Last Post on This Site

As of today, YofX has officially migrated to its new home: www.yofx.org. This site will remain up for archival purposes, but all new YofX posts will take place at the above address. Also, if you are following this via RSS, you can subscribe to the new feed here. Thanks for following and I hope to see you over at the new site.

A Mathematician Goes on Vacation 6

I don't get too many complaints about the uselessness of negative numbers, but every once in a while in a Prealgebra class somebody will claim that they're never used in the real world. Above is the photographic evidence from within an elevator in Nikola Tesla Airport (Belgrade, Serbia) that negative integers are indeed used. And if one is ever in such an elevator, one surely thinks fondly (for once) of their math teacher. For how else would we know where to go?

**This is the last real post to this site. Next week yofx officially moves to a new home: www.yofx.org. This site will remain up as an archive for us to refer back to.

Which Mathematical Function Are You?

Lee tipped me off on a great Facebook time-waster: the Which Mathematical Function Are You quiz. You've done plenty of these viral quizzes before, but none so squarely centered on your geek heart. They ask you the standard personality questions. Sometimes the selections are worth a few giggles. Then they determine which mathematical function best fits your personality. I am apparently Gaussian.

Lee is apparently the Riemann zeta-function.

Mystery and wonder are your "prime" delights in life. You seek to apprehend all the hidden, complex patterns in the universe. Some think you are quirky, but they just don't understand you: they have not learned to think outside the box, as you have. You are a misunderstood genius.

I'm curious how many functions the quiz outputs. Let me know what you got in the comments.

**Reminder YofX will be moving to www.yofx.org in 4 days on 7/20**

text2image fun!

text2image is a fun (and probably totally useless) way to transform any text into an image. Above, you are seeing the visual rendering of 'yofx'. I was thinking that this might be an interesting way for students to conceptualize a function. I hate to say it, but sometimes real-valued functions get boring. Another plus is that we don't actually know how the text gets transformed. Discovering properties of the function by playing around could make for an interesting exercise for students. Is it one-to-one, does an all-caps text string map the same as a lowercase string, what does the domain look like, is there a character limit, are all questions students might generate. I picked this up from Information Aesthetics. Check out that post. There are also some links at the bottom to similar trans-medium mappings.

ABBA = ABBA

I was dragged to an ABBA tribute concert last Friday night. I'm regrettably familiar with ABBA's music, Mama Mia veteran (even the sing-a-long), but it was the first time I realized the band's name is a palindrome. It is also the first time the name reminded me of a rhyme scheme. (Two revelations, one night.) What is the real origin of the name? According the Wpedia, it's an acronym for the first names of the bandmembers: Agnetha, Björn, Benny, Anni-Frid. I know, you'll never hear Dancing Queen quite the same way again. Anyway, let me know if you can think of any other palindromic bands.

**Reminder YofX will be moving to www.yofx.org in 6 days on 7/20**

Shunt Buster

Help! This one's killing me.

**Reminder YofX will be moving to www.yofx.org in 7 days on 7/20**

Something to Show Your Algebra Classes

I actually found a reference to variation that isn't in a text book. The Wired Science blog had a post on high-altitude wind generation (pretty interesting in its own right). They describe the relationship between wind speed and power generated like this...

Wind’s power — energy which can be used to do work like spinning magnets to generate electricity — varies with the cube of its speed.

I wonder how many of the students I tortured with variation would remember what it means if they read this article? Those are the questions that keep a math teacher up at night. BTW, if you're teaching variation. I've always found that students like knowing the world's most famous equation e=mc^2 is a direct variation equation.

Geek of The Week: Nick Hamblet

Not sure whether you have been following the comments on Prime Time? But, Nick, known to us in the comments as SumIdiot, came up with a nice proof showing that it's impossible to group the digits of a number n in primes so that you wind up with the prime factorization of that number. For example, the digits of 241 can be grouped as (2)(41), but 2 and 41 aren't the prime factors of 241. Another example, 573 could be grouped (5)(7)(3), but again the product (5)(7)(3) is not equal to 573. Enough.

What Nick actually showed was the larger result: any grouping of a number's digits, prime or not, will always have a product strictly less than the number itself. How did he do it? Here's his proof from the comments.

Given d+1 integers between 0 and 9, called a_0, ... a_d, let me write A=(a_d a_{d-1} ... a_0) for the number \sum_{i=0}^{d}a_i 10^i.

Consider the product obtained by splitting this digit string into (a_d ... a_s)(a_{s-1} ... a_0). So this is a product of a d-s+1 digit number and an s digit number (take s >= 1).

Now A=(a_d ... a_0) = 10^s(a_d ... a_s) + (a_{s-1} ... a_0) is at least as big as 10^s(a_d ... a_s). However, since 10^s is strictly bigger than (a_{s-1} ... a_0), A >= (a_d ... a_s)10^s > (a_d ... a_s)(a_{s-1} ... a_0).

So any integer is bigger than the product obtained by splitting it's decimal string into two pieces. It seems the general statement, splitting the decimal string into any number of pieces, follows by induction.

Clever! Nick has also given me the chance to break in a blogroll (Only on the new domain). He runs a real nice blog Sumidiot here.

**Reminder YofX will be moving to www.yofx.org in 11 days on 7/20**

Transform Your Cat with Math

This XKCD cartoon is a follow up to the Mystery Chord post. Anyone know any other good Fourier jokes?

**Reminder YofX will be moving to www.yofx.org in 12 days on 7/20**

Found Math

I found this on a notepad. And while it looks like math, I can't figure out how the numbers are related. Help!

**Reminder YofX will be moving to www.yofx.org in 13 days on 7/20**

Sudoku Variation

My mother sent this sudoku variaton my way. She is a total puzzle junky and found this in the International Herald Tribune. All the normal sudoku rules apply, but you also have to fill the shaded areas with 1 through 9. Thanks, Mom!

YofX Will Move To A New Home

In the next couple of weeks YofX will begin the move to a new home: www.yofx.org. This will not only be a move to its own domain, but also to a new platform, Wordpress. Here is the plan.

1) For the next two weeks, starting Monday, I will post to both this site www.yofx.blogspot.com and to the new site www.yofx.org. I hope that will give everyone the time to make the transition. (And don't freak out if the new site looks different. I'll be playing around with themes during this period.)

2) After two weeks, starting 7/20, all new posts will be found on www.yofx.org, and this site will be an archive.

If you are reading this blog via RSS, you can subscribe to the new site's posts and comments by following the links. You can even get it via email.

Let me know if there are any problems by commenting. I know this is a pain in the butt, so I want to make sure things go as smooth as possible for you all.

A Mathematician Goes on Vacation 5

This is the best picture I took all vacation. There is so much going on, but notice in particular how the foot of the table rests on the perimeter of the reflection of the table surface...momement of ecstasy! I recognize not everyone is that moved. (My wife just rolls her eyes.) I'm hoping if you read this blog. You might be geeky enough to appreciate it.

Tintin Calculus

Trying to figure out a name and some cover art for the calc text you just wrote? Look no further. I found this is the children's section of my library. And before you run to see if your library has it, be warned there isn't any Calculus (as we know it) in the comic. Calculus is a character that is the object of a sinister plot. Tintin then goes on to save Calculus, and probably the rest of the world too. Funny, I was googling Tintin and found an animated version of the comic online. Too lazy to read, watch it. And if you like your calculus affair with a little more calculus, click here.