Carnival of Mathematics #72

Welcome to the 72^nd 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 72^nd 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!)

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