Is there a reason why a series of the form $1+2+4+8+16+...$ called a Geometric series and another of the form $1+3+5+7+9+...$ called an arithmetic series?
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 does a capacitor function in a 120V AC motor circuit? I don't understand the direction of current flow when a capacitor is wired in series with the start windings in, say, a fridge or other AC motor  running at/under 120V AC. Wiring diagrams seem to suggest that voltage energizes the hot leg of the circuit and current flows through the run windings and then returns via the neutral leg. Without a capacitor, the same thing would happen to the start windings. Problem there I guess is that both windings would be in phase and thus no spin created for the rotor. So, a capacitor is wired in series with the start windings which I kind of understand. But I don't know how the voltage and current behave. Does voltage energize the hot leg, flow through the start windings and then charge the capacitor? When voltage on the hot leg oscillates down to zero, does the capacitor discharge back toward the starter windings, or does current flow through the capacitor to the neutral leg? Basically I don't understand where the capacitor's charge goes when the hot leg is hot and when it is not. Lastly, is the capacitor placed between (downstream from) the start windings and neutral, or could it be wired between incoming voltage and the windings? I am new to linux, but had a question. I am getting in the business of buying old computers, putting Linux on them, then donating them to students who don't have their own computer at home. I have gone through and installed Xubuntu on my system, installed/uninstalled all the software that I want/need, and now want to know if there is a way that I could make an ISO of my system, and put it onto ANOTHER computer, and still have all of my tweaks, and programs ready to go after the ISO has installed. That way I don't need to go through and spend an hour or two on every computer.   What programs would you recommend for creating an ISO like this?   Thanks, Tobin How do I parse a string to a float or int? In Python, how can I parse a numeric string like "545.2222" to its corresponding float value, 545.2222? Or parse the string "31" to an integer, 31?  I just want to know how to parse a float str to a float, and (separately) an int str to an int. What metadata does a LibreOffice file contain and how to remove it? I have searched the web a lot and could not find an answer that fits my situation. Here are two links that are quite contradictory:       My situation:  I've visited Portugal in December 2012 for 29 days on a Schengen visa valid from December 1st, 2012 to February 1st, 2013 for research purposes (I am a Ph.D. student). I want to visit Sweden from February 10th, 2013 to May 10th, 2013 (89 days). I have applied for a Schengen visa again (for research). How will the 90/180 rule work in my situation? Inspired by  which states limb loss as a recurring theme, I started thinking about the final lightsaber battle. After watching The Force Awakens the second time, I was not sure if      Kylo Ren   lost a limb or just lost his lightsaber. We definitely see      Rey slash at Ren’s right hand.   So knowing that context:      Did Kylo Ren actually lose his arm/hand? Proof for two sequences producing the maximum value when sorted I am trying to improve my discrete Math skills by doing some proof exercises. But I am struggling to understand how to start proving the following hypothesis:  $$ S = {x}_1{y}_1 + {x}_2{y}_2 + \ldots + {x}_n{y}_n $$ Where ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are ordering of two different sequences of positive real numbers, each containing n elements. S takes its maximum value when ${x}_1,{x}_2\ldots{x}_n$ and ${y}_1,{y}_2\ldots{y}_n $ are sorted in non decreasing order.  I was thinking that I should maybe use a proof by contradiction. Where the negation of the hypothesis is: S takes it minimum value over all ordering of the two sequences when both sequences are sorted into non increasing order.  However I am not sure my negation of the hypothesis is correct or how proceed from there. I do not want the complete proof because I am trying to learn how to do it myself but if some one can tell me how to make a start on this I would be grateful. Objective-C: Use singleton vs. use class as an object? A girl who transcends time I remember quite a bit, but can't seem to find the title or (female) author.   A girl accompanies her father as he captains a mission to travel at near-light speed in order to experience the effects of time dilation and return to Earth 100 years into its future. She leaves behind her boyfriend (Tal or Tel or something), who promises he'll find a way to stay with her despite the time travel that will render him, well, dead before her return. She's accompanied by a close friend who is deaf but lip-reads and speaks so well as to occasionally fool others into believing she is hearing. They spend a lot of time in the ship's garden. I believe he ends up either getting on a different ship to survive into the future via time dilation, or else having himself frozen. Either way, if I recall correctly, Earth isn't doing well at all by the time the mission with the girl returns. There's been a war or some other disaster. There's an extended period of vague, ambiguous, existential crap in which the girl (now a woman) eventually ends up transferring her consciousness into her own daughter, presumably in order to go on living. Everything wraps up somehow and the girl and her boyfriend walk together hand in hand on a desolate planet into the sunset near the end of time.   