Wolfram Alpha

Today I’m excited to be able to announce the launch of Wolfram|Alpha Pro—the biggest single step in the development of Wolfram|Alpha since its original introduction.

Over the two and a half years since we first launched, Wolfram|Alpha has been growing rapidly in content and capabilities. But today’s introduction of Wolfram|Alpha Pro in effect adds a whole new model for interacting with Wolfram|Alpha—and brings all sorts of fundamentally new and remarkable capabilities.

Starting today, everyone has access to Wolfram|Alpha Pro at wolframalpha.com. Unlike the “tourist” version of Wolfram|Alpha, though, you have to log in, and, yes, to get full capabilities there’s a subscription ($4.99/month, or $2.99/month for students). (Right now, you can try it for free with a trial subscription.)

So, what does Wolfram|Alpha Pro do?

There are some big things here. But at the level of the Wolfram|Alpha interface, they’re just summarized by little icons.

Let’s talk first about output. Once you’ve logged in, you have access to your history, and you can define favorites. You can also set preferences, like what location Wolfram|Alpha should assume, or what unit system you want to use. And you can do things like change the overall size of Wolfram|Alpha output.

As soon as you mouse over a Wolfram|Alpha output pod, you’ll immediately see:

(or, actually, clicking almost anywhere in the pod) does something very simple, but useful: it gives you an enlarged version of the pod, so you can for example see all the details of elaborate plots.

does something a lot of people have asked for: lets you customize output from Wolfram|Alpha, and get it in various formats—so you can put it directly into your presentation, or whatever.

Another much-requested capability, accessed with , is being able to download the raw data behind a Wolfram|Alpha output—say as a spreadsheet or the like.

(Needless to say, spreadsheets can’t faithfully represent the full breadth of data, units, etc. that Wolfram|Alpha generates, so Wolfram|Alpha Pro uses tricks like having separate sheets for “Raw Data” and “Formatted Data”.)

When one says “downloading data”, one might think just of data behind tables and plots. But Wolfram|Alpha Pro can download all sorts of other data too: 3D geometry data (say to use for a modeling program or a 3D printer), sound data, graph connectivity data, molecular specification data, etc.—in altogether more than 60 formats.

In addition to handling material in individual pods, Wolfram|Alpha also lets you download a complete output page as PDF—or CDF.

CDF (Computable Document Format) is the format that we introduced last year to let people create documents containing computations. It’s already gaining a lot of momentum in areas like textbooks and interactive reports. But now CDF is also part of Wolfram|Alpha Pro.

In all sorts of output pods, there’ll be a button labeled “Enable interactivity”. Click it and the pod will turn into CDF, that you can immediately interact with.

At a basic level, you’ll be able to resize any graphic, and rotate 3D graphics. But many kinds of graphics and other outputs will also sprout controls that let you directly modify and interact with them. (Often there’s a “More controls” section that opens out to give lots of additional controls.) And because CDF computation is done locally on your computer, the interaction is typically very zippy.

An interesting feature of CDF in Wolfram|Alpha Pro is that it effectively lets you create interactive programs directly from free-form linguistic input. You can tell Wolfram|Alpha to animate with respect to some variable, or somesuch, and it’ll generate a CDF that does that.

So there are all sorts of new things associated with output in Wolfram|Alpha Pro. But what about input?

Right below the main input box there’s a row of icons. Each of them brings out a “tray” for some special kind of input.

gives a special character keyboard, modeled after the soft keyboards that exist in Wolfram|Alpha mobile apps.

The other icons all relate to a big idea of Wolfram|Alpha Pro. With ordinary Wolfram|Alpha and its free-form linguistics, we’ve really opened up the kind of textual input that you expect a computer to be able to handle. But a big idea of Wolfram|Alpha is to go still further, and to allow input that isn’t text at all.

lets you give an image as input.

Once you’ve got the image in, it’ll be indicated by a little yellow box in the Wolfram|Alpha input field. And if you just hit Enter, Wolfram|Alpha Pro will do an automatic analysis of your image.

