text:
Nailers Ready to Begin 21st Season in Wheeling
By SHAWN RINE
Sports Editor
WHEELING – First-year coach Clark Donatelli says his team is going to play hard, fast and physical. Coming off back-to-back playoff appearances, the Wheeling Nailers would like nothing better than to take home the ultimate prize during the 2012-13 season.
The annual ritual that is the chase for the Kelly Cup, begins Saturday night in Cincinnati.
"You'll see guys working hard, finishing their checks, doing the little things," Donatelli said. "Mostly I want our stamp to be that we're a really hard team to play against – a hard-working team.
"We'll work really hard in our own zone and breaking out of our own zone."
The NHL lockout presented its sets of challenges for Donatelli and first-year pro assistant Zach Sonnefeld in terms of choosing the roster. They settled on two goaltenders, six defensemen and 15 forwards. Of that 23-man roster, 13 came down from the American Hockey League.
"The trickle-down effect with the NHL lockout, and each team I want to say there's 3-7 guys pushed down from the NHL, so 3-7 guys have to go to the ECHL which makes it a lot better and it's more competitive," Donatelli said. "It's good for the league and good for the Wheeling Nailers.
"Fans should come on down and watch us because you're going to get to see some really good prospects from Pittsburgh and Montreal."
It's apparent the vast majority of these guys would no be here if not for the work stoppage, but Donatelli insists there won't be any egos and promised there will be absolutely no special treatment.
"If they're working hard we will be able to live with the mistakes," the coach said. "As long as the effort is there and they're working hard, then we will be fine.
"If not, guys won't play and it will be that simple."
The higher-end talent that will partake in the league this year will make special teams even more important. Donatelli said this group has the ability to excel in the current climate.
"It's more the penalty killing. They're going to have to be in the shot lanes and block shots," Donatelli said. "You can't get away with cheating a little bit. If you're off by 6 inches the puck is going to be in the net.
"And one-touches are a must. You've got to get the puck down the ice – you can't fan on it and you can't not get it off the glass."
Charged with doing that will be a mixture of returnees and some newcomers. Adam Ross was acquired in a trade at midseason last year, while Peter Merth is starting his third season in Wheeling. Joe Stejskal is a former fifth-round pick of the Canadiens, Paul Cianfrini came over in an offseason deal with Toledo and Wild was in camp with Wilkes-Barre/Scranton.
McNeill, a sixth-round pick of the Penguins in 2010, is thought to have the most upside.
"I think our 'D' core, I am happy with it," Donatelli said. "You look at the 'D' core with the forwards, and they have to work as a unit of five.
"Our defense has to finish its checks, come back and track and come down low with support.
"I think they're tough and we've got some really good, stay-at-home-defensemen."
That group will be tasked with helping goaltenders Patrick Killeen (6-foot-4), who like Merth has already played two years in Wheeling, and Scott Darling (6-6) keep the puck out of the back of the Nailers net.
"They're both very capable of doing the job," said Donatelli, who noted there's still a chance Wheeling will see a goaltender – likely Peter Delmas or Robert Mayer – sent down from Hamilton. "They take up a lot of room and they move well.
"We're very fortunate that we have two good goalies here."
Scoring shouldn't be an issue.
Chris Barton is back after scoring 33 goals last season en route to being named to the ECHL All-Rookie team. He's joined by holdovers Paul Crowder, Cody Chupp, Ben Farrer, Zack Torquato and Cam Fergus.
Tom Kuhnackal (fourth round in 2010) and Dominik Uher (fifth rounder in 2011) are Penguins prospects with bright futures. Adam Payerl showed some grit while in Wilkes-Barre camp, while Bobby Farnham did the same with Hamilton.
Ian Schultz (6-2, 200), a former third-round pick by St. Louis is thought to be the team's thumper, though he has a game to go with his brawn. Stefan Chaput, a fifth-round selection by Carolina in 2006 has spent parts of the last five seasons in the AHL with various teams, while Phillipe Lefebvre jumped straight from the Quebec Major Junior Hockey League to the AHL with Hamilton last season.
Steve Zurevinski scored 47 goals in his college career at Quinnipiac, while the wild card could be Daultan Leveille, a former No. 1 pick by the Atlanta Thrashers in 2008. He spent the last four years at Michigan State.
"They've been playing the game a long time so we're just going to put our system in play," Donatelli said. "I'm sure they've played some form of it, so let the hockey sense take over.
"You've got to work hard, but you've got to work smart. The best guys, comparing them to guys in the NHL, are usually the hardest workers on the team. If you have a lot of skill, that's not going to get you there. You've got to have the work ethic to go along with the skill level."
This team came together slowly in the preseason, so fans might have to be a little patient as the parts get pieced together. One of the good things, according to Donatelli, is the Nailers open with four straight games on the road so it will give guys a chance to get to know one another a little better.
"I think it's a good thing because the guys are going to be living together and we'll be in the hotels and watching a lot of film," Donatelli said. "We'll be teaching them a lot and there won't be any distractions.
"They will already be moved in here so we will have their undivided attention on the road.
"I think that's going to be a plus because we're going to go into some hostile environments and it's going to be their opening nights. So we're going to have to be patient and weather the storm and come out and push the pace. But that is all part of the learning experience, and I anticipate us having a really good start."
Defenseman Zach Hansen will join forwards Peter Lenes and Christiaan Minella on injured reserve to start the season.