It was all really rather trashy and silly, I remember, and took itself entirely way too seriously, but I'd like to at least know what it was so I could read it again. Either it'll be worth a laugh, or it'll turn out to be surprisingly good. Subtracting from a specific column Encrypt home drive after installation I declined to encrypt to my home drive whilst installing ubuntu.  Is it possible to encrypt it after installation?  if so, how? My case here is that I was writing something for school, and my teacher explained an error which I really can't see. She referred to articles about &quot;dangling participles&quot;, which was previously unknown to me. I find it hard to relate the examples I've found about it to my situation. So this is a text I've written and the bold part is where the problem arises: (You could read only the bold part if you please)  Wandering, and lost in his thoughts, there is a deep despair occupying the mind of this man. He is barely aware of his surroundings, except for those few moments when the loud blissful voices break through the protective barriers, developed by his immense sadness and grave frustration, into his mind. ”How can they all possibly be so happy?” he thinks to himself. Staring blindly, with his head low, as he walks in a slow pace, whispering ”Mary, Mary, my Mary,” over and over again. Yesterday was her funeral. She had passed away from a severe type of cancer, at a relatively young age. It was his wife. They had been together since high school and were greatly attached to each other. Having spent nearly half his life by her side, we cannot but imagine his grief. Indeed, he could hardly picture a life without her. So, alone he roams in the midst of all the seemingly incessant cheering and noises, drowned by his sorrow.  Her comments on that part was:  we is slightly out of place here – see my comment below These few sentences are about him and his emotions, so ‘we’ seems out of place. If the sentence starts: ‘Having spent nearly half his life by her side’, the reader expects it to continue: ‘he’. After all we have not spent half our lives by her side.  Is she right? If so, could anyone try to explain why? CPU Emulation and locking to a specific clock speed If you had read my other , you'll know I've spent this weekend putting together a 6502 CPU emulator as a programming exercise.  The CPU emulator is mostly complete, and seems to be fairly accurate from my limited testing, however it is running incredibly fast, and I want to throttle it down to the actual clock speed of the machine.  My current test loop is this:      // Just loop infinitely.     while (1 == 1)     {                         CPU.ClockCyclesBeforeNext--;          if (CPU.ClockCyclesBeforeNext &lt;= 0)         {             // Find out how many clock cycles this instruction will take             CPU.ClockCyclesBeforeNext = CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].CpuCycles;              // Run the instruction             CPU.ExecuteInstruction(CPU.Memory[CPU.PC]);              // Debugging Info             CPU.DumpDebug();             Console.WriteLine(CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].ArgumentLength);              // Move to next instruction             CPU.PC += 1 + CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].ArgumentLength;                                                 }     }   As you can tell, each opcode takes a specific amount of time to complete, so I do not run the next instruction until I count down the CPU Cycle clock. This provides proper timing between opcodes, its just that the entire thing runs way to fast.  The targeted CPU speed is 1.79mhz, however I'd like whatever solution to the clock issue to keep the speed at 1.79mhz even as I add complexity, so I don't have to adjust it up.  Any ideas? Recovering lost photos on iPhone 5s after restoring from iTunes backup I used to have an iPhone 4s and all the data from there is synced in my iTunes in my Mac. I just got an iPhone 5s yesterday and decided then to plug it to my iTunes. There was a welcome message and 2 options: whether to set up as new iPhone or set up as old iPhone (4s contents).  So to be able to make everything fast, I chose the latter, but then all the new photos in my iPhone 5s were deleted and were replaced with all the contents from my 4s. Is there any way I could retrieve it? Do I need a Japanese transit visa when arriving at Narita and departing from Haneda? How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$? We know that wizards in the Harry Potter universe are subject to regular physical harm (e.g. witness injuries from being hit by Bludgers or just colliding with things when playing Quidditch).  Therefore, it's almost a certainty that an average wizard would be vulnerable to, say, a bunch of bullets.   