There’s some general analysis that always gets done, but a lot of the analysis depends on your image. If there’s text in the image, it’ll get OCR’d. If there are separate components, they’ll be identified. And so on.

But in addition to purely automatic analysis, you can tell Wolfram|Alpha Pro what to do with your image, just using standard free-form linguistics. In a sense, Wolfram|Alpha Pro is a direct beneficiary of the very powerful image handling capabilities that were added in recent versions of Mathematica. But the end result is that it’s able to do a very large range of image processing and image analysis—both “Photoshop-style”, and of a type usually seen only in specialized, expensive, image processing systems.

Particularly powerful is combining image upload with CDF—and getting interactive interfaces for image processing.

So what about other kinds of files? Well, Wolfram|Alpha Pro can handle about 60 types.

In each case, it can do general automatic analysis of what’s in the file. And you can specifically tell it what you want to do. For different types of files, the results are very different. Like here’s the result of uploading a sound file:

And here’s a general analysis of a pure binary file:

What about files that contain data? Here’s where it gets even more exciting. And actually the data doesn’t need to be laid out in a spreadsheet or CSV or whatever. lets you just copy a block of data from anywhere, and feed it to Wolfram|Alpha Pro.

To many people who’ve seen preliminary versions of Wolfram|Alpha Pro, this is then the part that’s most surprising and remarkable: Wolfram|Alpha Pro will automatically analyze the data, and generate a report about it.

The report is completely tailored to the particular data you give—and it can look very different for different kinds of data. Usually, though, it’ll contain some mixture of visualizations and analyses. It’ll have all kinds of charts and graphs and tables—often together with explicit conclusions generated by statistical and other methods.

And of course, it’s not just a static report. There are always all sorts of buttons and pull-downs that allow you to drill down, select different options, and so on. But the notion is that when you upload your data to Wolfram|Alpha Pro, it’ll immediately be able to tell you interesting things about it.

I’ll write more about this elsewhere, but in a sense the concept is to imagine what a good data scientist would do if confronted with your data, then just immediately and automatically do that—and show you the results.

We’re certainly not finished with everything that’s possible, but already in the version of Wolfram|Alpha Pro that we’re releasing today, I think what we can do with data is pretty impressive. Of course, it helps that we can build on all the sophisticated data and statistics-related capabilities that are now built in to Mathematica. And it also helps that we can make use of all the other parts of Wolfram|Alpha.

For example, if you read in data with dates, or units, or place names, or whatever, Wolfram|Alpha Pro is able to call on Wolfram|Alpha’s linguistic capabilities to understand whatever forms were entered. And when it comes to output, Wolfram|Alpha Pro can freely use the built-in knowledge in Wolfram|Alpha. So, for example, it can immediately place on a map cities or countries or whatever given in the data. But what is more, it can use its built-in knowledge to let you do things like automatically normalizing by population.

As everywhere in Wolfram|Alpha, we’re aiming for very broad and deep coverage. We want to implement every method and algorithm that’s relevant to analyzing data, and then we want to apply these automatically whenever and wherever they make sense. Already we’ve got lots of data handling and visualization, lots of standard and not-so-standard statistical methods, and lots of new methods, many original to Wolfram|Alpha Pro.

Taken with the other capabilities of Wolfram|Alpha Pro, it’s all a pretty major extension of ordinary Wolfram|Alpha—supporting a whole new model of using Wolfram|Alpha. In a sense the new capabilities emphasize more than ever the computational nature of Wolfram|Alpha: the ability to do complete, fresh, computations for every query.

We’ve been able to go a remarkably long way with the basic paradigm of ordinary Wolfram|Alpha. But now Wolfram|Alpha Pro dramatically extends this paradigm—and it’s going to be exciting to see all the new things that become conceivable. But for now, I hope that as many people as possible will use Wolfram|Alpha Pro, and will take advantage of the largest single step in the development of Wolfram|Alpha since it was first launched.

Remember that New Year’s resolution you made to lose weight this year? If you’re one of the many people around the world who pledged to get healthy and finally lose that weight, Wolfram|Alpha is here to help! Even with January behind us, there is still plenty of time to get back on track in 2012.