text:
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subset: commoncrawl


text:
Cold corporate Robot claws?
After 3 years, and $16K worth of purchases, I must say goodbye to Woot. While Woot used to be a nice friendly place, with funny notes, and decent support from above, Amazon has turned it into a money grubbing machine, that no longer appears to care about anyone.
Why would I say such a thing about everyone's beloved woot? Simple, I had to contact Customer service. Now, let me make some distinctions here. When I say Customer Service, I do not mean the forum mods, I mean the random drones who I waste time sending Email to, but never get replies from the same person. This does not build my confidence that when it comes time to get my refund on the item I don't want, that they'll be able to follow through, or even agree to the terms set forth by random name on Email stamped as random case number whatever.
This isn't just a giant rant, albeit I'd love nothing more than to rip into the soft underbelly of this abomination. instead, I offer constructive criticisms in the next few posts.
11 Answers answer
First. Ownership.
When I send an Email to Customer service, I expect a random person to answer the first one. I expect it to be given a random tracking number so they can follow it, and then I expect the same random number and random person to continue replying to my chain of replies. Instead, I have half a dozen case numbers, handled by a half dozen different people. If I wanted to talk to 3 dozen different people and get nowhere, I'd call my cable company.
Second. personal touch.
The replies I recieved in my Email co-respondance seemed annoyed that I would take time out of their day to ask for assistance. My point? neither Woot, nor the shipper showed that the TV had shipped yet. At the least, the TV was still in the originating state. Instead, the solution presented was "you could just refuse delivery, and when the TV comes back, we could refund it" No reply I recieved contained more words than I can count on fingers and toes.
Third. Some form of contact besides 8 hour delay Email.
It took me 2 1/2 days of waiting on Emails from woot. I may as well have been droping a letter at the post office. This gets back to the issue of Ownership, and having an issue handled by a single individual, instead of a random person every time. If one person were working with a single person until the issue were solved, there wouldn't be a 5 to 12 hour turn time on replies. I realize we'll never get a telephone number, but what about a LiveChat option? This site is open 24 hours a day, is it too much to ask for someone to be here at night?
Fourth. Stop censorship.
The thing that has me most pissed off is the fact Woot began summarily censoring all of my posts out of existance. Sure, my posts were somewhat inciteful, and angry, but at that point, I felt I had no other direction to turn, since customer service had already given me the rubber glove treatment, and told me to sit and spin. Anytime someone begins to post inflamatory things about your company, its because there is a serious problem that is not being addressed. If you don't like how pissed someone is, perhaps you should find the root problem, and fix the issue.
Woot took forever to ship me a 55 inch TV, I went looking for answers, found out it is not actually a 120Hz TV, title on the TV got changed after I bought it, I requested order get cancelled, Customer service told me to screw off, then eventually told me to wait until delivery, refuse it, then wait for a refund when they get the TV back.
I have worked in a tech support/customer service position for the last 5 years, and the behavior exhibited is a great way of losing long time customers.
Sorry to hear about your experience, I have passed on your feedback to the appropriate parties though so they may read through it and take action as needed to improve our customer experience.
(I know that sounds a little robo-mod, but it's all I can do.)
Honestly, this is Woot's MO, from day one. It was a known risk buying something from Woot that if something went wrong, you were SOL. There was no Customer Support or the like. The fact that you can actually e-mail someone, and get a response now, is amazing to me.
Oh, and stop throwing Amazon in there, Amazon has nothing to do with the daily business of Woot. In fact, Amazon has amazing Customer Service, so blaming them makes zero sense.
I'm not saying that your position doesn't suck, but this is also nothing new.
I'm with you. I had a bad customer service experience and was treated like an idiot, even though in the end I was correct and everything that I was being told was not true or accurate. It really soured me on Woot. I've stopped participating and have made one purchase to use up a lingering Jumbowoot coupon, but I'm pretty much done here. It's too bad, it didn't need to be this way. I think the final straw for me was when I posted a thread about it, other Woot users immediately jumped to conclusions and sided with Woot. Nevermind that if any other vendor on the Internet had done the exact same thing, I know for sure that no one would have been defending their actions. But, that's the way it goes.
@inkycatz: At this point, that is all I really hoped would happen with this. I can no longer justify the risk of something going wrong for an average savings of 3% to 10%. I thank you for my Dyson, my Razer mice, my Steel series Siberia headphones, and my wardrobe of American made T-shirts.
So long, and thanks for all the fish.
@waltertangofoxtrot: I replied to your other post too, but I wanted to give you a heads up here too. We've arranged to have the TV recalled and a full refund has been issued. Sorry again for all the issues.
I feel the need to step in and say that I have personally, luckily, never experienced an issue that was not resolved in a timely, customer-service oriented manner. I am so sorry, OP, that you feel the way that you do. Really, $16K? WOW
I have had only positive experiences with service, but I've never had problems beyond a misprinted shirt or a package that wasn't delivered. However, reading though the threads for a few of the recent TV sales, it seems like things got pretty messed up, largely because woot was only the intermediary between buyer/customer and totally-incompetent-drop-shipper. Woot, as a corporation, seems to be allergic to saying, "We're sorry, we really screwed up and we're going to learn from this." I don't blame service or the mods for being unable to say that, because it's coming from people above them, but I wish the folks in charge of corporate culture would learn the value of admitting that things went wrong. I think service does the best they can, but I suspect they're vastly overworked/understaffed, and their hands are tied much of the time with the new-ish drop shipping.
@waltertangofoxtrot: It's hard to leave a place that means so much to us. Godspeed.


text:
Small Firms Plan for Stronger Economy
Despite looming federal spending cuts, higher tax rates and rising health-care costs, small-business owners were more optimistic this month about the future state of the U.S. economy.
More than a third, or 35%, of owners said they expect the economy to improve in the coming year, according to a survey fielded from Feb. 4 to Feb. 13.
That's a significant boost from the 20% of owners who held that opinion in November and the 26% who said so in January.
In addition, only 16% say the economy will weaken in the year ahead, a major drop from the 43% who expected a weaker economy three months ago.
The responses from business owners in February represented the most positive outlook amongst business owners since the survey began last June.
The survey's "confidence index," which accounts for all the outlook components in the survey, shot to all-time high of 101.4. The initial June 2012 survey set the index at 100.
By comparison, last month's confidence index was 94.2, and the lowest reading, in November, was 83.9.
"Their confidence wasn't shaken by continuing public-policy debates," says Richard Curtin, an economist at the University of Michigan, who analyzed the results. "They expect the upward momentum of the economy to outweigh those concerns."
The findings are part of The Wall Street Journal/Vistage Small Business CEO Survey, a monthly economic indicator that takes the pulse of businesses that have less than $20 million in annual revenues.
Anticipating a stronger economy, small-business owners are making plans to take advantage of the upswing.
Seven in ten owners said they expect their sales to increase in the coming 12 months. They are also expecting greater profitability.
As a result, owners also are looking forward to having resources to hire and purchase assets like vehicles and equipment to grow their firms. Slightly more than half of owners say employment at their firms will increase, up from 47% in January. And 39% anticipate upping their investments in expenditures in the next 12 months, up from 32%.
The monthly survey, conducted jointly by the Journal and San Diego-based executive-mentoring group Vistage, polled 848 small-business owners from a variety of industries. It has a margin of error of plus or minus 3.5 percentage points.


