Archive for December, 2007

Three finger tricks for multiplying

December 31, 2007

hands-9x4.jpg

Many math sites teach the following method of using your fingers to remember the multiples of nine: to find the product of 9 times n, hold your hands out in front of you and fold down your nth finger from the left to separate the tens and the ones. For example, to find 9×4, you would hold down your 4th finger from the left as in the above photograph. The bent finger separates the tens and ones digits, so the configuration of 3 fingers (folded finger) 6 fingers gives the answer of 36.

While this method has enjoyed great popularity among students and teachers, there are two other lesser-known finger tricks for multiplying numbers. Click here to find out what they are!

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Birthday Math

December 30, 2007

Today is Shawna’s birthday, and I was reminded, as I am every time someone celebrates a birthday, of a problem my high school physics teacher posed to us when asked about his age:

Last year my age was a perfect square. Next year my age will be a perfect cube.

In fact, his age was the only solution to that problem.

I wondered if I could come up with such a description of my own age (Shawna’s too, but I’m not going to share that one). I wanted the description to be unique in some sense, and the best I could come up with was a minimal solution:

My age is prime, the sum of two consecutive composite integers, won’t be prime again for six years (sexy primes!), and is the smallest such age.

Does anyone else have a cool way of describing their age?  (Note the implication about my own description.)

The 23rd Carnival!

December 29, 2007

For the Carnival
Go to The Math Less Traveled
Read the Math Haikus

Yes, this edition of the Carnival is hosted by the blog The Math Less Traveled, a blog “dedicated to exploring beautiful mathematics”. The author, a computer scientist, also maintains another computer science blog:: Brent -> [string].

Speaking of compound interest

December 28, 2007

dollar.jpgIn yesterday’s post about the benefits of compound interest (especially if you happen to be frozen in cryonics lab for 1000 years), there’s a note that Fry would have earned an additional $1.2 billion if the interest on his account had been compounded continuously instead of annually. It’s not unusual to find places that compound quarterly, monthly, or even daily, but are there really institutions that compound continuously? The answer, surprisingly, is yes. (more…)

A penny saved…

December 27, 2007

futurama.jpgIn the Futurama episode “A Fishful of Dollars” (Season 1, Episode 6), Fry goes to the bank to check the balance on his old account. The teller explains, “OK, you had a balance of 93¢…and at an average of 2 ¼% interest over a period of 1000 years, that comes to 4.3 billion dollars.”

Question: Was the interest compounded annually, quarterly, or monthly? Click for the answer and loads of copyright info on the Title Screen

Perfect Spheres

December 26, 2007

littlesphere.jpgIn an odd connection both to yesterday’s post on spherical Buckeyes and TwoPi’s November post on how the official kilogram is losing weight (although by definition, its mass remains the same), it turns out that spheres are being used in a quest to redefine the kilogram. In particular, according to this article, Australian scientists are trying to create a perfect sphere out of a single crystal of silicon. In theory, once they have a perfect sphere they can count the number of atoms, and use that unchanging quantity as a way to define the kilogram. (more…)

Penzeys Buckeyes!

December 25, 2007

buckeyes.jpgToday’s recipe for Buckeyes is brought to you by the shape sphere. I first encountered Buckeyes in a Penzeys Spices catalogue, and they immediately became a holiday favorite: they are easy to make, even for kids, and taste fantastic. The recipe later appeared in one of the very first issues of the magazine Penzeys One (which is perhaps the most socially conscious and inclusive cooking publication I’ve ever read, sharing the stories and family recipes of regular folk around the US and world.) Click here for the recipe!

Polyhedral Calendars

December 24, 2007

[to the tune of that song from The Sound of Music]

Paper polyhedra with identical faces

2008 calendar in lovely typefaces

Downloading free stuff off of geeky web-rings

These are a few of my favorite things!

Thanks to Ole Arntzen of the IT Department at the University of Bergen (Universitetet i Bergen) for providing a customizable dodecahedral calendar generator. You select the shape, year, language (from approximately 50 options), format (ps or pdf), and whether the week starts on Sunday or Monday; the resulting postscript or PDF file can be saved and printed, and assembled into a polyhedral calendar.

