy?

Sir-Emo-Chappington Jun 25, 2015. Why does this Excel RIGHT function not work? Yeah. As Dave (@DaleV34) pointed out: there is no 31st of April (that would be 31/4/2011). Remove the discontinuity from tan(x) where odd multiples of pi/2. Why does the VIC-II duplicate its registers? By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. This shows that is an algebraic complex number. We know that , , and are algebraic numbers.