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I was wondering why C++ is a good choice to write a compiler. Of course C is good for this purpose too, because many compilers are written either in C or C++ but I am more interested in C++ this time. Any good reasons ? I was looking for that in the Internet, but I cannot find any good reasons.
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C++ has two sides to it. It has a low-level development side which makes it seem like a natural language for doing low level thing like code generation. It also has a high-level side (which C does not) that lets you structure a complex application (like a compiler) in a logical, object oriented way, while still maintaining performance. Because it has both the low and high level aspects to it, it's a good choice for large application which require low-level features or performance.
My experience does not agree with your premise here. In fact, for high-level general-purpose languages, it is a very common practice to write the compiler in the same language as the source language (the language being compiled). For example:
An exception is compiler front-ends written for existing compiler frameworks, such as GCC, LLVM or Polyglot, which are then written in the framework's language, or compilers that rely on existing parser generators such as Yacc. Since GCC, LLVM and Yacc are common, established tools written in C and C++, it gives an incentive to compiler writers to use them, which might lead to C and C++ getting a large share in the compiler implementation language distribution.
I tend to question the basic premise here. While C and C++ work perfectly well for writing compilers, quite a few other languages seem to work perfectly well for the task as well.
A bit depends on the language you're compiling though. For small, simple languages, C and Pascal work quite nicely. If you're going to compile something big and complex, your compiler gets big and complex too -- in which case, C++'s extra features for organizing and working with larger programs obviously come in handy. That isn't really very specific to compiling though, just features useful for larger programs in general.
I think it's also worth mentioning one other point. Beginners (seem to) think of compilers as mostly doing text manipulation, so they think something like Perl will be a massive help in writing compilers. In reality, most of the interesting parts of compilation don't really start until after you've built your AST. While I'm sure Perl can do the job perfectly well, its text manipulation capability doesn't really give it a huge advantage either (text manipulation is mostly in the lexer, and lexer generators for things like C all support REs anyway).
Compilers may be implemented in any modern language. However, one of the most important requirements from a compiler is to be fast.
C++ has a clear advantage here. Optimization in C++ does not come cheap. However, due the the low-level nature of this language, it is possible to manually optimize C++ code more than in any other language (except Assembly which is not portable).
To compile what to what? A compiler transforms a source code from one language (source language) to another (destination language), which doesn't indicate anything about the low-levelness of the destination language.
The language you pick to write a compiler depends on the context. For example, working on a project which compiles a language derived from PHP to a native PHP code, I used a mix of PHP and C# to write the compiler, because it made the most sense for me given my skills. Another person would pick Python, or Java and PHP, or C++ with a bit of JavaScript, or whatsoever.
C or C++ is a popular choice because of the support of compiler related tools (see the answer by Telastyn), and because those two languages allow you to go really native. But there is nothing wrong in choosing another language.
Note that in order to be more geeky, you may pick the source language to write the compiler itself. It's what happened for CoffeeScript compiler and many other compilers. It is also popular with the IDEs: one of the first Visual Studio was built using the same Visual Studio.
I suspect that the prime motivator for their use is that Lex/Yacc/Bison output is (primarily) in C. Since that's been the standard for so long, it has momentum.
Not that those are particularly good reasons...


text:
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On March 2, Public Campaign Action Fund and the League of Conservation Voters criticized several U.S. House members for voting against a measure that would've temporarily ended wasteful and unnecessary taxpayer subsidies for oil companies. The members--both Democrats and Republicans--all took tens of thousands of dollars in campaign contributions from oil and gas interests during their time in Congress.
The press release for each of the members criticized is below:
Public Campaign Action Fund
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email@example.com | (P) 202.640-5600 | (F) 202.640.5601


text:
News Release (Back to Menu)
Rutgers Students to Provide Legal Representation for Essex County Voters Challenged at the Polls on Election Day
October 15, 2008 –On Election Day, Tuesday, November 4, Essex County voters who believe that their right to vote has been unfairly denied can get legal assistance from students at Rutgers School of Law–Newark. "I fully expect that the record surge in new-voter registrations during this election cycle will exert pressure on the already under-staffed and over-burdened system and cause problems for many County residents at their polling place," said Professor Frank Askin, director of the law school's Constitutional Litigation Clinic, who has supervised the Voter Assistance Project for more than a quarter century.
In conjunction with his Election Law Seminar, Askin has recruited dozens of Rutgers law student volunteers who, under the supervision of faculty, will offer free legal representation to Essex County voters who are turned away at the polls.
Professor Askin advises that any Essex County resident who believes that he or she has been wrongly rejected at the polls should first report to the Commissioner of Registration at the Essex County Hall of Records at 470 Martin Luther King, Jr. Boulevard, Newark. Rutgers law students who have volunteered for the Voter Assistance Project will be at the courthouse to represent voters seeking a court order permitting them to cast a ballot. All representation will be conducted pro bono and on a non-partisan basis.
According to Professor Askin, the most common reason that potential voters have to see a judge is that their voter registration forms got lost and, therefore, their name was not on the books at their intended polling place. "If a judge is satisfied that the applicant made a 'good faith' effort to register, then a judge may give that person an order to vote," he explained. Essex County will have 16 judges assigned to Election Day duty this year.
Professor Askin also suggested that newly-registered persons take their sample ballots with them when they go to vote.
For more information about the Voter Assistance Project, contact Professor Frank Askin at 973-353-5687.


