Walking Randomly

73 is an awesome number.  In fact, one could argue that it’s the Chuck Norris of numbers.  Here’s why (courtesy of Wikipedia, and Number Gossip):

• The mirror of 73, the 21st prime number, 37, is the 12th prime number. The number 21 has factors 7 and 3.
• In binary, 73 is a palindrome – 1001001
• Of the 7 binary digits representing 73, there are 3 ones.
• Every positive integer is the sum of at most 73 sixth powers.
• In octal, 73 is a repdigit – 111
• Pi Day occurs on the 73rd day of the year (March 14) on non-leap years
• 73 is the largest integer with the property that all permutations of all its substrings are primes
• 73 is the largest two-digit Unholey prime: such primes do not have holes in their digits
• 73 is the smallest number (besides 1) which is one less than twice its reverse
• 73 is the alphanumeric value of the word NUMBER: 14 + 21 + 13 + 2 + 5 + 18 = 73

73 is also the edition number of this, the latest Carnival of Mathematics, to which I bid you welcome.  On with the show.

First up we have a mathematical calendar for 2011 courtesy of Ron Doerfler which focuses on Lightning Calculations.  I have written about Ron’s calendar before and highly recommend it to all.

The beginning of a new calendar year is an opportunity for all of us to sit back and take stock of everything that took place over the previous 12 months.  As a result you’ll find retrospectives of all kinds scattered around the internet and on TV such as The Best Tech Products of 2010, TV’s 11 best Watercooler Moments of the Year and so on.  Over at his blog, Wild About Math, Sol Lederman points us to a much more mathematical restrospective of the year 2010 by giving us a heads up about an awesome looking new book.

Next we have the 2011 Mathematics game from Denise of Let’s Play Math; the rules of which can be most simply stated as “Use the digits in the year 2011 to write mathematical expressions for the counting numbers 1 through 100.” Head over there to see more detailed rules, hints, tips, discussion and solutions found so far.

If all of that isn’t quite enough to sate your appetite for all things 2011 then I suggest that you take a look at Patrick Vennebush’s post entitled 2011 – Prime Time which inspired Brent Yorgey to follow up with Prime Time in Haskell.  I wonder if 2012 will inspire such mathematical and computational outpourings?

In her post, Two Planes, Tanya Khovanova stumbled across a seemingly innocent looking question in an old edition of Mathematics Teacher which made her take a deep breath and exclaim ‘Ooh, boy!’. Check it out to see what all the fuss is about.

In Redefining Great Britain, GrrlScientist highlights some new research that describes a clever way to redefine and redraw geographical areas using telephone communication networks — it relies on statistics and computing power.

Sander Huisman has a crack at inventing his own fractal based upon the q-gamma function using Mathematica and a heap of computer time.  The resulting fractal zoom looks great.  He’s also produced a really neat animation of a hinged tesselation.

How do you abbreviate the word ‘Mathematics’?  Some say ‘math’ others say ‘maths’ but which came first and which is the most popular?  In his post, Math/Maths in Google Books Ngrams, Peter Rowlett uses Google Ngrams to sample millions of books in order to try and determine the answer to these and similar questions.

The trapezoidal rule for numerical integration has been in the news recently and so John Cook of The Endeavour shows us Three surprises with the trapezoid rule.

Imagine that we want to bet on an event with m >= 2 possible outcomes, and that there are n >= 2 bookmakers taking bets on those outcomes. Note that the odds are known at the time the bets are placed, i.e., we have fixed-odds betting instead of pari-mutuel betting. We would like to know how to allocate our (limited) money, i.e., how much to bet on each outcome at each bookmaker. As we cannot foresee the future, we would very much like to lock in risk-less profits. In other words, we would like to find arbitrage opportunities (aka: “arbs”). In his post, Fixed-Odds Betting Arbitrage, Rod Carvalho discusses how, given the (fixed) odds posted by n bookmakers, we can detect the existence of arbitrage opportunities.

PhD student, Gianluigi Filippelli, considers a problem from way back in the 13th century in his post Fibonacci, Bombelli and imaginary numbers. Personally, I’ve always loved some of the historical aspects of mathematics and hope to attend a good course on it some day.

Finally, we have a post from Guillermo Bautista called Chess and the Axiomatic Systems where he provides an intuitive introduction to the notion of axiomatic systems through chess rules.

That’s it for this time but if you still need more mathematical blogging then check out The 12 Math Carnivals of 2010 and don’t forget to submit your articles to the forthcoming Math Teachers at Play carnival.

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