Happy Leap Day!

As mentioned earlier, January and February were added to the end of the previously ten-month-plus-winter Roman Calendar by Numa Pompilius around 713 B.C.E. From the start Februarius (February) had fewer days than the other months. Indeed, since the Romans didn’t like even numbers it was the only month with an even number of days at all: Martius (March), Maius (May), Quinctilis (July), and October all had 31 days, while Ianuarius (January), Aprilis, Iunius (June), Sextilis (August), September, November, and December had 29 days.

Another real-life heptagon!

I found this photo by Steven Pam, entitled 7, of the dome in the former Melbourne Magistrates Court in Melbourne, Australia. It makes me happy to see an example of a regular heptagon used in architecture. According to Wikipedia the original court was opened in 1914, but moved to Williams Street in 1995. In poking around the web, it looks like this might be the building on the northwest corner of Russell and LaTrobe streets. (There are some pictures of the outside here.)

I <3 µ∆±H CLΨβ-Semester Events

Math Club Semester Events

Meetings: (Lunch Hours)

• Thurs. March 6th
• Tues. April 15th

Events:

• PIE DAY- Thurs. March 13th Lunch Hr
• Career Night- Thurs. March 27th 7:00pm
• Math Night-(Pal Mac) Thurs. April 3rd 7-8:30
• Relay for Life– Sat. April 5th 7pm at SJFC

How to climb hills

Climbing a gently sloping hill is straightforward:  to get to the top, you just climb straight up the hill.  Climbing a steep hill is a different matter.  If you were to go straight up the side of the hill, following the shortest possible path to your destination, you would be stymied trying to climb a slope too steep for your legs to ascend.  The solution is to tack: climb the hill on an oblique path, one whose slope you can manage, and use switchbacks when necessary to continue toward your intended destination.  It follows that there is a critical slope where one’s strategy shifts from the direct attack to the construction of switchbacks.

An article by Marcos Llobera and Tim J. Sluckin in the Journal of Theoretical Biology (volume 249, 21 Nov 2007, pp 206-217) presents a simple model for human hill-climbing behavior, based on the notion of minimizing energy expended per unit of distance travelled in the desired direction.  They show that their optimization model predicts the expected switchback behavior of hill-climbers, and yields a good fit to observed human behavior.  In particular, their model predicts that the critical slope for hill climbing is significantly greater than the corresponding slope for descending hills, an asymmetry which has consequences for the evolution of systems hiking trails in hilly terrain. 

While L. C. Young is relegated to a single sentence and a citation, much of their analysis has a similar flavor to his generalized curves as solutions to variational problems.  Young used the example of a sailboat attempting to sail into the wind as a motivating example for his theory;  Young was interested in finding the optimal path subject to a constraint (a maximal slope in the hillclimbing context). Llobera and Sluskin arrive at a comparable conclusion by seeking to locally minimize effort expended.

[I first heard about this study at Yahoo! News, who in turn were channelling livescience.com; a quick web search reveals a flurry of postings on this, possibly the earliest a press release from the Univ of Washington.]

Juxtapositions: Song Charts

How’s this for a concept: take a popular song, and create a graph or chart that communicates the content of the song lyric or title. There’s a slew of these over on Flikr. My two favorites are:

#1) [featuring a lovely Venn diagram] (by “moved”)

and #2) [not at all mathematical, but funny nonetheless] (by “brianmn”)

Well, ok, maybe these are my favorites because they’re nearly the only ones where I knew what song they referred to (out of the nearly 200 examples on Flickr). I guess I’m just too old to be down with the hep music the cool kids listen to these days. **

Challenge: Create your own, and post them in the comments! (Bonus points for songs or charts with mathematical references.)

This graph-making exercise is vaguely reminiscent of my favorite powerpoint example floating the interweb: Peter Norvig’s devastating ppt adaptation of Abe Lincoln’s Gettysburg Address.

** True: I received my AARP membership card in the mail today. No foolin’! Heck of a thing for them to send out en masse to folk on some mailing list or other in hopes of drumming up support and new members. Makes me wonder what mailing list I’m on that AARP purchased…

Charts used with permission of boyshapedbox, who had posted them to flickr.

Card Tricks: The Year Game

Here’s a another math card trick. And by “math” I mean…well…counting. All the way to twelve. It’s really not that hard a trick.