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Ah. George, you should have thought about that. I understand your eagerness to share this exciting news, but perhaps an April-1st announcement detracted from the seriousness of this grand development.
Here's another desirable MPI feature. People talk about "error detection/correction". We should do that in MPI. Decide what the user *meant* to do, and do that "under the hood" rather than what they actually programmed. Now, *that* would be a competitive advantage! (E.g., I'm spending a lot of time trying to get good latency measurements... why can't OMPI just detect that and give me good latency measurements!)
Anthony Thevenin wrote:
does anymone think of an April fool's day???
George Bosilca wrote:
The Open MPI Team, representing a consortium of bailed-out banks, car
manufacturers, and insurance companies, is pleased to announce the
release of the "unbreakable" / bug-free version Open MPI 2009,
(expected to be available by mid-2011). This release is essentially a
complete rewrite of Open MPI based on new technologies such as C#,
Java, and object-oriented Cobol (so say we all!). Buffer overflows
and memory leaks are now things of the past. We strongly recommend
that all users upgrade to Windows 7 to fully take advantage of the new
powers embedded in Open MPI.
users mailing list


text:
*image shown is 5 x 8 or larger rug
*smaller sizes will not show complete pattern, will be scaled down to fit.
Additional 10% discount will be applied in cart once discount code is entered.
Name: Constellation MSR5432A
Manufacturer: Martha Stewart by Safavieh
Material: Silk
, Wool
Construction: Hand Knotted
Colors: Ivory/Beige
Made in: China
Description: This design explores the geometric sunburst motif so popular in mid-20th century textiles and wall coverings. Updated for today's interiors, the simple yet striking pattern of Constellation is achieved with a slight tonal shift of a single color. Skilled Tibetan rug artisans manipulate the texture of the weave to create the low-contrast sunburst design, which in turn enhances the delicate sheen of the hand-carded wool and silk yarns. This rug is especially beautiful for a bedroom or modern interior. All rug sizes are approximate. Due to the difference of monitor colors, some rug colors may vary slightly. We try to represent all rug colors accurately. (Constellation MSR5432A - Silk Rugs from Martha Stewart by Safavieh)
Other Related Patterns You Will
Related products are usually selected because they employ the same materials and colours of the product featured above but in different patterns and therefore are often perfect for use in the same or adjacent rooms.


text:
I recently started working on ArcMap. I want to make some changes to the edit tools.
For example I want to prevent the user from using the sketch tool when the time is between 1pm and 2pm
But I don't know where to start. If anyone has a simple example I would appreciate it.


text:
Source: Cape Wind [press release]
quote: Regarding water, it's a non-issue. Even in expensive areas, it's $50 per thousand cubic feet of treated water. A thermoelectric plant will evaporate 0.5 gallons of water per kWh, so that works out to $0.003/kWh. The real figure will be much less for untreated water. Interestingly, the water evaporated from the reservoir behind hydroelectric dams is over 10x greater per kWh. Source: http://www.nrel.gov/docs/fy04osti/33905.pdf
quote: Seawater isnt ideal for cooling or heat transfer as it contains lots of impurities.
quote: Assuming you live in interior Australia, that's a very extreme example inapplicable to the US and probably 99% of the world's population.


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Kentucky State Police troopers have apprehended 52 tons of food to help feed people during the holidays.
Commissioner Rodney Brewer says the "Cram the Cruiser" food drive netted 105,148 pounds of food statewide. Individual posts promote the campaign to collect enough food to fill a police cruiser over a 10-day period.
This year's effort was more than double last year's take of 50,931 pounds of food.
Brewer says employees at the Harlan post alone gathered nearly 11 tons of food.
The non-perishable food items are distributed to local shelters, food banks and needy families.


text:
Question: You have 9 English books, 7 French books and 5 German books. How many ways are there to make a row of three books in which exactly one language is missing (the order of the three books makes a difference) ?
I do not want to use permutations (nPr). My solution is: $$\left(\binom{16}{3} + \binom{14}{3} + \binom{12}{3}\right)\times 3$$ My logic is: pick 3 books out of English & French (16) + pick 3 books out of English & German (14) + pick 3 books out of French & German (12) and multiply by 3 since the order matters (and there are three slots).
Is my answer correct?


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Police in Kentucky are searching for an inmate who walked away from a work detail at a central Kentucky jail.
Hardin County Jailer Danny Allen told The News-Enterprise that 20-year-old Ryan Jones of LaFollette, Tenn., was last seen at Saunders Springs in Radcliff around 2 p.m. Friday. Guards couldn't find Jones an hour later, prompting the search.
Jones originally was arrested in Whitley County on charges of first-degree wanton endangerment and first-degree fleeing or evading police. The state transferred Jones to Hardin County in April for the work-release program. Jones was scheduled to be released in May.
Allen says based on Jones' phone conversations from Thursday night, investigators believe he is headed toward Dayton, Ohio.
Agencies in Dayton, Ohio have been notified of Jones' escape.
He is described as a white male, approximately 5-foot-8, and weighing 200 pounds.


