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Since 1987, almost 3 million have studied or trained abroad on an Erasmus exchange.

Over the past few weeks, we’ve highlighted a ton of different ways that Wolfram|Alpha can help you explore and analyze NFL statistics. Neither team has a perfect record at stake in this weekend’s Giants-Patriots Super Bowl, but it still promises to be a tough contest and a typically over-the-top cultural experience—so in our final blog post of the 2011 NFL season, we’d like to suggest a few more useful stat queries, as well as some more unusual ways to use Wolfram|Alpha on Super Bowl Sunday.

First, the stats. The Giants won their regular season clash with the Patriots this year, and with the new game-level history plots we just added to team and player results, you can clearly see that the Giants’ defense put the pressure on Tom Brady that week, holding his passer rating to its lowest point of the season:

Neither the Pats nor the Giants have ever won a game at Lucas Oil Stadium, but the Patriots have the better record on turf this year—and they haven’t lost a game since that week 9 clash with the Giants. But will Rob Gronkowski’s ankle injury cancel out that momentum? He had the most receiving yards of any tight end in 2011 and was a huge part of the Patriots’ offense. How big? Ask Wolfram|Alpha to divide Gronkowski’s receiving targets by overall Patriots passing attempts, and you can see that his team threw to him about 20% of the time. That’s a big burden to spread across the team’s other leading receivers.

Much of this year’s pre-game noise is about how the Brady-Manning Super Bowl rematch will play out. But they’re not the only returning players from 2007. In the last Giants-Pats Super Bowl, Giants running backs Ahmad Bradshaw (in his rookie year) and Brandon Jacobs were the leading rushers. Jacobs got the bulk of the carries in the regular season that year, but Wolfram|Alpha’s season total plot shows how Bradshaw has come into his own since then, despite being out for a few games in mid-season 2011.

Also returning will be 330-pound Giants offensive tackle Kareem McKenzie, for whom Wolfram|Alpha can compute some brand-new statistics—like that fact that the number of calories he’d burn playing 2 hours of football (2,830) is roughly equivalent to 7 bowls of chili con carne. (Note: unless you’re Kareem McKenzie, don’t try this at your Super Bowl party.)

Although they’ll probably have the roof up, it’s still good to know that fans in the area should be in for pretty good weather at Lucas Oil Stadium at 6:30pm this Sunday. And if you happen to be lucky enough to have a Super Bowl ticket and the Wolfram|Alpha app on your mobile device, don’t forget that you can use us to identify flights over Lucas Oil Stadium, if the tailgating isn’t exciting enough for you.

There’s a lot more to compute about this Sunday’s competitors, but we’ll leave the rest to you. And even though the season’s almost over, we’ll continue to expand and improve our NFL coverage. We’ll have more detailed player and team analysis, support for fantasy football, and much more by the time the 2012 season rolls around—and we encourage you to send us comments, suggestions, and just plain cool queries that you discover with Wolfram|Alpha.

Most of our users are aware that we release a new version of Wolfram|Alpha every week. Each version includes countless changes—including regular data updates to hundreds of sources, improvements to our natural-language parser and other core frameworks, and completely new areas of coverage.

This blog usually focuses on new datasets and functionality, and if you’ve been reading it recently, you know we’ve made some huge additions in just the last couple of months. We’ve introduced our own unique spin on NFL statistics. We’ve added the ability to visualize, compare, and purchase consumer products. And we’ve extended popular mathematics functionality like “Show steps” to more and more domains, most recently differential equations, as we highlighted earlier this week.

But the biggest change to Wolfram|Alpha since its launch nearly three years ago will be our next release, and we wanted you to be aware that it’s coming. We’re not going to let you know the details just yet, but what you’re going to find is a dramatic enhancement of functionality. You’ll be able to personalize your interaction with Wolfram|Alpha in ways that only our combination of algorithms, presentation tools, and data representation could make possible.

