Micah
Reputation
242/100 score
 Sep 6 answered Difference between closure of A and A? Sep 4 answered Complex Numbers - Weird Equation Sep 3 revised Inequality $(\sum_{k=0}^{2n-1}x^k / k!)(\sum_{k=0}^{2n-1}(-x)^k / k!)\leq1$ for all $x\in\mathbb R$ added 3 characters in body Sep 3 revised Inequality $(\sum_{k=0}^{2n-1}x^k / k!)(\sum_{k=0}^{2n-1}(-x)^k / k!)\leq1$ for all $x\in\mathbb R$ deleted 21 characters in body Sep 3 revised Inequality $(\sum_{k=0}^{2n-1}x^k / k!)(\sum_{k=0}^{2n-1}(-x)^k / k!)\leq1$ for all $x\in\mathbb R$ added 7 characters in body Sep 3 answered Inequality $(\sum_{k=0}^{2n-1}x^k / k!)(\sum_{k=0}^{2n-1}(-x)^k / k!)\leq1$ for all $x\in\mathbb R$ Sep 3 reviewed Leave Closed some important proofs about adjoint operators Sep 3 reviewed Reopen Determining North-South Line Via Watch Method: Theory & Reason Aug 31 comment Why do both sine and cosine exist? In some sense, it's a kind of coincidence, but in another sense it isn't; the reason we care at all about parameterizing circles is precisely that they're symmetric, and the ability to express $\sin$ and $\cos$ in terms of each other is a consequence of that symmetry... Aug 30 reviewed Leave Closed How to calculate a, b, center of a ellipse with given bonding box of an arc Aug 29 comment Prove $\sin^2(\theta)+\cos^4(\theta)=\cos^2(\theta)+\sin^4(\theta)$ Yes. One of those factors is identical to the left-hand side; the other one should look familiar for other reasons... Aug 29 comment Prove $\sin^2(\theta)+\cos^4(\theta)=\cos^2(\theta)+\sin^4(\theta)$ You could factor either side, but factoring the right side will be helpful and factoring the left side will not. Aug 29 comment Prove $\sin^2(\theta)+\cos^4(\theta)=\cos^2(\theta)+\sin^4(\theta)$ Try it and see! What do you get when you factor the right-hand side as a difference of two squares? Aug 29 reviewed Approve Prove $\sin^2(\theta)+\cos^4(\theta)=\cos^2(\theta)+\sin^4(\theta)$ Aug 29 answered Prove $\sin^2(\theta)+\cos^4(\theta)=\cos^2(\theta)+\sin^4(\theta)$ Aug 28 reviewed Leave Closed Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$ Aug 28 comment Has anyone ever explored $(\sin{x})^x$ , $(\cos{x})^x$, etc? Even defining your integrand is problematic whenever $\cos x < 0$. And even if you restrict yourself to intervals where this doesn't happen, you'll get singularities at the endpoints when $x$ is negative... Aug 27 revised Is there anything wrong with this proposed proof of the irrationality of Euler's constant? texifying, cleaning up some typos Aug 27 reviewed Reopen Recurrence relation for ternary sequence Aug 26 comment Why is the solution of an ordinary differential equation required to be defined on an interval? I'll probably write an actual answer later when I have time unless someone else does, but the short version is: you want the solution's domain of definition to be connected, because if it isn't then the "differentialness" of the equation isn't very meaningful.