text:
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I learned that the volume of a sphere is $\frac{4}{3}\pi r^3$, but why? The $\pi$ kind of makes sense because its round like a circle, and the $r^3$ because it's 3-D, but $\frac{4}{3}$ is so random! How could somebody guess something like this for the formula?
In addition to the methods of calculus, Pappus, and Archimedes already mentioned, Cavalieri's Principle can be useful for these kinds of problems.
Suppose you have two solid figures lined up next to each other, each fitting between the same two parallel planes. (E.g., two stacks of pennies lying on the table, of the same height). Then, consider cutting the two solids by a plane parallel to the given two and in between them. If the cross-sectional area thus formed is the same for each of the solids for any such plane, the volumes of the solids are the same.
If you're willing to accept that you know the volume of a cone is 1/3 that of the cylinder with the same base and height, you can use Cavalieri, comparing a hemisphere to a cylinder with an inscribed cone, to get the volume of the sphere. This diagram (from Wikipedia) illustrates the construction: look here
Consider a cylinder of radius $R$ and height $R$, with, inside it, an inverted cone, with base of radius $R$ coinciding with the top of the cylinder, and again height $R$. Put next to it a hemisphere of radius $R$. Now consider the cross section of each at height $y$ above the base. For the cylinder/cone system, the area of the cross-section is $\pi (R^2-y^2)$. It's the same for the hemisphere cross-section, as you can see by doing the Pythagorean theorem with any vector from the sphere center to a point on the sphere at height y to get the radius of the cross section (which is circular).
Since the cylinder/cone and hemisphere have the same height, by Cavalieri's Principle the volumes of the two are equal. The cylinder volume is $\pi R^3$, the cone is a third that, so the hemisphere volume is $\frac{2}{3} \pi R^3$. Thus the sphere of radius $R$ has volume $\frac{4}{3} \pi R^3$.
The volume of a sphere with radius $a$ may be found by evaluating the triple integral
$\displaystyle V = \iiint_{\ S}\mathrm dx\,\mathrm dy\,\mathrm dz,$
where $S$ is the volume enclosed by the sphere $x^2+y^2+z^2=a^2$. Changing variables to spherical polar coordinates, we obtain
$\displaystyle V = \int_{0}^{2\pi}\mathrm d\phi\int_{0}^{\ \pi}\mathrm d\theta\int_{0}^{\ a}r^2\sin\theta \mathrm dr = \int_{0}^{2\pi}\mathrm d\phi\int_{0}^{\pi}\sin\theta \mathrm d\theta\int_{0}^{\ a}r^2\mathrm dr = \frac{4\pi a^3}{3},$
as expected.
A complete answer using the disk method would be the following.
If you revolve $ y = \sqrt{ r^2 - x^2 } $ about the x-axis (and form a solid) you get the volume of a sphere.
Form a disk with height $f(x)$, and find its area.
The area of the red disk above is $ \pi r^2 $, or $ \pi f^2(x) $, or we could say $ \pi \sqrt{ r^2 - x^2 }^2 = \pi (r^2 - x^2) $ at any point x between x=-r and x=+r.
To find the volume of a sphere of radius r then, just add up the areas of infinitesimally thin disks on as x goes from -r to +r.
To work it out:
$ \int_{-r}^{r}{ \pi \sqrt{ r^2 - x^2 }^2 dx } $
$ = 2 \pi \int_0^r{ r^2 - x^2 dx } $
$ = 2 \pi ( r^2x - \frac{1}{3}x^3 )|_0^r $
$ = 2 \pi ( r^3 - \frac{1}{3}r^3 ) $
$ = \frac{4\pi}{3}r^3 $
Pappus's centroid theorem (second theorem) says that the volume of a solid formed by revolving a region about an axis is the product of the area of the region and the distance traveled by the centroid of the region when it is revolved. A sphere can be formed by revolving a semicircle about is diameter edge.
The area of the semicircle is $\frac{1}{2}\pi r^2$. The centroid of the semicircle can be found by intersecting two lines that both divide the area of the semicircle into two equal parts. One such line is perpendicular to the diameter edge through the center of the semicircle (this is a line of symmetry of the semicircle). Another such line is parallel to the diameter edge, $\frac{4r}{3\pi}$ away from it (verification of this is left as an exercise for the reader). When revolved about the diameter edge of the semicircle, the centroid travels $2\pi\cdot\frac{4r}{3\pi} = \frac{8}{3}\cdot r$, so the volume of the sphere is $\frac{1}{2}\pi r^2\cdot\frac{8}{3}\cdot r = \frac{4}{3}\pi r^3$.
To give you a larger perspective, the volume of an $n-1$-sphere in $\mathbb{R}^n$ is given by $C_n r^n$, where $r$ is the radius and $C_n=\frac{\pi^{n/2}}{\Gamma(\frac{n}{2} + 1)}$. For even $n$, this reduces to $C_n =\frac{\pi^{n/2}}{\left(\frac{n}{2}\right)!}$, and for odd $n$, it becomes $C_n =2^{(n+1)/2}\frac{\pi^{(n-1)/2}}{n!!}$, where $n!!$ denotes the double factorial.
Thus in the case $n=3$, the constant is $2^2 \frac{\pi^1}{3!!} = \frac{4 \pi}{3}$.
The point of this is to show you that the general formula also involves factors in the denominator, and that the formula for $n=3$ is not 'random' but rather fits into a general pattern.
I'll add a Chinese version for fun.
The ancient Chinese had another way to calculate this volume.
The principle is same as Cavalieri's Principle; the difference is using the intersection of two perpendicular cylinders, a "bicylinder", to pack the sphere. The Chinese name for this shape is 牟合方蓋 or "mouhefanggai" (meaning two square umbrellas).
Every plane (parallel to the cylinders' axes) intersects in a square with the bicylinder and intersects in a circle with the sphere (for more pictures and an animation, see http://phdfishman.blogspot.com/2010/02/blog-post_07.html ). This means that the volume ratio of the sphere to the bicylinder is proportional to the areas of the circles and squares: $ πr^2/(2r)^2= π/4.\ $.