You’ll still be able to use Wolfram|Alpha as you have in the past if you choose, but we think what we’ve put together represents the next big step in the evolution of computational knowledge, and one that will make Wolfram|Alpha an indispensable part of your online life.

Stay tuned! The announcement of this important release will be made on this blog.

EU leaders agree on urgent action to bring down youth unemployment, support small businesses and tap into the EU market, and set date for signing new treaty on economic policy coordination.

One year ago this week we sent out our first Wolfram Fun Fact! Since then, we have tweeted nearly 200 Wolfram|Alpha-computed facts, gained over 10,000 followers, and received some pretty amazing submissions from those followers.

To celebrate our first birthday, we thought we would share some of our favorite and most popular Wolfram Fun Facts from the past year:

round(log_12(vitaminC in a cubic light year of coffee/kg)))= meaning of lifehttp://bit.ly/hl98zt #FunFact— Wolfram Fun Facts (@WolframFunFacts)March 16, 2011

#FunFact The density of Saturn is less than the density of water. http://bit.ly/fpPOAX#science— Wolfram Fun Facts (@WolframFunFacts) March 30, 2011

#FunFact Which country in the European Union eats the most bananas per capita? http://wolfr.am/o8PvYG— Wolfram Fun Facts (@WolframFunFacts) August 11, 2011

#FunFact: There are almost 8 times more sheep than people in New Zealand wolfr.am/p902sL— Wolfram Fun Facts (@WolframFunFacts) August 24, 2011

#FunFact If Warren Buffett divided his wealth evenly among all living people, how big would your check be? wolfr.am/r2wRKd— Wolfram Fun Facts (@WolframFunFacts) September 28, 2011

#FunFact 10! seconds is exactly 6 weeks. wolfr.am/tZ2B1y— Wolfram Fun Facts (@WolframFunFacts) November 21, 2011

#FunFact 1 donkey power is equivalent to 0.3353 horsepower.wolfr.am/vUnLtx— Wolfram Fun Facts (@WolframFunFacts) December 2, 2011

#FunFact A nanocentury is about Pi seconds long. wolfr.am/AckgUT#math— Wolfram Fun Facts (@WolframFunFacts) January 17, 2012

If every kid in the US left out 2 cookies and a glass of milk for #Santa, how many calories would he eat? wolfr.am/v06Gjf— Wolfram Fun Facts (@WolframFunFacts) December 21, 2011

And some of the best user-submitted Fun Facts:

RT @Chris_Akiki: #FunFact: The energy of 6.8 trillion Big Macs would power the United States for a year. shar.es/32qBF— Wolfram Fun Facts (@WolframFunFacts) February 7, 2011

RT @rigginsconst: It would require 8.4×10^11 gallons of paint to cover the surface of the moon via @WolframFunFacts [That's a lot of paint!]— Wolfram Fun Facts (@WolframFunFacts) February 2, 2011

Now that’s a #FunFact! RT @tsilb: About 107 billion people have lived. Ever. http://bit.ly/jd9d25 cc @WolframFunFacts— Wolfram Fun Facts (@WolframFunFacts) May 10, 2011

@WolframFunFactsWhy I like WolframAlpha: wolframalpha.com/input/?i=%28ep…— briggsian logarithms (@deka_log) November 22, 2011

Don’t worry about not getting us a birthday present. If you really want to get us something, tweet some fun facts that you find in Wolfram|Alpha to @WolframFunFacts. Thanks for all the support, and here’s to another great year of Wolfram Fun Facts!

Wolfram|Alpha has become well-known for its ability to perform step-by-step math in a variety of areas. Today we’re pleased to introduce a new member to this family: step-by-step differential equations. Differential equations are fundamental to many fields, with applications such as describing spring-mass systems and circuits and modeling control systems.

From basic separable equations to solving with Laplace transforms, Wolfram|Alpha is a great way to guide yourself through a tough differential equation problem. Let’s take a look at some examples.

Wolfram|Alpha can show the steps to solve simple differential equations as well as slightly more complicated ones like this one:

Wolfram|Alpha can help out in many different cases when it comes to differential equations. Get step-by-step directions on solving exact equations or get help on solving higher-order equations. Even differential equations that are solved with initial conditions are easy to compute.

What about equations that can be solved by Laplace transforms? Not a problem for Wolfram|Alpha:

This step-by-step program has the ability to solve many types of first-order equations such as separable, linear, Bernoulli, exact, and homogeneous. In addition, it solves higher-order equations with methods like undetermined coefficients, variation of parameters, the method of Laplace transforms, and many more. So the next time you find yourself stuck solving a differential equation or wanting to check your work, consult Wolfram|Alpha!

You will soon be able to call on the Commission to make legislative proposals on EU policy. A new website has all the information on how to launch a “citizens’ initiative”.

If you paid any attention to last weekend’s NFL games, you know that we’re headed for another Patriots versus Giants Super Bowl. We’ll take a closer look at those two teams next week, including prior matchups, head-to-head player comparisons, and performance trends over the past few months. But while we’ve got a slight breather in the NFL schedule, we wanted to show you a few ways you can use Wolfram|Alpha to uncover interesting stats from the 2011 NFL season (and beyond).

The Indianapolis Colts turned from a possible playoff contender to a team just hoping to win a game after quarterback Peyton Manning was ruled out for the year. Manning’s absence was a big reason why the Colts’ offense had a hard time scoring points. This bar graph clearly shows the Colts having the lowest point production since 1993.

In fact, the Colts scored seven or fewer points in four different contests. One final way to understand just how much the Colts missed Manning is to look at Manning’s passing yards in 2010 compared to the total yards for the Colts offense in 2011.

A front-runner for NFL Rookie of the Year is Carolina’s Cam Newton. Newton proved to be a dual threat as he led all quarterbacks with 14 rushing touchdowns and threw for the 10th highest yards this season.

The NFL put in new rules regarding illegal hits for the 2011 season. Some of these rules are directly connected to a team’s passing game. With these new rules in place, passing stats around the league have jumped since recent years. Twice as many quarterbacks had more than 4,000 passing yards in 2011 than in 2010. Drew Brees led all quarterbacks with a new NFL record: 5,486 passing yards. Brees’s total is 1.32 times the total yards Jacksonville had all season. Jacksonville gained only 4,149 total yards in 2011—the lowest in the NFL.

Brees can also be considered a front runner for NFL MVP this season, along with Aaron Rodgers and Tom Brady. All three put up very impressive seasons. It should also come as no surprise that their respective teams ranked in the top three for points scored this season.

Out of 256 regular season games played, 10 games saw teams combine for more than 70 points. One playoff game broke the 70 point barrier too. Even with all that scoring, there were 10 games with less than 2 touchdowns.

For a season that nearly did not start on time due to the off season labor agreement between the owners and players association, the 2011 NFL season turned out to be a very exciting one. What are some of your favorite NFL stats from this season? Check back next week as we compare the New England Patriots and New York Giants before their Super Bowl rematch.

Proposals would introduce a single set of rules giving individuals more control over how their personal data is managed and used.

What rule gives the integer sequence 3, 10, 17, 18, 7, …? Wolfram|Alpha can easily find that this sequence comes from a simple cubic polynomial, -x3 + 6x2 - 4x + 2.

A different sequence, 1, 1, 3, 7, 22, 82, 333, 1448, … can be identified as the sequence of the polyhexes. After that, the input sequence of the polyhexes recovers the above sequence.

Wolfram|Alpha can recognize millions of different sequences. Rules for the sequence terms are either recognized algorithmically or as part of the On-Line Encyclopedia of Integer Sequences (OEIS), such as 8, 14, 38, 68, 98, 104, 194, 224 ….

Sequences that have been given names historically have many interesting mathematical properties. Wolfram|Alpha gives the notation, description, terms, formula, recurrence relation, ordinary and exponential generating function, a table program, and a plot. The results for the sequence of the tetrahedral numbers are shown here.

If one asks Wolfram|Alpha for a specific property of a sequence, say a generating function, with a query such as generating function of the multichoose sequence, one obtains additional information, such as a plot of the generating function.

Conversely, we can ask Wolfram|Alpha to calculate the series (-1 + 1/Sqrt[1 - 4x])/(2x) at x = 0 to order 12, giving a result that recovers the sequence terms of the multichoose sequence. Another input is the Dirichlet generating function sequence of the tritriangular numbers. The result contains Riemann zeta functions. Specific sequence formulas can also looked at, such as the sequence of the Lah numbers formula.

In addition, many sequences come with recurrence relations, as seen in the sequence of the cubes recurrence relation. The cubes fulfill a linear recurrence relation of order 4. For the recurrence relation without the concrete initial conditions for the cubes, Wolfram|Alpha gives the general solution of the recurrence relation a(n) = -a(n - 4) + 4 a(n - 3) - 6 a(n - 2) + 4 a(n - 1) as a cubic polynomial in n.

Using the CDF-only interactive results with Wolfram|Alpha with CDF allows us to investigate many modular properties of sequences. Even simple sequences, such as the sequence of numbers that are not squares, show unexpected features if the differences are plotted modulo m. All of these results are displayed interactively.

While most sequences are just monotonously increasing, some show a rich behavior of going up and down, for example, plot of the sequence of Recamán numbers. Looking up EKG sequence table program also gives Mathematica code for generating the first n terms of the sequence, which can be directly used in Mathematica through the WolframAlpha[] function. For example, here’s a plot of the terms. After 2, each term is the smallest number not already used that shares a factor with the previous term.

Once the sequence terms are available in Mathematica, many more investigations of the sequence are possible. For instance, one can visualize the sequence as a 3D curve.

To view the full content of this page, please enable JavaScript in your browser. Learn more here.

To view this content, please install Wolfram CDF Player. You can install the free CDF Player here.

var cdf = new cdf_plugin(); cdf.addCDFObject("A826f7e3de7dbd42b6221654265335694", "http://blog.wolframalpha.com/data/uploads/2012/01/integercdf.cdf", 400, 490);

We hope that the combination of Mathematica’s analysis programs and OEIS recognition will prove useful for everyone.

New plan aims to address gaps in EU’s animal welfare legislation, providing better protection for animals and empowering consumers to shop wisely.

Last week we announced our partnership with global sports statistics company STATS LLC and demonstrated how Wolfram|Alpha now allows users to access and compute football statistics using natural language. Since our original announcement, we’ve had a weekend’s worth of exciting playoff games. Miss any of the action? Ask Wolfram|Alpha about last weekend’s NFL games. Wolfram|Alpha not only returns the games and their final scores, but also provides a summary of team statistics leaders (and losers) across all four matchups. You can instantly see that in a high-scoring weekend, the Patriots led the way with six touchdowns and 509 total yards of offense.

At a glance, you can also see why the regular season matters: in three out of four games, the team with the home-field advantage racked up a win. Only the Packers failed to claim victory in their home stadium, as the Giants won their sixth postseason away game since 1990. Wolfram|Alpha can also show you that Tom Brady threw for three times as many touchdowns on Saturday as Tim Tebow did in both of his 2011 postseason games combined, and that Lardarius Webb (the Ravens player with the most interceptions in 2011) continues to be stingy on defense with two picks this postseason, both against the Texans.

If last weekend was any indication, then fans should be in for a treat with this weekend’s NFL games. The 2011 AFC championship features the Patriots versus the Ravens in Gillette Stadium, where the Ravens have won only once.

To get a better look at this year’s matchup, we can compare New England versus Baltimore, and Wolfram|Alpha gives us a side-by-side comparison of the two teams’ performance, both in the regular season and in the postseason so far. It looks like it will be up to the Ravens to keep up with or slow down the Patriots’s high-powered offense.