There may likely be spell(s) to protect from projectiles - witness Dumbledore's  deployed when Voldemort sent a bunch of glass at him during the  at the end of Harry Potter and the Order of the Phoenix (according to , possibly an unusually powerful Protego or the Silver shield).   But:   those spells obviously take effort/energy/time to cast (not everyone's Dumbledore) AND more likely than not most Death Eaters wouldn't recognize a Muggle gun for a threat (or realize what kind of threat) till too late.   So, the guns should at best allow an over-matched OotP member (e.g. Harry or Hermione) to greatly equalize the power between any regular Death Eaters and themselves, and even perhaps help against Voldemort (who can't be killed with a bullet, but, at best, would need to expend magical energy and time into conjuring a shield, and, at worst, be stopped/interrupted/driven off).  So I'm looking for an explanation - ideally in-universe, but possibly just some statement by JKR - of why the Muggle-born OotP - who are likely very much at ease AND familiar with Muggle technology and live in the late 20th century - do not use guns. Or, for that matter, ANY Muggle technology of the late 20th century? Cue Arthur C. Clarke's "indistinguishable from magic" meme.  Even if they are on some kind of idiotic moral crusade to never kill their opponents (even the Jedi aren't this dumb), given the time-frame, non-lethal weapons would have already existed, such as rubber bullets and tasers.  NOTE: Please don't offer the "if they do it, Death Eaters would start using guns as well" theory. First, Death Eaters would have used the guns if they knew how to, anyway. Second, the guns, like any "secret weapon", could be reserved for strategic battles, say the defense of Hogwarts in Deathly Hallows.    The origin of the question stems from two things.  First, Harry's fascination with all things that are different in the magical world (e.g. moving photographs), based on his knowledge of the Muggle material world, as well as the somewhat amusing cluelessness of the "Muggle artifacts" expert, Mr. Weasley, regarding Muggle items and how they work.   Basically, from the books, it's clear that the Wizarding world wouldn't know details about guns or what they are for or how they work.  The second thing is it's clear, at least initially, that wizards are afraid of Muggles finding out about them. Hence all the efforts to cloak their society (basically, do you REALLY want every Muggle gunning for you, even with Magic)? The idea of how control over the Muggle world seems to be more indirect, by Death Eaters asserting mind-control over the government. This means there's an implicit understanding by Death Eaters that they don't stand a chance against armed Muggles even given the magical disparity.  Considering Harry and Hermione's overall adaptability and inventiveness (and brains in the latter case), it's mind-boggling that the idea of fighting Death Eaters with modern technology completely slipped their mind. I mean, it's a basic part of human myth (see Steel vs. Magic themes in Conan books, or Beowulf, or heck, A Yankee in King Arthur's Court). So it's not like the idea of using technology against magic would be impossible to come up with. The question begs itself - why not? Considering the fact that Rowling generally tried to be logical and consistent in building the HP universe, I feel like there must be some in-universe explanation for this that I just didn't notice.   (in-universe answers only unless there are some authoritative out-of-universe statements that are part of canon). Thus is a picture of both of my hard-drives:    My C Drive and my D drive. I want to put Ubuntu onto my D Drive. Now my question here is if i do install onto my D Drive then how should I do it in order to retain use of the drive. I intend to partition about 60 gigs from it. Now after doing that I should still have about 830 gigs left. I want to still be able to use that in Windows. So how and will I be able to retain use of the drive after Installing? I have installed once before and I believe i did it wrong because not only could Windows not recognize my D drive but I also lost all the data on it.   My computer is a Lenovo Y700 It is a UEFI (I believe i got that right). Why can't ARIMA model large lags and/or long range dependence? ARIMA cannot model large lags (obtained from autocorrelation plot) and long range dependency (hurst exponent $H &gt; 0.5$). Why is it so? Ward model implementation: specular component too weak I'm trying to implement the Ward shading model, the anisotropic, computationally efficient version:       This is how I made it:    float alphaX=0.5, alphaY=0.5; // asinotropic roughness float minFloat= 1.e-6;   vec4 Ward(vec3 L, vec3 N, vec3 V) {     vec3 H= normalize(L+V);     float NdotL= max(dot(N,L),0.0);     float NdotV= max(dot(N,V),0.0);      vec3 e= vec3(1.0,0.0,0.0);     vec3 T= normalize(cross(N,e));     vec3 B= normalize(cross(N,T));     float HdotT= max(dot(H,T),0.0);     float HdotB= max(dot(H,B),0.0);     float HdotN= max(dot(H,N),0.0);      float beta= -2.0 * ( pow(HdotN/alphaX, 2.0) + pow(HdotB/alphaY,2.0) ) / (1.0 + HdotN);     float den= max(minFloat, 4.0 * pi * alphaX * alphaY * sqrt(NdotL * NdotV) );     vec4 specular= Ps * 1.0/den * exp(beta);     return (Pd + specular) * NdotL; }   But I get a result similar to a lambertian surface or Oren-Nayar model, where the specular component is absent: