Mathematics Weekly Newsletter - Friday, August 29, 2014

Top new questions this week: What is the average of no numbers? I have two programs that both behave nearly identically: they both take in any numbers you give them and can tell you the average and how many numbers were given. However, when you don't give them any … (average) (convention)   asked by Supuhstar 35 votes answered by Ittay Weiss 75 votes How to find ${\large\int}_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx$ Please help me to find a closed form for this integral: $$I=\int_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx\tag1$$ I suspect it might exist because there are similar integrals having closed forms: … (calculus) (integration) (definite-integrals) (logarithms) (improper-integrals)   asked by Oksana Gimmel 29 votes answered by Tunk-Fey 24 votes Disproving an "almost true" trigonometric identity The plausible looking "identity" $$\sin(\frac{\pi}{51})+\cos(\frac{\pi}{74})=\frac{3}{2\sqrt 2}$$ is not true, but it is close indeed: $$LHS=1.0606\color{blue}{598...}$$ … (trigonometry) (algebraic-identities)   asked by pew 22 votes answered by WimC 5 votes When does L' Hospital's rule fail? This thought jumped out of me during my calculus teaching seminar. It is well known that the classical L'Hospital rule claims that for the $\frac{0}{0}$ indeterminate case, we have: $$ … (calculus) (teaching)   asked by Bombyx mori 20 votes answered by JimmyK4542 15 votes What is the motivation for quaternions? I know imaginary numbers solve $x^2 +1=0$, but what is the motivation for quaternions? (soft-question) (math-history) (quaternions)   asked by zerosofthezeta 17 votes answered by Frunobulax 21 votes how to get $ f(x) $ if we know $ f(f(x))=x^2+x $ how to get $ f(x) $ if we know $ f(f(x))=x^2+x $ Is there elementary function of $f(x)$ satisfy the equation? (functions) (functional-equations)   asked by user694345 16 votes answered by lhf 8 votes Can one deduce whether a given quantity is possible as the area of a triangle when supplied with the length of two of its sides? Recently I have found a question like following: In triangle $ABC$, $AB=AC=2$. Which of the following could be the area of triangle $ABC$? Indicate all possible areas: [A] $0.5$ [B] $1.0$ … (geometry) (triangle)   asked by Khandaker Mustakimur Rahman 16 votes answered by mweiss 36 votes Greatest hits from previous weeks: Best book ever on Number Theory Which is the single best book for Number Theory that everyone who loves Mathematics should read? (number-theory) (soft-question) (big-list) (reference-request)   asked by Prasoon Saurav 80 votes answered by Moor Xu 68 votes How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen? So I'm tutoring at the library and an elementary or pre K student shows me a sheet with one problem on it: Put 9 pigs into 4 pens so that there are an odd number of pigs in each pen. I tried to … (arithmetic)   asked by zerosofthezeta 105 votes answered by Amzoti 176 votes Can you answer these? Is there a name for graphs with the following property? The property of the graph is the following: For any vertex, there is a hamiltonian path starting with this vertex, but the graph is not hamiltonian. The following graph is a small example: … (graph-theory) (terminology) (hamiltonian-path) (knight-tours)   asked by Peter 4 votes Handwaving gone wrong My motivation for this question is twofold: On one hand, I'm studying algebraic topology, where - at least in the book written by Hatcher - there is quite a lot of handwaving (e.g. maps are continous … (proof-writing) (examples-counterexamples) (big-list)   asked by Paul 5 votes Game involving points on $[0,1]$ You're given a list of $22$ points in $[0,1]$ (not necessarily distinct), and you're asked to select, at every iteration, $2$ points to be substituted by their midpoint. After $20$ iteration, you … (puzzle) (game-theory) (combinatorial-game-theory)   asked by Katy 9 votes New blog post: Binary quadratic forms over the rational integers and class numbers of quadratic fields. by Will Jagy on Aug 23 I wrote an article with Irving Kaplansky on indefinite binary quadratic forms, integral coefficients. At the time, I believe I used high-precision continued fractions or similar. It took me years to …

Subscribe to more Stack Exchange newsletters Unsubscribe from this newsletter or change your email preferences by visiting your subscriptions page on stackexchange.com. Questions? Comments? Let us know on our feedback site. If you no longer want to receive mail from Stack Exchange, unsubscribe from all stackexchange.com emails. Stack Exchange, Inc. 110 William St, 28th Floor, NY NY 10038 <3