The other game this weekend pits the New York Giants versus the San Francisco 49ers for the 2011 NFC conference championship. Want to know what we might expect to see on Sunday? Maybe we should ask about games with the 49ers versus Giants in the 2011 regular season. The 49ers pulled out a close one in mid-November at home, thanks largely to the foot of David Akers, who was good on all four of his field goal attempts.

Or you might just ask about the last Giants victory against the 49ers, which happens to have been more than three years ago (largely thanks to two rushing touchdowns by Brandon Jacobs, in the midst of one of his strongest seasons).

Who will win this rematch? Wolfram|Alpha isn’t predicting the outcome of games yet, but it does provide users with a unique and powerful way to access and compute football data. We are excited, as are many of you, by the potential impact Wolfram|Alpha could have on the world of sports data, but we know we have plenty of work to do. We have already received a lot of suggestions from excited users who are eager to explore more data from the NFL (and other sports) in Wolfram|Alpha. So when you sit down to watch this weekend’s conference championships, get the laptop out or bring up the Wolfram|Alpha app on your iPhone or Android device. We don’t yet offer real-time data, but Wolfram|Alpha can still help you see how the players on the field performed this season, try to predict the outcome of the game, or be your own commentator. Let us know what works, what doesn’t, and what we’re missing. And of course, have fun!

Teachers, are you looking for a new way to integrate technology into your classroom? How about through a dynamic textbook or pre-generated lesson plans? Students, are you looking for some extra help or practice in your classes? How about using interactive demonstrations and widgets to help understand the concepts you are learning? The Wolfram Education Portal is the answer for students and teachers alike!

We are happy to announce the launch of the free Beta version of the Wolfram Education Portal. The portal comes equipped with a dynamic and interactive textbook, lesson plans aligned to the common core standards, and many other supplemental materials for your courses, including Wolfram Demonstrations, widgets, and videos. The Education Portal currently contains full materials for Algebra and partial materials for Calculus, but will continue to grow and improve with your comments and feedback.

We developed the interactive textbook by working with the CK-12 Foundation, a non-profit organization with the mission to produce free and open source K-12 materials aligned to state curriculum standards and customized to meet student and teacher needs. The available Algebra textbook takes CK-12’s Algebra I FlexBook and makes it dynamic with our technologies.

In the future we hope to add many cool and exciting features for teachers and students to explore, including community features, problem generators, web-based course apps, and the ability to create your very own personalized content!

The Wolfram Education Portal was built with the technology from Mathematica, and Wolfram|Alpha, and the Computable Document Format (CDF). Please take a minute to check out the education portal in its beta phase and let us know how we can make it better suit your needs.

The EU wants your opinion on ways to help workers when companies restructure.

Since Wolfram|Alpha launched in 2009, we’ve often said that its knowledge base covers what you’d find in a pretty good reference library—and many of the new features we’ve highlighted over the past two and a half years have indeed been very reference-y: global agriculture data, public school statistics, species information, and tons of other socioeconomic, scientific, and mathematical content. Of course, Wolfram|Alpha has always been much more than a mere repository of reference data: we’ve made it possible for people to explore, compare, compute, and interact with all that data in unprecedented ways.

We’re not about to stop our work in those domains. But now that we have a kind of critical mass of essential information about the world, we’ve begun to reach “outside the library” and experiment with more everyday kinds of topics. Within the past couple of months, we’ve shown you how Wolfram|Alpha can tell you about planes flying overhead or help you to shop for appliances and consumer electronics. And now that the NFL playoffs are in full swing, we’re proud to announce that you can now use Wolfram|Alpha to explore statistics for every NFL team, game, and player from the past 25 years.

Which means you can now get immediate, accurate results to all kinds of natural-language queries. You could ask Wolfram|Alpha to compare passing yards for Aaron Rodgers, Drew Brees, and Tom Brady. Or ask about Steelers games with a combined score over 80 or Packers games with more than 400 passing yards. You can delve into player versus team matchups, too—how about Ben Roethlisberger games versus the Broncos or Drew Brees games versus the 49ers with more than 300 passing yards?

