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 Jun 10 accepted Find an orthogonal matrix $Q$ so that the matrix $QAQ^{-1}$ is diagonal. Jun 10 asked A recursive formula for $a_n$ = $\int_0^{\pi/2} \sin^{2n}(x)dx$, namely $a_n = \frac{2n-1}{2n} a_{n-1}$ Jun 10 comment Find an orthogonal matrix $Q$ so that the matrix $QAQ^{-1}$ is diagonal. Side note: The eigenvector for eigenvalue 3 is (1,1,1) Jun 10 asked Find an orthogonal matrix $Q$ so that the matrix $QAQ^{-1}$ is diagonal. Jun 1 comment How do I enter the equation $y=\sin\frac{2\pi }{3}x$ into Wolfram Alpha? You should use chat for questions like this. chat.stackexchange.com/rooms/36/mathematics May 31 comment Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct? Note that interpreting it as $$x^2=2$$ demonstrates a problem-solving technique for 'infinite things'. You can use it for other problems involving infinite things which converge. See the solution for problem 4 in this question as an example: math.stackexchange.com/questions/407047/… May 31 comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) Let's take an example: 5*5=25. The reason you find it so easy is because you have used it so many times in your life. You don't actually have to 'actively remember' things. Another example is 4+5=9, one 'real way' of finding out that 4+5=9 is by drawing 4 circles and 5 circles, then counting how many total circles there are. We're just so used to addition and multiplication that they have become second nature. An analogy is that when we come across new math in our life, it requires effort to learn it, but after lots of using that math it becomes second nature. May 31 comment Probability of k out of m microbes splitting. My mistake: I've corrected my comment. May 31 accepted Probability of k out of m microbes splitting. May 31 comment Probability of k out of m microbes splitting. Remark:'the probability of having $m+k$ microbes in the $n+1$th generation given you had $m$ in the $n$th' is equivalent to 'the probability of $k$ microbes splitting and $m-k$ microbes disintegrating in the transition from the $n$th to the $n+1$th generations', because $(m-k)+2k=m+k$ May 31 revised Probability of k out of m microbes splitting. added 49 characters in body May 31 comment Probability of k out of m microbes splitting. Are you referring to the probability that k out of m microbes will split ? May 31 comment My son's Sum of Some is beautiful! But what is the proof or explanation? @hyg17 read this, it's worth your time! graphics8.nytimes.com/images/blogs/freakonomics/pdf/… May 31 asked Probability of k out of m microbes splitting. May 31 comment Find Probability that a player will win Nth match Here's a working link for Dilip Sarwate's broken link: courses.engr.illinois.edu/ece313/sp2009/Problems.html May 30 accepted Confusion regarding probability of microbe producing everlasting colony. May 30 asked Confusion regarding probability of microbe producing everlasting colony. May 25 awarded Talkative May 24 accepted What does it take to get a perfect score on the Putnam? May 24 revised Studying for the Putnam Exam fixed 'not all steps'