## Posts Tagged ‘Wolfram Alpha’

### Alpha’s Curious Filter

April 19, 2011

For no reason that I can think of, I decided to see how much Wolfram Alpha knew about probability, so I typed “probability of a full house” into the search box and got the following: I thought that was pretty cool, especially since it includes the derivations, so I asked a few more questions, such as “probability of at least 2 red cards in a 5 card hand“: Odd that it will count the numerator but not the (easier) denominator $\binom{52}{5}$.  At this point, I thought I’d try a standard probability question (balls in an urn) that might be harder to parse because of the additional statements: “probability of drawing a blue ball from an urn contaiing 5 blue balls and 7 red balls“.  However, I missed the ‘n’ key when typing “containing” and got the following: So, yeah, OK, Wolfram Alpha doesn’t provide “adult” content (why the quotes?), and I’m pretty sure I know what it’s reading as “adult”, but c’mon.  Note that fixing the typo doesn’t alleviate the problem, but it does cause Alpha to hiccup and request more computing time.  With variations on the wording, I’ve also had it return a picture of a blue ball along with the HTML code to generate it.  Nice.

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### Rounding Up – Way Up

September 23, 2010

Ever heard of Dudeney numbers?  Neither had I, until yesterday, when I discovered them completely by accident while reading (Wikipedia, what else?) about narcissistic numbers.  A Dudeney number (named after famous English mathematician and puzzle author Henry Dudeney) is a number that is the cube of the sum of its digits.  For example, $4913 = 17^3 = (4+9+1+3)^3$

There are only six Dudeney numbers.  Neat numbers, but I was a little disappointed by that.  What to do next?

Generalize, of course!  Generalized Dudeney numbers (discussed here, but the link appears to be dead, so I used Google’s cached version) are numbers that are some power of the sum of their digits: $234256 = 22^4 = (2+3+4+2+5+6)^4$ $12157665459056928801 \times 10^{20} = 90^{20} = (1+2+\cdots+0+0)^{20}$

The largest number on the above site is $547210^{25662}$, which has 147253 digits.  The site links to Wolfram Alpha to confirm this.  Here’s where it gets weird: How many digits is that?  About $10^6$?  About a million?  What kind of rounding is that?  It gets worse.  Try a number with just 100,002 digits (despite what Alpha says).  I think Alpha is a great tool, and I’ve had (far too much) fun playing with it, but I’m a tad disappointed (that’s twice in one post).  So, hey, get on that, Wolfram.

### The Wolfram Alpha Bandwagon

May 18, 2009 I knew that Wolfram Alpha was coming, but couldn’t quite figure out what it was so I didn’t keep too close an eye out for it.  Then I read on Teaching College Mathematics and the Number Warrior that it was up, and I was pretty impressed with the screen shots.    Since then, I’ve been playing around with it, and I’m impressed.

It solves problems: (See how you can switch from exact forms to decimal approximations?  With series, you can even tell it to use more terms.)

It gives you data: (My favorite part is the info at the bottom, about population density and population growth.  I can see those as being useful for writing problems in stats or calculus.  I wasn’t able to get it to predict the population in a given year or predict when it would be a certain population, except once accidentally when it said the US population would be something like 4 quadrillion some year in the distant future.)

It also converts units.  I know that you can do this easily on Google, but this gives you a whole selection and you can pick the one that you like best. And you get to look up cool stuff, like cities, movies, colleges, and names: So all in all, it seems like it’s a combination of many of the things I like about Wolfram’s MathWorld, Wikipedia, and Google.  It doesn’t supplant any of them, but it’s quite user-friendly and I’m looking forward to seeing what else it does.
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