Plug those queries into a search engine and you’ll get a few million links to wade through. But Wolfram|Alpha returns specific, accurate results (powered by data from global sports statistics company STATS LLC) and automatically generates visualizations of team and player performance over time.

Curious about this weekend’s second-round NFL playoffs? Ask Wolfram|Alpha to compare the Broncos and Patriots or compare Tim Tebow and Tom Brady in 2011 and you’ll get a head-to-head comparison of team and player statistics for the current season. But what about past matchups? Try Giants versus Packers games—or if you want to see how the Packers previously fared with a home-field advantage, you could even ask about Packers home games versus the Giants. Wolfram|Alpha generates some summary statistics over all the games that meet those conditions, but you can also click on individual games to go directly to a more detailed view of each contest.

From analyzing our logs, we know that most people try fairly simple sports queries on Wolfram|Alpha: usually just team or player names, maybe paired with a specific season. And for any year from 1985 to the present, Wolfram|Alpha now has those queries covered: try asking about the Pittsburgh Steelers or Drew Brees in 2002 (or even Da Bears in 1985) to
get a concise statistical summary. But to be honest, there are plenty of online resources available if all you want is a big, static table of team or player statistics. Our goal is to do for sports what we’ve done for hundreds of other areas of human endeavor: give you direct answers to specific questions through an intuitive natural-language interface.

So we encourage you to dig a little deeper: ask about postseason sack yards for the Cowboys in 1995, the most points scored by a safety, or the Saints running back with the most yards per reception. Looking for team rankings? Try asking for the NFC East team with the most rushing touchdowns. Or even—sorry, Rams fans—the NFL team with the worst 3rd down conversion percentage.

So what are the limitations? As I said, right now we only have data from 1985 on, so queries about the “all-time best” team or player by any given metric or even about career-level stats for players aren’t supported; the results would be incomplete and misleading in most cases. We’ve also limited ourselves to the most common, top-level statistics; you can’t yet ask for most detailed splits (e.g. “sacks in the last two minutes of the half,” “pass completions when ahead by eight points,” and so on). And we aren’t yet supporting direct queries about play-by-play data. But all of those things are in the works, along with a lot more analysis and visualization of player and team performance.

You should also see Wolfram|Alpha’s ability to understand many more questions about our existing NFL knowledge base improve over the course of the next few weeks. And you’ll be a large part of that. Just like when Wolfram|Alpha first launched, we’re not quite certain how people are going to explore this data once they realize they can do much more than just type in their favorite team or player. So we’ll be paying close attention to your inputs, seeing what works and what doesn’t, and beefing up Wolfram|Alpha’s ability to understand and compute the most popular types of queries that roll in.

In addition to professional football, we’ve also got data on basketball, baseball, and more coming soon. We know we’ve only scratched the surface here, and we’ll continue to develop and enhance our pro football coverage throughout the year—so even after this season ends, we invite you to keep sending your comments and suggestions and sharing your favorite Wolfram|Alpha football queries.

For more examples and a complete list of NFL team and player stats you can explore, visit the Wolfram|Alpha Guide to Pro Football Statistics.

We need your opinion on how to give EU shoppers a better choice of cash-free payment methods, especially online – by spurring competition in the electronic payments market.

There’s been very little change in top-level internet domains (like .com, .org, .us, etc.) for a long time. But a number of years ago I started thinking about the possibility of having a new .data top-level domain (TLD). And starting this week, there’ll finally be a period when it’s possible to apply to create such a thing.

It’s not at all clear what’s going to happen with new TLDs—or how people will end up feeling about them. Presumably there’ll be TLDs for places and communities and professions and categories of goods and events. A .data TLD would be a slightly different kind of thing. But along with some other interested parties, I’ve been exploring the possibility of creating such a thing.

