Archive for December, 2010

Girth Units

December 7, 2010

This Brian Regan video isn’t new, but I saw it recently for the first time and found it hilarious (Thanks for the link Michael!).    And timely, given the holiday season.

Enjoy!

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Carnival of Mathematics #72

December 3, 2010

Welcome to the 72nd Carnival of Mathematics!  Have you been waiting all day (sorry!) for it, filled with Anticipation?  If so, that would be most appropriate, since according to this site the song Anticipation by Carly Simon was the 72nd best song of 1972.

The prime factorization of 72 is 23·32, which has a cool kind of symmetry.  Inversions also have a cool kind of symmetry, and are explored by Patrick Vennebush in Inversions « Math Jokes 4 Mathy Folks posted at Math Jokes 4 Mathy Folks.

In 1889 Nellie Bly went around the world in 72 days (a world record at the time, albeit only for a few months).  Thanks to the wonder of the internet, you can read all about it in her book.  She seems like a creative kind of gal, and might well have enjoyed the post about enclosures by Miss Nirvana in Creating Nirvana: Homeschooling: Box Assemblage posted at Creating Nirvana.

The number 72 is the sum of four consecutive primes (13+17+19+23).  It’s also the sum of six consecutive primes (5+7+11+13+17+19).  Because the primes are consecutive, the summation is pretty easy to remember.  Mnemonics also help make things easy to remember, and in Madhava’s Mnemonic Mathematics, at JOST A MON, Fëanor presents a medieval mnemonic for pi from South India.

If you want to know how fast your interest-bearing money is going to grow, you can use the Rule of 72:  dividing 72 by the annual interest rate is a pretty good estimate for how long it will take your money to double.  For example, at a 6% annual interest rate, your money would double about every 72÷6=12 years.  (This is just an estimate, and works pretty well whether the interest is compounded quarterly or daily.)    Money is one aspect that people consider when choosing a career.  Speaking of careers, Maureen Fitzsimmons presents Top 50 Blogs About Careers in Science at Masters in Clinical Research, saying, “When considering a new career, it’s always helpful to learn from people already in the field. These 50 blogs can provide that insight about science careers.”

The human body is made up of 72% water, although since I got that fact from Wikipedia I might have to retract it later.  In the post Rates of Scientific Fraud Retractions at Deep Thoughts and Silliness, Bob O’Hara explains, “OK, this is stats really – I do a quick analysis of retraction rates to see if Americans really retract more often than anyone else.  (Ha!).”

The number 72 is divisible, or nearly so, by all of the integers from 1 to 9.  In particular, it has a remainder of Two when divided by 5 or 7, and a remainder of Zero when divided by the other seven numbers, making it a bit of a Zero Hero.  For ways that you too can be a Zero Hero, see our next post, Singapore Math: 52 Ways to Become a Zero Hero by Yan Kow Cheong at Singapore Math.

World Records allow people from all across the globe to compete for bizarre bragging rights.  For example, just this past August, Patrick Lomantini set a World Record by continuously cutting hair for 72 hours in Witchita, Kansas.  A simpler way to connect to your worldwide brethren is through podcasts.   Peter Rowlett demonstrates this effectively in Math/Maths LIVE from MathsJam! at Travels in a Mathematical World, saying, “My American podcast co-host Samuel Hansen visited the UK in November and we did a mathematical tour. As part of this, you can listen to two podcast recordings made live before audiences. This is the first one, from the MathsJam recreational maths weekend.”

Another World Record was set this year by Jeff Miller of Chicago for the longest amount of time continuously watching sports TV: also 72 hours.  And another Podcast worth listening to is Math/Maths LIVE from Greenwich!, also posted by Peter Rowlett, with the note “This is the second one, from Greenwich.”

John Hart Ely, an oft-cited legal scholar, was born 72 years ago today.  It seems likely that he would be fairly well read, and so might have particularly appreciated the post The PiSBN Project by Geoff Robbins at Artificial Philosophy, which was “A personal coding project to find ISBN numbers in Pi.”

The number 72 is the smallest number whose 5th power can be written as the sum of five smaller fifth powers:
725=195 + 435 + 465 + 475 + 675
If you had to wait for an elevator when there were five unevenly spaced elevators you’d probably be happy if you’d read Where to wait for an elevator — The Endeavour by John Cook at The Endeavour.

And finally, the number 72 is 66 in Base 11.  That’s nice and straightforward.  But MarcCC at Good Math, Bad Math likes to look at arguments that are not as straightforward; his post Obfuscatory Vaccination Math (suggested for this Carnival by colleague GrrlScientist) takes a somewhat confusing argument and examines it more closely.

That’s it for this month!  Good luck to all the Putnam takers tomorrow, and the next Carnival of Mathematics will occur in January (with a Math Teachers at Play in between!)

Sierpinski hiding in the Sistine Chapel

December 2, 2010

It was the second day in Rome, an intense day of walking and walking and WALKING, made all the harder by the youngest member of our family twisting his foot near the Colosseum.  And in a bout of bad timing, this was also the day we had tickets to the Vatican Museum (tickets that cost significantly less than 10 Billion Euros, I’m happy to say), so sore foot or not we forged ahead.