Studies throughout the decades have shown that regular diet and exercise is the number-one way to get healthy. Wolfram|Alpha can offer you a variety of different ways to start, track, and maintain your new healthy lifestyle.

Query how to lose weight, and Wolfram|Alpha will bring up a formula where you can enter all the information needed, including your intended physical activity level, to figure out how many calories you should be eating every day in order to reach your target body weight:

Once you’ve filled out all your information, you’ll be able to see all sorts of different data. You’ll come across a “weight loss regimen duration pod”, which will show you how long it should take you to meet your goal if you stick to the plan. A little further down the page is information on what your caloric intake should be in order to maintain your weight once you’ve reached your goal. Wolfram|Alpha also shows you what your ideal body weight should be based on the information you entered into the formula.

Now, everyone is different, and the ideal body weight for all people of the same age, same gender, and same height is definitely not the same across the board, so don’t worry if your personal target differs from the “ideal body weight.” You know your body and goals best!

Other pods on the page will show you comparison charts; if you want to lose your weight in four months or in half a year, Wolfram|Alpha shows you the different caloric intakes necessary for each frame of time. If you aren’t able to be moderately active or if you plan on being extremely active, we’ll show you how your daily required caloric intake will change. Play around with the formula, figure out what regimen works best for you, and start your new healthy lifestyle right away!

Now that you’ve got your caloric intake numbers set, you can use Wolfram|Alpha to figure out how many calories are in the food that you’re eating! You can either query a food directly or you can use one of the many widgets that other Wolfram|Alpha users have created for a quick answer. With all the options we’ve got, you’ll be able to find accurate calorie counts for all the foods you’re eating every day—even the ones you’d pick up at some fast food restaurants:

The next step is to get a better idea of how many calories you’re burning when you exercise. Typically, you need to burn 500 more calories than you eat every day in order to lose one pound per week. This handy widget will help you to accurately figure out not only your caloric burn, but also what other activities are equivalent to the specific activity you’ve just queried. Awesome, right?

As we stated before, possible results will vary from person to person. Make sure to consult a medical professional before starting any new weight-loss regimen.

It can be really hard to make the necessary changes required for losing weight and getting healthy. We all know it. But we at Wolfram|Alpha also know how integral the right tools can be in securing a victory and long-term success. So get yourself a food journal (or make yourself a spreadsheet using Mathematica) and start tracking your caloric intake and caloric burn with our data and widgets. Let Wolfram|Alpha help you to reach your goal this year of becoming a healthier person!

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.

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!

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.

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.

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.

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.

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!

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.

What do your alarm clock, thermostat, coffeemaker, car radio, anti-lock brakes—and almost every other electrical and mechanical device you encounter in your daily life—all have in common? They are all examples of “control systems,” one of the most ubiquitous yet unseen modern technologies. A control system is any system or device that controls or regulates the behavior of another system. Using various kinds of sensors and actuators, these systems automatically control most common appliances, industrial processes, and even your body’s own biological processes!

Take your home’s humble thermostat. The temperature of your home depends on many factors, especially how long and how recently the home’s furnace was on. With a thermostat installed, the reverse is also true: the state of the furnace depends on the temperature of the house (it comes on if the temperature is too low, and turns off if the temperature is too high). There is a closed loop of causation formed between the home’s temperature and the state of the furnace. By design, the thermostat creates a kind of closed loop called a “negative feedback loop,” which tends to stabilize the temperature around a desired value. Most control systems are like this: sensors feed information back into the system, which is then used to decide on an action.

In Version 8 of Mathematica, we added lots of functions that analyze, design, and simulate a variety of systems, including control systems. We have now incorporated these capabilities into Wolfram|Alpha with the ability to understand some common systems by name.

A simple example is the integrator. An integrator is a system that accumulates the values of some input over time. For example, the amount of gas your car has used since you last filled up is basically an integral of the position of the gas pedal over that time. Put another way, gas is consumed at a rate proportional to how far the gas pedal is depressed. Typing “control system: integrator” into Wolfram|Alpha gives a list of properties, graphs, and an interactive response plot where you can see what happens to the output for several common inputs:

Another standard type of control system Wolfram|Alpha knows about is the PID controller. Usually in the form of a programmable microchip, a PID controller can electronically control something based on the value (or a proportion of the value), the total accumulation (integral), and the rate of change (derivative) of some quantity. Type “PID controller,” and Wolfram|Alpha gives you a custom “calculator” that allows you to vary the strength of the proportional, integral, and derivative “gains” and shows how these variations affect the properties of the controller:

In addition to this repertoire of standard control systems, which we will be expanding in the near future, Wolfram|Alpha can also understand and analyze custom systems, specified using either state space or transfer function models. These models provide a general framework to mathematically describe the input-output behavior of systems and are commonly used to model a complex process, whether a natural phenomenon, a control system, or something else. Wolfram|Alpha is equipped to handle both continuous- and discrete-time systems modeled using this framework.

In a state space model representation, variables are related to each other using ordinary differential equations. Some of these variables are the “input,” others are the “output,” and some are just internal to the system, called “state” variables. Wolfram|Alpha uses the standard convention, in which input variables are denoted by u, output variables by y, and state variables by x. As of this writing, Wolfram|Alpha can only analyze linear state space models, which are expressible as a system of vector differential equations:

x′(t) = Ax(t) + Bu(t)
y(t) = Cx(t) + Du(t)

…where A, B, C, and D are matrices of complex numbers. For example, “A: {{1,0},{1,-1}} B: {{0.2},{1}} C: {{-1.3,1}} : response to the input u[t] = sin(8t)” shows what the state vector x does when this system is fed the input sin(8t):

The other way to represent a control system is with a transfer function. A transfer function is a ratio of U(s), the Laplace transform of the input u(t), over Y(s), the Laplace transform of the output y(t). In general, a transfer function is an n-by-m matrix of functions, where n is the number of outputs and m is the number of inputs.

Using either transfer function or state space inputs, you can specify a discrete model by entering a nonzero sampling period, such as 0.2:

You can also ask about specific properties or groups of properties. For example:

Experiment by creating your own control systems or just play around with a standard system like the PID controller. You now have all the tools you need to analyze and test them. Whether you are a engineering student or someone trying to solve the world’s pressing problems, we hope this new feature will make controlling things a little easier.

It’s been an exciting year for us here at Wolfram|Alpha, and we wanted to say thank you to all of our loyal blog readers. We thought we would take a look back at 2011 by sharing some of this year’s most popular Wolfram|Alpha Blog posts. This year we saw some exciting content additions, brand-new ways of accessing and interacting with Wolfram|Alpha, and an arsenal of apps for students and professionals alike.

Each of these are only highlights of the blog posts of 2011. For a little extra reading, you can visit the 2011 archive to see all of the blog posts from this year.

January:
We released version 2.0 of our API, making it easier for for a broad range of software developers to take advantage of Wolfram|Alpha.

February:
For Valentine’s Day, we showed that even computational knowledge engines know the language of love.

March:
QR codes seem to be everywhere these days. Did you know Wolfram|Alpha can generate them?

April:
Wolfram|Alpha gained the ability to compute ranking and summary statistics about income tax rates in US states with the new US income tax data.

May:
We celebrated the second anniversary of the launch of Wolfram|Alpha!

June:
Wolfram|Alpha ventured into the microblogging wilderness known as Tumblr.

July:
We shared the ability to look up the moon phase for any date. What phase was the moon in when you were born?

August:
Wolfram|Alpha became interactive with the incorporation of Computable Document Format (CDF).

September:
Using data from the National Center for Education Statistics, we shared the ability to look up data on nearly 108,000 public schools in the US.

October:
What would you do with 1,818 pounds of pumpkin? Wolfram|Alpha found a few options.

November:
What’s that in the sky? Is it a bird? Is it a plane? Yup, it’s a plane! See what planes are overhead with Wolfram|Alpha.

December:
By incorporating Best Buy’s public APIs into Wolfram|Alpha, we provided a new kind of shopping.