With Wolfram|Alpha and Mathematica—as well as our annual Data Summit—we’ve been deeply involved with the worldwide data community, and coordinating the creation of a .data TLD would be an extension of that activity.

But what would be the point? For me, it’s about highlighting the exposure of data on the internet—and providing added impetus for organizations to expose data in a way that can efficiently be found and accessed.

In building Wolfram|Alpha, we’ve absorbed an immense amount of data, across a huge number of domains. But—perhaps surprisingly—almost none of it has come in any direct way from the visible internet. Instead, it’s mostly from a complicated patchwork of data files and feeds and database dumps.

But wouldn’t it be nice if there was some standard way to get access to whatever structured data any organization wants to expose?

Right now there are conventions for websites about exposing sitemaps that tell web crawlers how to navigate the sites. And there are plenty of loose conventions about how websites are organized. But there’s really nothing about structured data.

Now of course today’s web is primarily aimed at two audiences: human readers and search engine crawlers. But with Wolfram|Alpha and the idea of computational knowledge, it’s become clear that there’s another important audience: automated systems that can compute things.

There are product catalogs, store information, event calendars, regulatory filings, inventory data, historical reference material, contact information—lots of things that can be very usefully computed from. But even if these things are somewhere on an organization’s website, there’s no standard way to find them, let alone standard structured formats for them.

My concept for the .data domain is to use it to create the “data web”—in a sense a parallel construct to the ordinary web, but oriented toward structured data intended for computational use. The notion is that alongside a website like wolfram.com, there’d be wolfram.data.

If a human went to wolfram.data, there’d be a structured summary of what data the organization behind it wanted to expose. And if a computational system went there, it’d find just what it needs to ingest the data, and begin computing with it.

Needless to say, as we’ve learned over and over again in building Wolfram|Alpha, getting the underlying data is just the beginning of the story. The real work usually starts when one wants to compute from it—so that one can answer specific questions, generate specific reports, and so on.

For example, in our recent work on making the Best Buy product catalog computable, the original data (which came to us as a database dump) was perfectly easy to read. The real work came in the whole rest of the pipeline that was involved in making that data computable.

But the first step is to get the underlying data. And my concept for the .data domain is to provide a uniform mechanism—accessible to any organization, of any size—for exposing the underlying data.

Now of course one could just start a convention that organizations should have a “/datamap.xml” file (or somesuch) in the root of their web domains, just like a sitemap—rather than having a whole separate .data site. But I think introducing a new .data top-level domain would give much more prominence to the creation of the data web—and would provide the kind of momentum that’d be needed to get good, widespread, standards for the various kinds of data.

What is the relation of all this to the semantic web? The central notion of the semantic web is to introduce markup for human-readable web pages that makes them easier for computers to understand and process. And there’s some overlap here with the concept of the data web. But the bulk of the data web is about providing a place for large lumps of structured data that no human would ever directly want to deal with.

A decade ago I suggested to early search engine pioneers that they could get to the deep web by defining standards for how to expose data from databases. For a while there was enthusiasm about exposing “web services”, and now there are all manner of APIs made available by different organizations.

It’s been interesting for me in the past few years to be involved in the emergence of the modern data community. And from what I have seen, I think we’re now just reaching a critical point, where a wide range of organizations are ready to engage in delivering large-scale structured data in standardized forms. So it is a convenient coincidence that this is happening just when it becomes possible to create a .data top-level domain.

We’re certainly not sure what all the issues about a .data TLD will be, and we’re actively seeking input and partners in this effort. But I think there’s a potentially important opportunity, so I’m trying to do what I can to provide leadership, and further help to accelerate the birth of the data web.

Finding the tangents and normals of a mathematical function or relation is one of the most common exercises in any calculus course. In this post, I’ll show you the newest functionality in Wolfram|Alpha for discovering and investigating them.