Now the question becomes calculating the volume of the bicylinder (white). It is also very difficult, so add a cube (red) packing the bicylinder (white). Now when the plane intersects the cube, it forms another larger square. The extra area in the large square (the big square from the cube minus the smaller square from the bicylinder), is the same as 4 small squares (blue). As the plane cutting through the solids moves, these blue squares will form 4 small pyramids in the corners of the cube with isosceles triangle sides and their apex at the edge of the cube. Moving through the whole bicylinder generates a total of 8 pyramids.
Now we can calculate the volume of the cube (red) minus the volume of the eight pyramids (blue) to get the volume of the bicylinder (white). The volume of the pyramids is: $ 8 *\frac{1}{3} r^2*r=\frac{8}{3} r^3 \ $, and then we can calculate that the bicylinder volume is $ (2r)^3-\frac{8}{3}r^3=\frac{16}{3}r^3 $
Finally, using the ratio of the volumes of the bicylinder and the sphere from above, the sphere's volume is $ \frac{π}{4}*\frac{16}{3}r^3=\frac{4π}{3}r^3 $
Now you can see that 3 is from the pyramids and 4 is from the cube! They are not random.
This picture shows the geometric relationships.
In the diagram below on the left, we will assume that the the size of $\triangle PQR$ is infinitesimal compared to $\triangle PNO$, and thus, the green arc and the segment $\overline{PR}$ are essentially equal in length. Note that both $\angle NPO$ and $\angle QPR$ are complementary to $\angle OPQ$, and therefore, equal. Thus, the right triangles $\triangle PNO$ and $\triangle PQR$ are similar (corresponding sides are colored similarly). Since $\triangle PNO$ and $\triangle PQR$ are similar, $$ \overline{NP}\cdot\overline{PR}=\overline{OP}\cdot\overline{PQ}\tag{1} $$ The inner circumference of the green annulus on the sphere to the right is $2\pi\overline{NP}$ and its outer circumference is $2\pi\left(\overline{NP}+\overline{QR}\right)$, while its width is $\overline{PR}$. Therefore, its area is between $2\pi\overline{NP}\cdot\overline{PR}$ and $2\pi\left(\overline{NP}+\overline{QR}\right)\cdot\overline{PR}$.
The circumference of the red strip on the cylinder to the right is $2\pi\overline{OP}$, while its width is $\overline{PQ}$. Therefore, its area is $2\pi\overline{OP}\cdot\overline{PQ}$.
According to $(1)$, the difference between the area of the green annulus on the sphere and the red strip on the cylinder is less than $2\pi\overline{QR}\cdot\overline{PR}$. Summing $\overline{QR}$ as we walk down the sphere gives $2\overline{OP}$ (one as $\overline{NP}$ increases and one as it decreases), thus, the difference between the area of the sphere and the area of the cylinder is less than $4\pi\overline{OP}\cdot\max\overline{PR}$, which can be made to vanish by making $\overline{PR}$ as small as we wish.
Thus, the area of the sphere is equal to the area of the cylinder. Since the circumference of the cylinder is $2\pi r$ and its height is $2r$, we get that the area of the cylinder, and therefore the sphere, is $4\pi r^2$.
To compute the volume of the sphere, we just sum the surface area of all spherical shells times their thickness: $$ V=\int_0^r4\pi t^2\,\mathrm{d}t = \frac43\pi r^3\tag{2} $$
I wanted to post this as a comment to the answer by Justin L. but it is my first posting here so I couldn't. Archimedes was so proud of his proof that the volume of a sphere is two-thirds of the volume of a cylinder of the same height and diameter that he asked that a sculpture illustrating this would be placed at his tomb. The tomb was later found by the Roman orator Cicero who describes it as follows:
"I managed to track down his grave. The Syracusians knew nothing about it, and indeed denied that any such thing existed. But there it was, completely surrounded and hidden by bushes of brambles and thorns. I remembered having heard of some simple lines of verse which had been inscribed on his tomb, referring to a sphere and cylinder modelled in stone on top of the grave. And so I took a good look round all the numerous tombs that stand beside the Agrigentine Gate. Finally I noted a little column just visible above the scrub: it was surmounted by a sphere and a cylinder."
The American painter Benjamin West imagined the scene in his 1797 painting "Cicero Discovering the Tomb of Archimedes".
This was first "guessed at" by Archimedes, by what fraction of the volume of a cylinder a sphere is. That is, a sphere that is contained within that cylinder. From that, he figured out $4/3$.
You can do it these days with the tools of calculus. One way would to use the Disk Method, over the graph of a semicircle. Another would be to use spherical coordinates and calculate the 3D Integral.
All of these methods should give you $\frac{4}{3} \pi r^3$
Note that it's not just $r^3$ because it's "3D"; but also because it's the only way the dimensional analysis would work; that is, the units would have to be in $\text{distance}^3$. But that might be what you said, but just clarifying.
To expand on what anosov_diffeomorphism said:
Suppose we agree that the surface area of a sphere is 4 π r2 (If we do not agree on this, that would be a great question to ask on this site, and then someone can edit this answer to link to it!). Now if I have a sphere of radius r, and I increase the radius by a tiny amount, dr, then the new, expanded sphere has a volume that is bigger, by the volume of the thin spherical shell that was just added. If dr is small enough, then it doesn't much matter whether we look at the inner or outer radius of that shell, and we can just say that the shell's volume is approximately 4 π r2 dr. So the difference in volume between two spheres of radius $r_1$ and $r_2$ is $\int_{r_1}^{r_2}$ 4 π r2 dr, which is 4/3 π r^3
Integration. $$\int 4\pi\cdot r^2 dr = 4/3 \pi r^3.$$
If we already knew that the surface of the sphere is $4\pi r^2$, then we could go like this:
We could divide the surface into small polygons (you can imagine them infinitesimaly small). The area of these polygons approximate the area of the surface. Now the volume of the sphere would be approximated by the pyramids obtained from the polygons, each of them having volume $(1/3)*\text{base}*\text{height}$.
Since height is approximately $r$ (as we make the polygons smaller) and the bases together give the area of $4\pi r^2$, we arrive to $V=\frac43 \pi r^3$.
(Although I have to admit that I liked this better as a way of deriving the formula for the surface area from the volume.)
To add to the approach of @bobobobo, it can be shown that we can construct the volume $V_n$ of an $n$ dimensional sphere from the volume $V_{n-1}$ of an $n-1$ dimensional sphere using the following recurrence relation:
$$V_n = 2r V_{n-1} \int_0^{\frac{\pi}{2}}\cos^n\theta d\theta$$
using this relation starting with $V_0 =1$ we get:
$$V_1 = 2r V_0 = 2r$$
$$V_2 = \frac{\pi}{2}r V_1 = \pi r^2$$
$$V_3 = \frac{4}{3}r V_2 = \frac{4}{3}\pi r^3$$
$$V_4 = \frac{3\pi}{8}r V_3 = \frac{1}{2}\pi^2 r^4$$
This expands on the answer by MatrixFrog which starts with the formula for the surface area $A$ of a sphere of radius $R$, namely $ A_R = 4 \pi R^2$.
I will show mathematically that the assumption that the volume of a shell of small thickness $t$ is approximately given by $V \approx 4 \pi R^2 .t$ is valid, using high school maths and no calculus.
Let us model the sphere (radius $R$) as a set of concentric, contiguous shells of common thickness $t$. The outermost shell is defined by an outer (zero-thickness) sphere of radius $R$ and by an inner (zero-thickness) sphere of radius $R-t$. The innermost shell is defined by an outer (zero-thickness) sphere of radius $t$ and its inner boundary is the centre point of the sphere; the innermost shell is therefore a small sphere.
Now let us express the volume of the major sphere as the sum of the volumes of the shells (with outer radii: $ x=t,2t,3t,...,R-t,R$). And let us approximate the volume of each shell by the product of its surface area $A_x = 4 \pi x^2$ and its thickness $t$. So $$ V_R \approx \sum_{x=t}^{x=R} 4 \pi x^2 t \approx 4 \pi t \sum_{x=t}^{x=R} x^2. $$ Now let us replace $x$ by $i.t$ and define $N = R/t$, then we obtain:-
$$ V_R \approx 4 \pi t \sum_{i=1}^{i=N} i^2t^2 \approx 4 \pi t^3 \sum_{i=1}^{i=N} i^2. $$
Using the power sum formula:- $$\sum_1^N k^2 = (N/6)(N+1)(2N+1) = \frac{2N^3+2N^2+2N+1}{6}$$ we get $$ V_R \approx 4 \pi t^3 \frac{2N^3+2N^2+2N+1}{6}. $$ replacing $N$ by $R/t$ $$ V_R \approx \frac{4}{6} \pi t^3 \left[ \frac {2R^3}{t^3}+ \frac{2R^2}{t^2}+ \frac{2R}{t} +1 \right] \approx \frac{4}{3} \pi \left[ R^3+ R^2t+ Rt^2 + \frac{t^3}{2} \right]. $$
Now clearly as $t \rightarrow 0$ so all the terms in $t$ also go to zero and we are left with $V_R \rightarrow \frac{4}{3} \pi R^3.$
$$ \begin{array}{rlcccc} \large\mbox{Cone:} & {\rm d}V & = & \pi\left(r \over h\right)^{2}h'^{2}\,{\rm d}h' & = & \pi r^{2}h\, \overbrace{\left(h' \over h\right)^{2}\,{\rm d}\left(h' \over h\right)}^{1/3} \\[3mm] \large\mbox{Cylinder:} & {\rm d}V = &&& = & \pi r^{2}h\,\phantom{\left(h' \over h\right)^{2}} \underbrace{\,{\rm d}\left(h' \over h\right)}_{\vphantom{\Large A}1} \end{array} $$
Also, according to the Gauss Theorem, any volume is a sum of pyramids: $$ V = \int_{V}{\rm d}V = \int_{V}{\nabla\cdot\vec{r} \over 3}\,{\rm d}V = \int_{V}{\vec{r}\cdot{\rm d}\vec{S} \over 3} $$ We can think the cone is a "perfect sum of pyramids" since we just need to integrate ( with the vertices as the origin ) over the base.
Archimede found that the volume of a ball is 2/3 of the volume of its enclosing cylinder : a hat box with a basket ball fit inside. Why exactly 2/3 ? This is the pure beauty of maths. Archimede found this beautiful result and was so fond of spheres and cylinders.
Now, what is the volume of the cylinder ?
VC = area of the base disc × height
So VC = π r2 × 2 r = 2 π r3.
The volume of the ball is 2/3 × VC = 4/3 × π r3.
This is my attempt at determining where the $\frac{4}{3}$ in the equation for the volume of a sphere ($\frac{4}{3} \pi r^2$) comes from.
I concluded my answer by conceptualizing the definition of a sphere with respects to its derivative (a circle) and the basic definition of such.
If we choose to define a circle by its circumference ($2\pi r$), then it follows that its area is equal to $\int_0^r 2\pi t dt = \pi r^2$ where it's center is located at the origin of a cartesian plane.
We should note that a sphere is scaled by its horizontal and vertical surface-components (circles). With this we can define a sphere as $(2\pi r)_{xy}(2\pi r)_{xz}=4\pi r^2$, or the Surface Area of a Sphere. A sphere defined as such holds true that its volume (or area) is equal to $\int_0^r 4\pi t^2dt=\frac{4}{3}\pi r^3$.
Note: I am using the term scaled specifically to avoid confusion in the usage of multiplication vs. addition.
Proof (by Contradiction): If you add the horizontal and vertical surface-components of a sphere, you will find that you have the circumference of a circle multiplied by a scalar factor of 2 or $(2\pi r)_{xy}+(2\pi r)_{xz}=4\pi r=2*2\pi r$.
Proof (by Conceptualization): You are are integrating across a 3-Dimensional object that has both height (on the xy-plane) = $r_{xy}$ and width (on the xz-plane) = $r_{xz}$.