In addition to all of that wonderful new content, we also released a slew of apps for iOS:

Wolfram Course Assistants

Algebra | Pre-Algebra | Precalculus | Calculus | Multivariable Calculus | Statistics
Music Theory | Astronomy | General Chemistry | Physics I | Physics II | Mechanics of Materials

Wolfram Reference Apps

US States | US Presidents | Words | Investment Calculator | Mortgage Calculator | Fractals
Gamings Odds | Sun Exposure | Flight Information | Password Generator | Tides Calculator

Wolfram Professional Assistants

Network Admin | Lawyer

Wolfram Personal Assistants

Genealogy and History | Personal Finance | Travel

What was your favorite addition to Wolfram|Alpha this year? Is there anything you would like us to cover in 2012? Let us know in the comments. Happy New Year!

One of the hottest holiday gifts this season is Apple’s iPhone 4S. Inside every iPhone 4S comes the power of Wolfram|Alpha through the personal assistant, Siri. Siri represents the first major use of Wolfram|Alpha in a voice-based consumer environment, highlighting Wolfram|Alpha’s understanding of free-form linguistics.

What better way to utilize that new iPhone 4S than to impress your family and friends. We thought we would assist in blowing your grandma’s mind at upcoming holiday get-togethers by sharing some examples of the amazing things that can be done with Wolfram|Alpha and Siri. While we do provide the answers to many of the fact-based questions asked of Siri, it is possible to query us directly by prefacing a question with “Wolfram” (pronounced Wolf-rum, not Wolf-ram).

Momentum is important when trying to impress, so it is best to start off slow. We advise beginning with a few of these queries:

• How many calories in a bagel?
• What is an 18% tip on $86.74 for four people?
• Who is the richest man in the world?

Now that they are intrigued, move on to some more impressive queries:

• What is the price of gasoline in Chicago?
• What was the price of gold on August 12, 2010?
• When is the next solar eclipse?

Now it’s time to blow some minds:

• Say “Wolfram, planes overhead” to see a list of the planes visible from your current location.
• Say “Wolfram, International Space Station” to show exactly where the ISS is located.
• Say “Wolfram, Mark Zuckerberg’s net worth divided by total number of Facebook users” to see how much money each Facebook user would get if Mark Zuckerberg shared his money equally.

And then top it all off with some of the more fun questions you can ask:

• What is the airspeed of an unladen swallow?
• How many licks does it take to get to the center of a Tootsie Pop?
• “Who is the man that would risk his neck for his brother man?”
• Who loves orange soda?

Mission accomplished: your relatives should be thoroughly impressed.

And, for those of you still doing your last minute holiday shopping or in need of a stocking stuffer idea, give the gift of Wolfram|Alpha. Available on iOS, Android, Nook and Kindle Fire, our mobile apps let you access the full power of Wolfram|Alpha wherever and whenever you need it—even beyond what’s possible with Siri. With a wide selection of apps to choose from, ranging from calculus to genealogy, you’ll find something for everyone!

To learn more about all that is possible with Wolfram|Alpha, check out our examples page.

Happy Holidays!

We are pleased to add our latest work in the domain of radiation shielding to our ever-widening repertoire of highly technical and challenging areas. Although this was one of the earliest features added to Wolfram|Alpha, we have now significantly expanded the functionality of the area that permits users to ask about the shielding efficacy of numerous materials against multiple radiation sources. Most importantly, we have now included the computations for shielding against that most dreaded radiation—the gamma ray. We think these new features will be extremely useful in helping people to better understand the common shielding gadgets they might see every day (such as at the dentist’s office or when getting an X-ray).

At launch we had information only for beta radiation (electron beam) but now have added alpha particles, protons as well as photons to our collection. Additionally, we have significantly improved the natural-language capabilities in this domain. For example, asking Wolfram|Alpha “At what thickness of lead is 3 MeV gamma radiation halved in intensity?” immediately returns the thickness of the lead sheet as the result. Or maybe you’re interested in figuring out how far alpha particles travel through air. Just ask, “What thickness of air will shield 5 MeV alpha particle radiation?” What if there is a glass window? Once again, the query is at your fingertips: “What is the maximum electron radiation that a 2″ thick plate glass can block?“

