A voltmeter is connected in parallel across the load. Why?
Why are ammeters used in series and voltmeters in parallel?
How do I delete one of two Ubuntus on my PC Frequency of the sound when blowing in a bottle I'm sure you have tried sometime to make a sound by blowing in an empty bottle. Of course, the tone/frequency of the sound modifies if the bottle changes its shape, volume, etc.   I am interested in understanding how the tone/frequency of this sound can be (approximately) calculated from the shape of the bottle. Is there some formula?  If you have any references about this please post them in your answers.  Being a mathematician I keep hearing that the principal tone is given by the first eigenvalue of the Laplace operator, and I'd like to understand the physical explanation. How to calculate the integer part of the value of the following equation?  $$y=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\ldots+\frac{1}{\sqrt{1000000}}$$  It should be calculated in a special way, after all the equation is so long. What is the difference between convolutional neural networks and deep learning? What are the shell's control and redirection operators? How many complements are in "I ask you to clean the room"? How many complements are needed in the below sentence?     "I ask you to clean the room."   This sentence above has one complement or two complements? Firefox application associations not working in the 'Downloads' window How can I find the difference between two angles? 'The average person' or 'an average person'? Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$ More Question Filtering options I realize that this may be a big request, but...  I think that instead of tabs on the recent question activity pages, or more likely as a new tab, adding a more advanced filtering option.  For instance, being allowed to exclude tags, filter by accepted answers or not, and, most importantly, being able to combine multiple filters!  E.g.: Filtering posts with tag Javascript without tags Jquery and AngularJS with no accepted answers and a score >= 0.  I feel like this is a biggish change that, if implemented as a new tab, wouldn't be that hard to implement, but would be very useful. Set the default permission when creating a file Retrieve Windows 8 Product Key from mainboard My new laptop came preinstalled with Windows 8. Naively, as I am, I just formatted the harddrive and installed fine old Ubuntu. Now I want to install Windows 8 for dual boot again, but I have no DVD and do download the ISO one needs a product key. That key is not on the back of the laptop anymore but somewhere on the mainboard.  Is there any way to recover the product key from the mainboard using Ubuntu? How to add http:// if it doesn't exist in the URL Bash built-ins with no manual entries For any natural number $n\ge 1$, given pairs $(a_1,b_1),(a_2,b_2),...,(a_n,b_n)$ of integer numbers, there exist integer number $c$ and $d$ such that  $$\prod_{i=1}^{n}(a_i^2+b_i^2) = c^2+d^2$$    My initial approach is  Base Case: $(a_1^2+b_1^2) = a_1^2+b_1^2$ which is true. (Although it is trivial)  Prove the statement is true when $n=2$: We have $$(a^2+b^2)(c^2+d^2) = (ac-bd)^2+(ad+bc)^2$$ (Thanks André Nicolas for pointing it out)   So if $a,b,c,d$ are integers, $ac,bd,ad,bc$ are all integers and integers are closed under addition and subtraction. Hence $(ac-bd),(ad+bc)$ are integers.   Inductive Hypothesis: $\prod_{i=1}^{n}(a_i^2+b_i^2) = c^2+d^2$ is true  Inductive Step: $$\prod_{i=1}^{n+1}(a_i^2+b_i^2) = \prod_{i=1}^{n}(a_i^2+b_i^2)\cdot (a_{n+1}^2+b_{n+1}^2) = (c^2+d^2)\cdot (a_{n+1}^2+b_{n+1}^2)$$  Where $c$ and $d$ are integers.   But when we apply $n=2$, we have  $(c^2+d^2)\cdot (a_{n+1}^2+b_{n+1}^2) = (e^2 + f^2)$ where $e$ and $f$ are integers.  Hence, by the principle of induction, the statement we needed to prove is true. Why Wi-Fi is getting turned-on automatically in iOS 11 Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +) Ubuntu on a USB stick - boot in both BIOS and UEFI modes Limit of ${a_n}^{1/n}$ is equal to $\lim_{n\to\infty} a_{n+1}/a_n$