The simplest example of a tangent is the “tangent line” to a one-dimensional curve in the plane. Graphically, the tangent line is a line that “just touches” the curve at some point, so that if it were moved just slightly, this one point of contact would become two.

If you ask Wolfram|Alpha for the tangent line of a specific function and point, it gives it in both graphical and algebraic/numerical form:

Notice that near the point of tangency, the line and the curve are nearly identical; the line does almost exactly what the curve does near that point. This is exactly why tangents are important: it’s often much easier to answer questions about linear functions, and tangents provide a way of approximating a complicated relationship with a linear relationship (a line or a plane). It’s also why the tangent is called the “linearization” or “linear approximation” of the relation.

For example, suppose you need to know the square root of 3.9. A very rough estimate would be 2, since 3.9 is roughly 4, and 2 = sqrt(4). Even better would be to linearize the function y = sqrt(x) at the point x = 4 and use this to find an estimate:

This says that the linear approximation to sqrt(x) at x = 4 is x/4 + 1. Plugging x = 3.9 into this approximation yields 3.9/4 + 1 = 1.975, which is pretty close to the actual value of sqrt(3.9), an irrational number whose first six digits are 1.97484.

You can also ask Wolfram|Alpha for the slope of a tangent line to a function at a point, which is another common calculus question (it’s actually equal to the derivative of the function at that point).

What about higher-dimensional functions? A function or relation with two degrees of freedom is visualized as a surface in space, the tangent to which is a plane that just touches the surface at a single point. For example, here’s the tangent plane to z = sin[xy] at x = 1, y = .9, as displayed by Wolfram|Alpha:

The “normal” to a curve or surface is a kind of the complement of the tangent. The “normal line” to a one-dimensional curve is perpendicular to the tangent line and goes through the same point on the curve:

The normal to a surface in space is also a line. It is the unique line that is perpendicular to the tangent plane at that point:

Tangents and normals to higher-dimensional surfaces exist as well. Of course, no plot is possible, but Wolfram|Alpha will give you algebraic and numerical representations of the tangent and normal to any multidimensional surface and any point:

I hope that this new functionality will be used by both students to check their understanding and by professionals to solve practical problems. Enjoy!

Proposals to encourage more online commerce would make it easier to shop on the Internet across the EU – contributing to economic growth and job creation.

The next time you go stargazing, bring the power of computation along with the Wolfram Planets Reference App and Wolfram Stars Reference App for iOS. Both apps provide access to real-time data and the computational power of Wolfram|Alpha in order to perform advanced calculations and provide data on the planets and stars.

Exploring all of the planets in our solar system is easy with the Wolfram Planets Reference App. Using real-time data on the eight major planets, as well as dwarf planets and minor planets, the app can: compute a planet’s orbital properties, including orbital period and distance from the Earth and Sun; provide physical properties like radius, rotation period, and number of moons; and show information about a planet’s atmosphere, including atmospheric pressure, average temperature, and major constituents.

Impress your friends by finding out which planets are visible from your current—or from any—location, then perform advanced physical astronomy computations using stationary orbits, escape velocity, and Kepler’s third law like it’s no big deal, all from the same app!

It’s impossible to count all of the stars, but with the Wolfram Stars Reference App, you’ll have access to real-time data on over 100,000 of them. For easy browsing, stars are sorted into groups such as the Northern or Southern Sky stars; brightest stars; nearest stars; and giant, supergiant, and main sequence stars. The app also allows you to enter any star name to get information and to examine and compare properties for each star, such as its magnitude, spectral class, temperature, mass, lifetime, and distance from Earth.

Using the power of Wolfram|Alpha, compute a star’s current sky position from your location, find out whether it is visible, learn the times of the star’s next rise and set, and perform advanced astronomical calculations using the Stefan-Boltzmann law, Wien’s displacement law, blackbody luminosity, and mass-luminosity relationship.

Both the Wolfram Planets Reference App and Wolfram Stars Reference App can be found on the iTunes App Store for $0.99.