Additionally, we have long had extensive information on all the radioactive isotopes present on our planet, which we have now combined with the new shielding protection data. For example, iodine-131 and cesium-137 are two of the prominent radioactive isotopes that are commonly used for a variety of purposes. A quick look at iodine-131 shows us that the primary decay mode for this isotope is beta radiation, and we have now added an approximate calculation to show what thickness of some common materials would block this radiation. We can look up the same information for cesium-137 as well. This is quite useful information, as iodine-131 is used extensively in medical imaging as well as biological and chemical research, and cesium-137 can be used in the treatment of cancer, in measuring metal thickness and fluid flows in industrial settings, and in the irradiation of food and spices.

We hope these new features are useful for radiation workers who work with radioactive materials and various shielding requirements on a daily basis as well as for casual users who want to find information about isotopes and associated ionizing radiation and the protective shielding measures. We now have detailed coverage of the shielding behavior against alpha, beta, and gamma radiation and are working toward extending our work to include more particulate radiation (neutron and more).

Just in time for the holidays, we’re introducing a new functionality that provides consumers with a unique approach to shopping. By leveraging data from Best Buy’s public APIs, Wolfram|Alpha users will now be able to browse more than 35,000 appliances and consumer electronics products. Wolfram|Alpha’s intuitive natural-language interface helps you hone in on the precise products you need, while its powerful data visualization capabilities give you an innovative overview of any shopping category.

We’ve taken the strengths we’ve developed in math, science, and socioeconomic data and created something equally unique and useful for online shoppers. Type in the name of a product category—”dishwashers” or “tablet computers,” for example—and Wolfram|Alpha generates a comprehensive, custom analysis. What are the typical dimensions and other physical characteristics of other products in this class? How common is a given product feature? Wolfram|Alpha helps you to answer these questions.

Type in a specific product name or model number—say, “Blackberry 38548-002”—and Wolfram|Alpha will highlight that product’s rank within the entire product category. From a glance at the plots below, you can see that this tablet falls pretty squarely in the middle of the pack with regard to price and generally on the low-end to average range for a variety of physical and performance attributes.

If you’re curious about a particular property of a product, click “Show details” to get a more focused set of plots, as well as a list of all relevant products, sorted only by that property:

Click a product image or name to generate a custom Wolfram|Alpha analysis for that product or click a price, cart image, or “Buy from Best Buy” link to go directly to that product’s page on the Best Buy website.

Combining our natural-language interface with data from Best Buy’s public APIs also allows users to do more intuitive searches. Renovating your kitchen and need a dishwasher that fits specific dimensions? Enter “dishwashers narrower than 25 inches” into Wolfram|Alpha to get a list of dishwashers that meet your needs. Building a new entertainment center and need to find a narrow Blu-Ray player within a specific budget? Try asking Wolfram|Alpha for the “narrowest Blu-Ray player under $100.” For bargain-hunting photographers out there, it is even possible to ask Wolfram|Alpha to find “the lightest digital camera under $100 with a pixel resolution greater than 12MP.”

Having trouble choosing between two or more products? You can also type their brand and model numbers into Wolfram|Alpha to generate a direct comparison:

These are just a few of the examples made possible with this new feature in Wolfram|Alpha, and it’s the first step in providing our users with a brand-new approach to online shopping. More products and product categories will become available in the near future.

Today we are happy to add a new addition to our line of Course Assistants for iOS: the Wolfram Mechanics of Materials Course Assistant. The app was created specifically to aid those taking their first mechanics of materials class.

The app covers topics applicable to mechanics of materials, mechanics of deformable bodies, solid mechanics, and statistics. More specifically, the app can calculate the normal stress on and extensional strain in a body; determine the Young’s modulus, Poisson’s ration, and shear modulus of an object; and search for material properties of alloys, plastics, and woods.

It can even solve for the effects of temperature changes on a member, use Hooke’s law for uniaxial stress and plane stress, and calculate the extensional strain and flexural stress in pure bending beams.

The Wolfram Mechanics of Materials Course Assistant can be found in the iTunes App Store for $4.99. Also, learn more about other Wolfram Course Assistant Apps.