Start by taking a deck of cards (if a few are missing it’s not a big deal) with the jokers at the bottom. Have a Volunteer From The Audience pick a card, memorize it, and put it back on top of the pile. Then hand the pile of cards to The Volunteer and let them cut the deck a few times. You can turn around or hide your eyes if you want to; it really doesn’t matter, but it looks a little more impressive.

Godzilla Math

How much does Godzilla weigh?

A good question. And since the life-size version doesn’t seem to be in New York at the moment, we’ll have to use a smaller replica and then multiply by a scaling factor. Our Godzilla, shown below eating Buffalo-Chicken Dip, lives in our house and occasionally visits Our Best Friend Craig over at Puntabulous (whose Guest Debates and Story of a Snake Wrangler are simply brilliant).

A “Paltry Geometric Dilemma”

One of the greatest “math” scenes in a movie appears in Better Off Dead, starring John Cusack. Watch his geometry teacher (Vincent Schiavelli) in action (transcript below).

The three cardinal trapezoidal formations hereto made orientable in our diagram by connecting the various points HIGK, PEGQ, and LMNO, creating our geometric configurations, which have no properties, but with location (Ohh!) are equal to the described triangle CAB quintuplicated. Therefore, it is also the five triangles composing the aforementioned NIGH – each are equal to the triangle CAB in this geometric concept! (laughter)

Therefore, in a like manner the geometric metaphors can derive a repeated vectoral sum. This was your assignment, and I would like to see the results.

My favorite line: “which have no properties.” Indeed.

The 1000th Carnival of Mathematics is here

Head on over to JD2718 for the 1000th Carnival of Mathematics! That’s 1000 Base 3, which is how it managed to follow the 26th Carnival. It’s quite a large shindig so should provide good reading for a while.

JD2718 has hosted the Carnival twice before; he’s a fellow New Yorker (over on the other side of the state) and in his Blog Evolution Meme explains that he started his blog to discuss teaching in New York City (where he is a high school math teacher) but now also posts about puzzles, culture, travel, politics, and food.

Enjoy!

Murphy’s Law and other sites

Because apparently I have waaaaayyyyy too much time on my hands, one of my students introduced me to a new time sink: this list of Cool Math Sites. I had seen some of the sites on the list (which is organized by topic, and updated regularly) but there were quite a few I hadn’t heard of.

Snow Sculptures

Interested in snow sculptures? The 18th Annual Budweiser Select International Snow Sculpture Championships was held in Breckenridge, Colorado at the end of January, and featured an impressive array of entrants. (Not, however, the thumbnail at the side; that’s the snow sculpture of Inuyama Castle in Japan. I couldn’t find any ISSC photos that were public domain.) Each team was given a 10’×10’×12′ block of packed snow and five days to carve it out.

Those Boring Venn Diagrams

Eddie Izzard on Venn and his diagrams. The first 45 seconds are the mathy bit. (Warning: NSFW)

Math Mistakes: missing the point (or, uh, not)

The accompanying photographs depict a road sign in Prescott Arizona.

When I first saw this, and it registered in my mind what the sign actually said, I half expected to see shards of red glass along the roadway, along with bits of chrome and the other assorted detritus of scores of fender-benders as driver after driver got distracted, trying to decipher what they had seen.

Then reality set in, along with the cold realization that most of the drivers around me would notice nothing wrong.

I can attest to the fact that there is no shoulder on that road for the next 1500 ft, not 150 ft as the sign (inadvertently?) proclaims.

For more decimal point fallacies (mostly involving pricing confusion between integer cents and decimal parts of a dollar), see Mr Silva’s Math Website.

I can’t resist sharing another favorite from my photo album, even though it isn’t mathematical. It speaks to one of my pet peeves: errors in usage of quotation marks and apostrophes.

One hopes they went out of business because of bad grammar.

Today’s Weather

Here’s what yesterday’s Democrat and Chronicle predicted for today’s weather:

Medical Math Mistakes: Muddled Milliliters

The article “In the Lab: Simple Math Errors Can Imperil Patients” by Nicholas Bakalar in the Health Section of the New York Times last month related an experiment in which difficulty with math computations led to doctors measuring incorrect dosages of medicine.

In response to a simulated emergency, doctors had to collect and inject 0.12 mg of epinephrine. Both speed and accuracy were measured.