Archive for April, 2008

Math Card Tricks: Finding the selected card

April 13, 2008

Deck of cards Another card trick to amaze friends and family! For this you need an ordinary deck of 52 cards. (It is OK if it has more or fewer, but you do need to know exactly how many cards are in the deck.)

Shuffle the deck, and then have a Volunteer from the Audience think of a number between 1 and 20. Give the deck to The Volunteer, and tell them to remove that many cards from the deck while your back is turned. If it makes them feel better, they can shuffle the cards again afterwards. The Volunteer should put the removed cards out of sight and not tell you how many cards were taken, although it is fine for The Volunteer to tell the rest of the audience. Click to read the rest of the trick!

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Moving the 6

April 12, 2008

George Mach posed this problem to one of his classes (out at Cal Poly SLO in California), and my dad passed it along for posting here. The answer may be surprising, in the sense that it’s not something that can be easily guessed. Here’s the question:

Find a whole number ending in 6 which is doubled if you move the 6 from the end to the beginning. (e.g. the number 316 almost works because 631 is close to the double of 316, but not quite)

I’ll post the answer here tomorrow…. The answer is past the jump!

Friday Fun!

April 11, 2008

In honor of Friday, here’s a short (2 minutes, 44 seconds) video of Bruce Stringbean and the Sesame Street Band singing “Born to Add”:

Thanks to The Wizard for bringing this to my attention!

Hexagons in Nature: The Giant’s Causeway

April 10, 2008

The Giant’s Causeway (Clochán na bhFómharach: the little stone pile of the Fomorians) off of northeast coast of Northern Ireland was formed many years ago by the giant Finn MacCool, as explained here. An alternate theory has it being formed sixty million years ago by lava cooling quickly (possibly by coming into contact with water) after a volcanic explosion. We may never know for sure which of those stories is true, but what is true is that a lot of the basalt rocks formed into hexagonal columns.

Photo by code poet; licensed under Creative Commons Attribution ShareAlike 2.0

I’d heard of these rocks before, but encountered them again in a photo by Lyn Miller under Found Math on MAA Online. Her photo was taken at Devils Postpile National Monument in California near Yosemite, which also has an impressive array of columns that average two feet in diameter.

Photo by Daniel Mayer; licensed under Creative Commons Attribution ShareAlike 1.0

Finally, if you google “hexagon lava” you find posts like this. It gives Lava Lamp a whole new meaning.

Mixing Up Music: When is a random shuffle random?

April 9, 2008

Last Saturday (April 5), a listener contacted Weekend Edition on National Public Radio wondering why, when her Ipod was on random mode, the same songs kept coming up. Math Guy Keith Devlin (of the monthly math column Devlin’s Angle) answered her question by explaining that randomness is different from uniform distribution: unless your Ipod is set to simply shuffle the songs or to play certain favorites more than others (which are both options), the random mode really is random: when a song finishes, it’s just as likely as any other song to be picked to played next. Indeed, if you play enough songs (where enough depends on just how many songs you’ve got on there) you’d absolutely expect there to be times when the same song is played not just frequently, but several times in a row.

You can listen to the 4½ minute NPR snippet over here.

Thanks to Daniel Birmajer for bringing this to our attention!

Real life nonagons: Bahá’í Houses of Worship

April 8, 2008

The Bahá’í Faith was founded about 150 years ago by Bahá’u’lláh and has followers from all over the world. According to Bahá’í International Community,

the Bahá’í Faith brings new social principles appropriate to the needs of a global society, such as the oneness of mankind, the equality of rights and opportunities for men and women, the abolition of all forms of prejudice, the essential harmony of science and religion, universal education, the need for a universal auxiliary language, and the elimination of extremes of poverty and wealth.

From a mathematical point of view, an interesting fact about the Bahá’í Faith is that all Houses of Worship must have nine sides. There are currently seven temples in the world (plus another that had to be demolished and yet another being built), and while they each have a unique design, they all exhibit this nonagon structure. Click here to see photographs of the temples and satellite pictures showing their nine-sided shapes!

Spreadsheet Errors: Part 2

April 7, 2008

Last month I posted about the European Spreadsheet Risks Interest Group (EUSRIG) and their database (www.eusprig.org/stories.htm) of spreadsheet errors that make the news in some form. I promised a few more examples, so here they are:

Several of the stories pointed out budget miscalculations that occurred because of errors in spreadsheets. In Houston, for example, an audit report in 1999 found “Finance and Administration (F&A) was undercharged $25,652 for rent in fiscal 1999 due to an error in a spreadsheet formula.” (p. 2 of the audit; the recommendation immediately following was to charge F&A $25,652) (Story #55). Click for two more stories, including what happened in a court case where a spreadsheet mistake was discovered after the initial judgment!

Tax Math, Inca Style

April 6, 2008

Still working on those 1040 tax forms? One thing to think about as you read and read and reread the instructions is how the whole process would be different if there was no written language. It’s probably up for debate whether that would make it easier or harder.

The Incas, whose empire in South America began around 1200 and was strongest from about 1450 to 1532, didn’t have a written language that we are aware of, but they did a great job of keeping track of things. To do so, they used quipu (or khipu), which were knotted strings. Different knots and string colors indicated different amounts and types of items.

This picture below shows a quipu representing crop yield for several plants over three different years. Click below to see photos of quipu and learn about the connection with taxes!

