I've had some fun with Wolfram|Alpha in previous posts, and now they can be made even more fun.

Any Wolfram|Alpha search, without any programming, can be turned into a widget you can place on your website as easily as embedding a video!

In July of last year, I posted about a trick with Wolfram|Alpha, which the widgets make it even easier to present.

Instead of typing everything in directly, they can enter the numbers in the following widget, make sure you can't see the screen, and give you the three numbers that result:

Wolfram|Alpha has even helped make the method itself easier. Instead of performing it as Martin Gardner originally described, you can get the first number by taking the leftmost number of the group and subtract twice the middle number from that. Next, add the rightmost number. Divide that by 2, and you've got the first number you need!

For example, given the default numbers of {4, 9, 18}, you would do 4 minus 18 (twice the 9 in the middle) to get -14, and then add 18 (the rightmost number) to get 4. 4 divided by 2 = 2, so now you know the equation begins with 2x².

To get the second number, take the middle number and subtract the leftmost number from it, such as 9 - 4 = 5 in our example. From that result, subtract the number you got in the previous step. The result of the previous step was 2, so we figure 5 - 2 = 3. That gives us 2x² + 3x (plus 3 because the result was a positive 3).

As before, the leftmost number is the constant itself, so we get 2x² + 3x + 4 as the original equation! You can find several good videos on adding negative numbers, as well as subtracting them, over on YouTube.

Similarly, for the Wolfram|Alpha Factorial Trick, it just becomes a simple matter of submitting a simple number as input, and noting the result:

Creating widgets like these can be handy for simple quizzes, too. If you're learning the Instant Magic Square for example, you could quickly develop a widget that gives you a random total from 21 to 100. Similarly, if you want an effective way to practice the Day of the Week For Any Date feat, you can start with input that generates random date on Wolfram Alpha and develop that into a widget that gives you random dates.

The following video will give you an idea of how easy it is to create a Wolfram|Alpha widget. When you're familiar with making simple widgets, check out their blog for new features as they become available.