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• Today, 10:41
Here is this week's POTW: A charge $-q_1$ is located at the origin of a $y$-axis and a charge $-q_2$ is located at $y=d$. At what point along...
0 replies | 9 view(s)
• Today, 10:40
Congratulations to the following members for their correct submission: kaliprasad My solution is as follows: For the entire system...
1 replies | 50 view(s)
• Yesterday, 15:53
mathmari replied to a thread Open cover in Analysis
I think that it holds that there is for every $n \in \mathbb{N}$ an $0 < x < 1$ such that $\frac{1}{n} \in \left(\frac{x}{2},\frac{3x}{2}\right)$,...
3 replies | 48 view(s)
• Yesterday, 15:42
Hello and welcome to MHB! :D We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This...
1 replies | 59 view(s)
• Yesterday, 14:43
mathmari started a thread Open cover in Analysis
Hey!! :o Let $\mathbb{R}$ provided with the metric $d(x,y)=|x-y|$. I want to check if the collections of sets S_1=\left \{\left (\frac{x}{2},...
3 replies | 48 view(s)
• Yesterday, 09:31
I like Serena replied to a thread Right triangle. in Geometry
Google translates triangle as sankakkei. And searching for sankakkei shows that this word is also used for a three dimensional puzzle of triangles....
19 replies | 193 view(s)
• Yesterday, 00:37
Here is this week's POTW: ----- Suppose $f$ is analytic on a simple closed contour $c$ in the complex plane. Prove $\displaystyle\int_c... 0 replies | 34 view(s) • Yesterday, 00:31 Opalg gets honorable mention for his near perfect solution. Since his overall argument is solid, I’ll post his solution below. Just note that in... 2 replies | 123 view(s) • April 24th, 2018, 13:16 Hi Tony. I recommend you read up on our guidelines for posting challenge problems, found here. 1 replies | 47 view(s) • April 24th, 2018, 07:48 Not just for the next term, but for the whole sequence! In fact, your prediction and mine both say that the$(n+1)$th term minus the$n$th term is... 9 replies | 141 view(s) • April 24th, 2018, 06:54 My own best guess was to look at the differences:$\frac 13, \frac 16, \frac 1{10}$. The next difference might be$\frac 1{15}$, although it does... 9 replies | 141 view(s) • April 24th, 2018, 06:37 Hi hm2018April, and welcome to MHB! Mathematicians hate problems like this, because there usually isn't a single, "correct" solution. You need to... 9 replies | 141 view(s) • April 24th, 2018, 06:14 Can you give us any idea where the series comes from? Technically the next term in the series could be argued to be anything. -Dan 9 replies | 141 view(s) • April 24th, 2018, 03:57 Hello hm2018April and welcome to MHB! :D We ask that our users show their progress (work thus far or thoughts on how to begin) when posting... 9 replies | 141 view(s) • April 23rd, 2018, 15:52 I like Serena replied to a thread Special Relativity in Physics It's the other way around. 11 replies | 135 view(s) • April 23rd, 2018, 15:26 I like Serena replied to a thread Right triangle. in Geometry For the record, something like that is called a sangaku. A drawing that exhibits a proof, without any words, expressions, or symbols. Admittedly my... 19 replies | 193 view(s) • April 23rd, 2018, 15:04 I like Serena replied to a thread Right triangle. in Geometry You mean just drawings? (Wondering) Something like this: \begin{tikzpicture} %preamble \usetikzlibrary{arrows} \def\a{sqrt(17)} ... 19 replies | 193 view(s) • April 23rd, 2018, 13:37 I like Serena replied to a thread Right triangle. in Geometry To be honest, I only used trigonometry because it means I have to use fewer words to explain those ratios! (Rofl) 19 replies | 193 view(s) • April 23rd, 2018, 13:20 I like Serena replied to a thread Right triangle. in Geometry Trigonometry is only used in the first step. We can replace it with non-trigonometry by observing that triangles ABC and ACD are similar, meaning... 19 replies | 193 view(s) • April 23rd, 2018, 12:55 I like Serena replied to a thread Right triangle. in Geometry Let's make a drawing: \begin{tikzpicture} %preamble \usetikzlibrary{arrows} \def\a{sqrt(17)} \def\b{sqrt(68)} \def\c{sqrt(85)} ... 19 replies | 193 view(s) • April 23rd, 2018, 09:13 I like Serena replied to a thread Special Relativity in Physics Indeed, the distance travelled is$v\Delta t' = 240\text{ lightyear}$. So we have$\Delta t' = \frac{240\text{ lightyear}}{v}$and$\Delta t =...
11 replies | 135 view(s)
• April 23rd, 2018, 08:57
Let $A = \begin{bmatrix}0&1\\1&1\end{bmatrix} = \begin{bmatrix}\varphi_0&\varphi_1\\ \varphi_1&\varphi_2\end{bmatrix}$. By induction, \$A^n =...
2 replies | 64 view(s)
• April 22nd, 2018, 22:40
topsquark replied to a thread Special Relativity in Physics
So what we have here is \Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}} where \Delta t' is measured by the observer's clock and \Delta t...
11 replies | 135 view(s)
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