Tax Math, Aztec Style

April 5, 2008

Having tax woes? The Aztecs, who lived in Central Mexico and whose empire was particularly strong between the 12th and 15th centuries, shared your pain. They might not have had to fill out 1040 forms, but they did have to pay taxes, and the calculations were not simple, according to a paper published April 4 in Science Magazine which deciphered the mathematics of two codices from around 1540-1544. (“Aztec Arithmetic Revisited: Land-Area Algorithms and Acolhua Congruence Arithmetic” by Barbara J. Williams and María del Carmen Jorge y Jorge; see the abstract here.) Click to read more about Aztec math and taxes!

It’s Carnival Time!

April 4, 2008

Clown in the Carnival The 30th Carnival of Mathematics is up, featuring many intersting posts and some interesting facts about the number 30 (including that 30 is the first Giuga number)!   This Carnival is hosted by The Number Warrior, a blog by Jason Dyer (who teaches high school mathematics).  The Number Warrior also has a recent post I liked that uses triangles on the unit circle to prove 1+csc2θ=cot2θ directly (instead of the way I usually prove it, by starting with sin2θ+cos2θ=1 and dividing through by sin2θ).

Head on over and enjoy the fun!

Mathematical Mindreading: Splitting up Piles

April 3, 2008

crystal.jpgHere’s another mindreading trick with which to amaze your friends and family! Start with a pile of pennies (or beads or paper clips or poker chips etc.) You’ll need to know in advance how many pennies there are: for this example we’ll assume that there are 20 pennies in the pile. It’s not a big deal if your Audience knows that you know how many pennies there are, although if you do this trick more than once it is most impressive to use a different number of pennies each time. Click to find out how to do this mindreading trick!

I Am Not Bruce Wayne (and 7 Other Facts)

April 2, 2008

Having recently been tagged by Ξ, I present seven little-known facts about myself. The official meme is “7 interesting things about me”. I can promise that these seven things are indeed about me, but I make no guarantees about the interesting part.

  1. I was born and raised in L’Étoile du Nord, moved to the desert with less than 10 inches of rain per year, then to the mountains with over 100 inches of snow per year—both in the southwest—then became a Cornhusker for a while, and finally settled here in the 11th state.
  2. I taught myself to juggle when I was eight. I used golf balls (not something I recommend to first-time jugglers), and somehow managed not to break everything in my parents’ living room. I graduated college with 3 credits in juggling (Beginning, Intermediate, and Advanced), and I can now juggle 4 balls or 3 of just about anything else (though not chainsaws—why does everyone always ask me that?). My favorite performance was passing knives and (lit) torches simultaneously with my instructor at our spring show.
  3. I celebrated my birthday on 06/06/06 and nothing bad happened.
  4. I am a video game geek. My first system was the venerable Atari 2600 (I still have it). I played Karateka on my Commodore 64 (where I learned how to program in BASIC). I believe that Day of the Tentacle is one of the greatest computer games ever made. I downloaded the shareware version of Doom using Kermit, saved it to a 3.5″ floppy disk, and copied it to the server at my high school. I wanted to bring Aeris back, too.
  5. I am 51% nerd and 68% pure.
  6. I love to play poker. I’m not into Hold ‘Em as much as I am dealer’s choice games. My favorite variants are Do Ya?, Black Mariah, Two-Card Guts, and Screw Your Neighbor. Note: When playing poker with a bunch of mathematicians, the question, “Man, what are the odds?” tends to interrupt the game while the odds are computed.
  7. I am a cruciverbalist. I do the New York Times crossword in pen (even on Saturdays), and I used to do the Monday edition without the Down clues. I once played a single game of Text Twist that lasted more than 4 hours. I’ve played Word Whomp more than 10,000 times. Sadly, I still stink at Scrabble.

There you go.  Feel free to jump in with your own “7 things” in the comments.  If anyone wants to learn how to juggle, stop by my office.

Well, first you take a left at the Giant Pineapple…

April 1, 2008

road-coloring.jpgAre you tired of stopping to ask directions? Looking for a way to get from Here to There even if you get lost and aren’t really sure where Here is? Then the Road Coloring Theorem is just the theorem for you!

Intrigued? The Road Coloring Theorem is an algorithm for getting to a specific point on a graph that works no matter where you start. For example, take a look at the graph below:

road-coloring.jpg

Suppose this graph represents a series of one-way streets, and you want to get to Yankee Stadium the Yellow Dot. If you start somewhere — anywhere — and follow streets according to the pattern “blue-red-red, blue-red-red, blue-red-red” you’ll arrive there just in time to get a hot dog! Want to go to the Ultimate Elvis Extravaganza Impersonator Contest Green Dot instead? No matter where you are when you start, if you follow “blue-blue-red, blue-blue-red, blue-blue-red” roads, there you’ll be!

But wait, there’s more! According to the Associated Press, this same algorithm could be applied to retrieving lost emails.

How much would you pay paper would you need for such an algorithm? 500 pages, like part of the Four Color Theorem? 150 pages, like Andrew Wiles proof of Fermat’s Last Theorem? The creation of this algorithm required only eight pages of ordinary notebook paper, and one pencil. Oh, and one genius.

Until recently, the idea that any graph could be colored in such a way to allow these universal driving directions was known as the Road Coloring Problem, posed 38 years ago by Benjamin Weiss and Roy Adler. The solution came just last September to Avraham Trahtman, a mathematician at Bar-Ilan University in Israel, and has been making its way recently around the news sites (see for example, The Jerusalem Post on February 8 and The Times yesterday.)