[Postscript added 12/24:  A bit of experimentation suggests that the calendar generator implements the Gregorian calendar for all years, even those prior to the introduction of the Gregorian reform.  Caveat lector! ]

Juxtapositions: Killer Sudoku

December 23, 2007

killer-sudoku.jpgIn a comment on an earlier post aboout Sudoku and Kakuro, Batman mentioned a combination of the two games known alternately as Killer Sudoku, Samunamupure or Sum Number Place. As in traditional Sudoku, Killer Sudoku is played on a 9×9 grid in which the digits 1-9 are placed so that each digit appears once in each row, each column, and each 3×3 grid (nonet). As in Kakuro, groups of cells (cages) add to given sums, and within each cage the digits must be distinct. Click to read more and see an enlargement of the game pictured here at the left.

Jeopardy Does Analytic Geometry

December 22, 2007

On Thursday, December 20, the Final Jeopardy clue, in the category “Snack Brands”, was (emphasis mine)

Each unit in this brand, introduced in 1968, is a hyperbolic paraboloid, & they fit together for perfect storage.

Anyone who’s had my Calculus III course should know the answer, because it’s one of the examples. Here’s what they look like (courtesy of Wikimedia Commons):

hyperbolic paraboloid

Oddly enough, this isn’t the first mention of hyperbolic paraboloids on network TV. They also showed up on The Simpsons, in Treehouse of Horror IX, as Homer and Kang argue on the Jerry Springer Show:

Homer: You lousy two-timing [bleep-bleep]! I’m gonna [bleep]!

Kang: Oh yeah? Well [bleep] hyperbolic paraboloid! [bleep] yo mama!

I guess it’s an insult as well as a quadric surface.

Knots in the News

December 21, 2007

knot.jpgKnot theory is the branch of mathematics used to classify and analyze different types of knots. The mathematical focus is primarily on knots that have already formed, but recently two physicists from UC San Diego, Dorian M. Raymer and Douglas E. Smith, examined why knots form. Their article, “Spontaneous knotting of an agitated string,” appeared in the October 16 issue of the Proceeding of the National Academy of Sciences. (more…)

More Christmas Math!

December 20, 2007

christmastree.jpgI posted recently about Christmas math, but in digging around it turns out that there is more out there than I’d realized (and I also found a Hanukkah Math Song, so check back Dec 21, 2008!). Here are some more Christmas math tidbits, including one from the TV series Futurama: (more…)

Why Doesn’t This Work?

December 19, 2007

A common example of integration by parts used in many Calculus II classes has students compute

\int e^x \sin x\, dx

by integrating by parts twice, then rearranging terms to arrive at a solution. This technique is handy for many functions whose derivatives eventually repeat, that is, functions satisfying

f^{(n)}(x) = cf(x)

for some integer n and some constant c. (Question: Is there a name for such functions? I feel like I should know this.) When does this technique fail?

The qibla (or, “a little hajj math”)

December 18, 2007

December 17th marked the beginning of the hajj, the annual pilgrimage to Mecca.  The hajj is the fifth pillar of Islam, and is expected at least once in the lifetime of every Muslim who can afford to undertake the journey.  (This year an estimated 2 million people will take part in the hajj.) (more…)

A computer that really CAN read your mind…

December 17, 2007

crystal.jpg Want to play another mind-reading game? Check out this Mindreader Applet by Anup Doshi. In this game you enter a supposedly random* sequence of digits 0 and 1 and the computer tries to predict your next move. The computer scores a point each time it correctly predicts your move; you score a point each time it doesn’t. Can you beat the computer? To get a sense of how the program is working, try moving in a predictable sequence (101001010010100) and see how long it takes for the computer to figure out the pattern.

* Click here for Scott Adams’ take on random number generation.

The original version of this game was created by Professors Yoav Freund and Rob Schapire, based on work of Claude E. Shannon and D. W. Hagelbarger in the 1950s.