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I looooove pretzels fresh out of the oven. They really are best when still warm and sprinkled with cinnamon and sugar (or kosher salt, if that is your thing). But, unless you want to eat the entire batch of pretzels in one sitting, you really only get to eat one super fresh pretzel (two, if it's the weekend). So here is a solution: partially bake the pretzels, freeze them, then bake them up as you need them.
Wednesday, March 4, 2009
Fresh Pretzels
I looooove pretzels fresh out of the oven. They really are best when still warm and sprinkled with cinnamon and sugar (or kosher salt, if that is your thing). But, unless you want to eat the entire batch of pretzels in one sitting, you really only get to eat one super fresh pretzel (two, if it's the weekend). So here is a solution: partially bake the pretzels, freeze them, then bake them up as you need them.
27 comments:
- Nasreen said...
What's the not frozen baking directions?
- March 4, 2009 at 8:44 PM
- Meg said...
There is nothing better than a warm soft pretzel!
- March 4, 2009 at 8:52 PM
- Amanda said...
YUM!! Hot pretzels are one of my favorites! Thanks for posting this..so excited!
- March 4, 2009 at 9:02 PM
- veganmomma said...
Is there something I can use in place of bread flour?a
- March 4, 2009 at 11:28 PM
- BellaTrixx said...
oh man!! i was just drooling over the idea of yummy warm pretzels fresh from the oven earlier today! sounds like a great weekend mission for me!
- March 5, 2009 at 12:11 AM
- Run Saraah said...
What a fun idea for appetizers!
- March 5, 2009 at 12:35 AM
- jodye said...
I've been dying to make soft pretzels for such a long time, but I forgot until just now! These look delicious, thanks for the reminder!
- March 5, 2009 at 1:24 AM
- Hey it's Natée said...
Vegan Dad- I am loving your blog!
I'm a vegetarian working my way towards veganism. Giving up dairy has been my biggest hang-up, but you make it look so easy! My mouth is watering just perusing through your blog. I am anxious to try out your recipes... I want to try them all out! Thank you for sharing!
- March 5, 2009 at 10:08 AM
- Kelly said...
I too love pretzels. Very tasty. I might have to try this recipe. It's a little different than the one I have made in the past which required that the bagels were boiled in the water/baking soda mixture.
- March 5, 2009 at 10:43 AM
- VeganMama said...
YUM!! My pretzels generally come out hard as a rock. Looking at your recipe I'm guessing I use too much WW flour. Hmm... would using WW pastry flour help them to be softer?
- March 5, 2009 at 11:01 AM
- Hello Veggie said...
You are so right, they are BEST fresh out of the oven! Great post.
- March 5, 2009 at 5:05 PM
- Sue G. said...
- March 5, 2009 at 6:51 PM
- Vegan Dad said...
Bake for 10-12 mins, until golden brown.
- March 5, 2009 at 8:23 PM
- Vegan Dad said...
You need the gluten from the bread flour to get the right chewy texture. I suppose you could add about a tbsp of vital wheat gluten to achieve the same effect.
- March 5, 2009 at 8:24 PM
- Vegan Dad said...
I don't think so. Like I mentioned in the above comment, you need gluten to get the right texture, and pastry flour is too soft. Perhaps you need to adjust the wet:dry ratio.
- March 5, 2009 at 8:27 PM
- Jamie the Foodie said...
i am so making these this weekend! i will slather them with butter & then garlic powder...just like you find at the mall! i hate using yeast, but this seems do-able...not too intimidating!
- March 5, 2009 at 9:24 PM
- JENNA said...
oh man i want one of those so bad!
- March 5, 2009 at 11:34 PM
- Eating Consciously said...
Cinnamon sugar pretzels are my favorite!
- March 6, 2009 at 6:13 AM
- DJ said...
These look superb - and part-baking them is a great idea!
- March 6, 2009 at 8:50 AM
- miss v said...
i love hot pretzels and mustard!!! thank you for this recipe!
- March 6, 2009 at 9:29 AM
- jd said...
Too funny... I just did a post about soft pretzels earlier this week :)
BTW, I love your advice for partially baking the pretzels & then freezing them to bake for later.
Too bad I didn't have that tip in mind earlier - my bf & I ended up eating way too many pretzels when we made them, just so they wouldn't go bad.
Yea, that was the reason... LOL!
Great post!
- March 6, 2009 at 4:00 PM
- JohnP said...
I recently made pretzels, and two of us ate the entire batch within a day. Bad, bad, bad! Your freezing idea is, perhaps, my salvation, and I will be trying it.
- March 6, 2009 at 7:22 PM
- Karina said...
Hi Vegan Dad,
I made these last night, topped with cinnamon and sugar. They were extremely tasty! Next time I'll try adding some vital wheat gluten as you suggest, since I have only regular flour.
- March 6, 2009 at 9:55 PM
- chow vegan said...
Yum! Fresh pretzels, that sounds so good right now!
- March 7, 2009 at 2:10 PM
- Sarah said...
I heart homemade pretzels!
- March 8, 2009 at 10:30 PM
- happyherbivore.com said...
i need to move to canada. I was just saying how much I was craving a pretzel the other day and the only "stands" in the malls here add in obscene amounts of butter. ew. hooray!!
- March 11, 2009 at 9:39 AM
- Nasreen said...
My husband and I just enjoyed these! I am not a great bread maker, but these came out more amazing than anything from the mall! I'm glad I decided to freeze half the batch, although I wish I had made several batches for freezing. Thanks VeganDad!!!
- March 20, 2009 at 2:22 AM


text:
Can I customize Package Explorer to treat a folder as a file?
Actually, I want to keep a .app file in my project as a file. But when I keep it in Eclipse, it is treated as folder.
Can I change this behavior of Eclipse for Project Explorer? Actually my .app is a file for Mac OS, so it should be treated as file only, which is unfortunately not.
Can I change it programmatically?
This is also posted on Stack Overflow. http://stackoverflow.com/questions/11035519/eclipse-how-can-app-file-be-treated-as-a-file-in-package-explorer-for-mac-os
Can anyone add an eclipse tag also here? I can't as I have less than 300 reputation.