What's geometric about a "geometric progression"? An arithmetic progression is $a+0b, a+1b, a+2b, ..., a+nb$ A geometric progression is $ab^0, ab^1, ab^2, ..., ab^n$. Multiplication is arithmetic, so why is a geometric progression not also an &quot;arithmetic&quot; progression? A line being extended be iteratively adding a constant length is a geometric construction, so why is an arithmetic progression not also a &quot;geometric&quot; progression?
Arithmetic and geometric sequences: where does their name come from? Where does the name of these two famous types of sequences come from?  The article  of Wikipedia says that the geometric sequence is called like this because every term is the geometric mean of its two adjacent terms. Though it is true, it only reduces the question to: why is the geometric mean geometric (in opposition to the arithmetic mean).   Continuing my investigation on , I was told that a square with the same area than a rectangle with sides $a$ and $b$ has their geometric mean $\sqrt{ab}$ for side. That's again totally true, but a square with same perimeter than this rectangle of sides $a$ and $b$ has their arithmetic mean $\frac{a+b}{2}$ for side!  Thus, my question: Who coined these names? And why? Why is the geometric mean more geometric than the arithmetic mean?
How to Avoid Precision Errors While Creating Numpy Arrays? Possible Duplicate:             What is correct? The jury was divided or The jury were divided? I am told that the latter is accurate because all of the jury do not have the same opinion in the particular case. Then, how does the subject verb agreement fit in 'The jury is still out' ? I mean, 'The jury is out' would allude to a situation were the opinion on a matter is (are?) still divided. There appears to be a poltergeist in my speakers (no, really) I've no idea if there's a suitable Stack Exchange for poltergeists. It appears to be software, hardware or virus related, so I thought I'd try here, seeing as Ghostbusters is just a film, so I can't call them.  I'm not going mad, and this isn't a joke.  There's what appears to be a radio stream coming out of my speakers, except I can only hear it when the volume knob is turned down to the min setting whilst the speakers are on, which makes no sense. Sometimes it's French, which also makes little to no sense.  The speakers are Logitech 5.1s, I forget the model number, and I'm running XP 64bit. If that makes a difference.  I'd suspect it could be some sort of crazy virus, but I've been randomly killing processes whilst the poltergeist is active and it hasn't killed it, so I'm not sure about that.  Once again, I'm perfectly sane and this really isn't a joke. Perhaps other people have had this problem but have been too afraid of the reaction to ask anyone (please don't have me committed to an insane asylum).  Googling for strange noises coming from speakers didn't really get me anywhere. Has anyone heard of a virus that can do this and affect the volume controls on the hardware in that way? Drawing text and line-dasharray Is it possible with TileMills and CartoCSS? How do I get powdered mammoth tusk? Am I missing something? I can find plenty of tusks, but I just don't know if I can make them into powder myself or do I have to find them for sale? How to solve "Extra junk at end of file" when using apt? I'm trying to configure some proxies for a guest virtual machine and now I'm getting:  sudo apt-get update E: Syntax error /etc/apt/apt.conf.d/95proxy:4: Extra junk at end of file   The content of the file is:  cat /etc/apt/apt.conf.d/95proxy   Acquire::http::proxy  "http://10.0.0.60:3128/" Acquire::ftp::proxy "http://10.0.0.60:3128/" Acquire::https::proxy "http://10.0.0.60:3128/" This question is a bit more subjective, but I'm hoping to get some new perspective.  I'm so used to designing for certain screen size (typically 1024x768) that I find that size to not be a problem.  Expanding the size to 1280x1024 doesn't buy you enough screen real estate to make an appreciable difference, but will give me a little more breathing room.  Basically, I just expand my "grid size" and the same basic design for the slightly smaller screen still works.  However, in the last couple of projects, my clients were all using 1080p (1920x1080) screens and they wanted solutions to use as much of that real estate as possible.  1920 pixels across provides just under twice the width I am used to, and the widescreen makes some of my old go to design approaches not to work as well.  The problem I'm running into is that when presented with so much space, I'm confronted with some major problems.   How many columns should I use?  The wide-format lends itself to a 3 column split with a 2:1:1 split (i.e. the content column bigger than the other two).  However, if I go with three columns what do I do with that extra column? How do I make efficient use of the screen real estate?  There's a temptation to put everything on the screen at once, but too much information actually makes the application harder to use.  White space is important to help make sense of complex information, but too much makes related concepts look too separate. I'm usually working with web applications that have complex data, and visualization and presentation is key to making sense of the raw data.  When your user also has a large screen (at least 24"), some information is out of eyesight and you need to move the pointer a long distance. How do you make sure everything that's needed stays within the visual hot points? Simple sites like blogs actually do better when the width is constrained, which results in a lot of wasted real estate.  I kind of wonder if having the text box and the text preview side by side would be a big benefit for the admin side of that type of screen? (1:1 two-column split).   For your answers, I know almost everything in the design is "it depends".  What I'm looking for is:   General principles you use How your approach to design has changed   I'm finding that I have to retrain myself how to work with this different format.  Every bump in the resolution I've worked through to date has been about 25%: 640 to 800 (25% increase), 800 to 1024 (28% increase), and 1024 to 1280 (25% increase).  However, the jump from 1280 to 1920 is a good 50% increase in space--the equivalent from jumping from 640 straight to 1024.  There was no commonly used middle size to help learn lessons more gradually.    To help focus the question a little bit, I had a project that was somewhat similar to Atlassian JIRA, an issue management system.  There were about six different types of records the client wanted to keep, all of them could potentially be related to each other.  Gathering data wasn't the core problem, although it did play a part.  The more important side of the problem was creating a system which would suggest potential relationships between the records and helped the analysts recognize patterns in the reported incidents.  There were different types of analysts that focused on the different problem domains, and due to the nature of their exploratory type of work, they didn't know what they wanted.  They just knew they had to make sense of a lot of data, draw correlations, and characterize classes of issues.    (Originally asked here: , but told that this might be more appropriate)    For the bounty: Stretch your minds a bit.  The pat answer "Make everything bigger" has a limit to how useful the answer is.  We are talking about users who have to make sense of a lot of data and find relationships between records.  If I simply bump up the size on everything they are going to be very limited in what they can see on the screen--particularly because the vertical is so constrained. Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$. Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.  So $(a^2+b^2)(c^2+d^2) = a^2c^2+a^2d^2+b^2c^2+b^2d^2$  and $(ac+bd)^2 = a^2c^2+2acbd+b^2d^2$  So the problem is reduced to proving that $a^2d^2+b^2c^2\ge2acbd$ but I am not sure how to show that List sorting by custom field I dont know how to sort a list of SObject Case.  I have a List&lt;Case&gt; newCases which i iterate over in for cycle, where i save Cases to my new List&lt;Case&gt; casesList.  for (Case newCase : newCases) {             if(newCase.Case_Content__c == '111' &amp;&amp; newCase.Status == '24'){                 String cuid = newCase.CUID__c;                 cuidSet.add(cuid);                 casesList.add(newCase);                 casesList.sort(); //TODO sorting by CUID__c             }         }   What i need to do is, to sort this new list by field CUID__c. So the Cases with same CUID are together.  Thank you for any help :) I want to turn my system on automatically every day. So I use the below code in my Python script, but sudo asks me for a password every time:  os.system('sudo sh -c "echo date \'+%s\' -d \'+ \        24 hours\' &gt; /sys/class/rtc/rtc0/wakealarm"')   How can I run this script without sudo asking for the password every time? Windows Subsystem for Linux (WSL): what can't I do with the Ubuntu application for Microsoft Windows? Suppose we have a magnetic field directed into the computer screen. Assume that there is no gravitational field. Now suppose we have a stationary positively charged particle in the magnetic field. The magnetic force is given by $$\mathbf{F}=q\mathbf{v}\times\mathbf{B}$$  Since $\mathbf{v}=0, \mathbf{F}=0$.  Now pick a reference frame moving to the left with constant velocity. In this frame, the particle is moving to the right with constant velocity. So, the magnetic force is directed upwards.  From what I've learnt in physics, forces are independent of choice of reference frames as long as the frames are inertial. But in the 2 inertial reference frames I have chosen, I get 2 different magnetic forces. How do we reconcile this? At what point is the ~/.bashrc file created? What's the difference between Kage Bunshin no Jutsu and Tajuu Kage Bunshin no Jutsu? While the Kage Bunshin no Jutsu seems to be taught, the Tajuu Kage Bunshin no Jutsu is sealed, so nobody can learn the jutsu. Does that mean that there's a difference between these jutsus, aside from the number of Kage Bunshin created?   Or, why was the Tajuu Kage Bunshin no Jutsu sealed away? If there's no other difference, everybody could use this without reading the sealed scroll. Repeat copies of array elements: Run-length decoding in MATLAB It has come up in game a couple of times that a player might want to cast a spell that has a casting time of 1 bonus action using their "main" action (if they have another bonus action they also want to take on that turn, such as giving bardic inspiration, or controlling a Bigby's hand, etc.)  On the face of it, it seems obvious that something (a bonus action) that is usually much faster than a full action could be done as your full action.  Although the question comes up most often with respect to spellcasting, if I house rule this, I would rule that any bonus action can be taken as a regular action instead; however, I would not allow the same type of bonus action to be taken twice (so no giving bardic inspiration to two allies on the same turn, for instance).   Are there any abusive or overpowered combinations I should be wary of if I were to allow a character to take 2 bonus actions instead of one regular action and one bonus action on a turn?   The issue of casting two bonus-action spells would not come up because the rule against casting 2 spells on your turn unless one of them is a cantrip with a casting time of 1 action would still be in effect:  PHB p. 203 (under Bonus Action casting time)     You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.   I know it's hard to prove/justify a negative answer to a question like this, but I'd be happy to get answers that say you don't think there would be any issues if you describe how you came to that conclusion. 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. What is the difference between "I've been to China" and "I've gone to China"? Both are in the present perfect, but one uses the verb 'to go' and the other 'to be'. Is there a rule for this?  Is there any chance that the differences between "I have been" vs. "I have gone", are differences in English dialect (I don't know if this is the right word).  Edit Could I say that North American English speakers use "I have gone", and maybe U.K speakers say "I've been"? Or vice versa. Why are packages in the official Ubuntu repositories older than the latest (upstream) versions from Debian Sid, PPAs, the authors, etc.? How do I check to see if a column exists in a SqlDataReader object?  In my data access layer, I have create a method that builds the same object for multiple stored procedures calls.  One of the stored procedures has an additional column that is not used by the other stored procedures.  I want to modified the method to accommodate for every scenario.  My application is written in C#.