The museums were absolutely amazing, with cool things like actual Babylonian script (no idea what it means because it wasn’t clearly numbers, but still):

Plus, because it was a Friday night and the Museums aren’t always open then (last we heard it was a summer thing, extended through October), there weren’t many people in the main part of the museum.  It was dark, and we could look out from nearly empty rooms into nearly empty courtyards:

But the museums are long.  Really long.  I can’t find the dimensions, but according to my city map they look about 1/3 of a mile, and you basically walk around near the entrance then then down one whole side the entire 1/3ish mile length on the second floor, and then you go return on the bottom floor.  By the time we reached the end of the second floor we were already carrying our younger son, and we still had to walk back to get to the exit [and then walk to the Metro, and then the hotel.  And it was almost 10pm.]  But still, at this halfway point is the Sistine Chapel, and that is not to be missed, no matter how tired.

So we went in the Sistine Chapel, which was the one area that was completely crowded, plus it was really loud in there because the guards kept saying SHHHHHHHHH into the microphones and then a recorded voice came on overhead to tell everyone that this was a place of worship and to be quiet, and this was repeated loudly in 8 different languages.  So after about 15 seconds of admiring the ceiling we decided to call it a day and begin the trek back.  But then, right near the exit, TwoPi suddenly whispered, “It’s a Fractal!”  And so I looked at the floor:

See all those Sierpinski Triangles???? They go all the way to Stage 3!

The entire walk back we stopped at every souvenir stand (they’re all over the museum) and had this conversation:

“Do you have any picture of the floor of the Sistine Chapel?”
“You mean the ceiling?”
“No, the floor.”
“No, sorry.”

But then the next day we went to the Mouth of Truth (a giant face where you stick your hand in the mouth, and it gets bit off if you’re a liar), which is part of the church Santa Maria in Cosmedin.  The exit from the Mouth of Truth area goes through the church itself, and lo, there were MORE Sierpinski triangles on the floor!

Here:

and here

and smaller ones here:

and curved ones here

There were some other neat shapes, too, like these

and these, which looked just like a quilt

and these

The pieces were all laid out in sections, like…well, I really did think of quilts every time I looked at the floor:

There were even swirly parts that formed a giant infinity.

After taking 800 pictures we finally left, but a few hours later we were at the Basilica of San Clemente, which is a medieval Church built on top of a 4th century church built on top of a Temple of Mithras, and at the most modern level the floor has the same kind of design.  We sat and rested our tired feet admired it, but didn’t take any pictures because a Mass was about to start and we didn’t want to intrude.

So what was going on?  It turns out that this style of floor is called cosmatesque, and Our Friend Wikipedia describes it as:

a style of geometric decorative inlay stonework typical of Medieval Italy, and especially of Rome and its surroundings. It was used most extensively for the decoration of church floors, but was also used to decorate church walls, pulpits, and bishop’s thrones. The name derives from the Cosmati, the leading family workshop of marble craftsmen in Rome who created such geometrical decorations.

So it’s not terribly surprising that we saw three similar floors within 24 hours, even though we’d never seen anything like it before.  Sierpinski is hiding out all over the place.

Clocks Around Rome, Part II

December 1, 2010

A few more clocks to show!

Up in the Pincian Gardens, where all the Math Guys are, is a water clock created back in 1867.  It only worked for about 40 years, however, and then was in disrepair for about a century.  Fortunately, only three years ago the clock was restored and now it totally works. Yay!  Here’s what it looked like when we were approaching it:

And here’s what it looked like when we were standing in front of it:

(Many of the clocks in Rome used Roman numerals, heh heh.)

Here’s a close up of the water portion:

The water pours first on one side, then the other.

Finally, here’s a close up of the plaque, which tells a little about it, if you read Italian:

And a 2007 article here by Brian Barrow which tells even more, including:

The timepiece is the result of the work of two men: Father Giovan Battista Embriaco, a Dominican priest and scientist (1829-1903), and the Swiss-Italian architect Gioacchino Ersoch (1815-1902). Apart from teaching physics and mathematics, Embriaco had the hobby of constructing mechanical water clocks (see box) in which the continuous emptying and filling of containers at the ends of a balanced arm produced the rocking motion which took the place of the traditional pendulum by moving a notched wheel at regular intervals.

 

Despite seeing quite a few neat clocks in Rome, we missed the six-hour clocks.  We’d found information about these on a site of Curious and Unusual things in Rome [a fabulous resource!], where it said:

When clocks finally began to appear on important churches and public buildings, some of them had a dial with only six hours, not twelve as in ordinary clocks, so to divide the day into canonical hours, when the prescribed prayers were to be recited. The bells, instead, rung up to twelve times, despite the dial, and the hours were counted up to 24! For instance, at the 21st hour (i.e. around 4 pm in summer) the dial would have shown III, and nine tolls of the bell would have been heard.

Only two of these dials are still extant, in the main cloister of Santo Spirito in Sassia complex, near the Vatican, and on the façade of Santa Maria dell’Orto’s church, in Trastevere district (pictures on the right).

We did sneak over the Santo Spirito, but couldn’t find the clock and there was a wedding just getting out (all the cars had big bows on the antenna; we saw this in another wedding procession the next day) so we didn’t really want to stand and look around.  I’m still not sure where it is.

BUT, as a bonus, we did unexpectedly run across two more sundials in the museum in Ephesus.

 

Ephesus was a Greek city before it became a Roman city before it became a Turkish city, which probably explains the Greek.  (Although it’s interesting that it’s letters instead of numbers.  Unless the letters are also numbers?  And if not, aren’t some letters missing?  I’m so confused.  Most of the stuff in the courtyard was unlabeled, so I couldn’t find out anything additional.)

Next up, even more math in Rome!  Unless I don’t get to it before Friday’s Carnival of Mathematics, in which case the Carnival will be the next up.