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!)

Carnivals and Clowns. Clowns who shouldn’t be allowed to grade.

The Carnival of Mathematics #62 is up today at The Endeavor, and I can tell you right now that I’m totally jealous of the giant Dorito Sierpinski.    Now I’m looking forward to seeing Nerd High!

Speaking of Carnivals, though wonder of wonder we’re posting about #62 on the day it appears, there was also a Math  Teachers at Play #22 up at math hombre [hey, author John works with a friend of mine!  Yup, the math world is getting smaller by the second.]

So that’s the carnival news.  And clowns, you ask?  Well, I’m thinking that the clowns are the faculty of  my department, for  coming up with a grading scheme that’s so absurd I’m really tempted to use it in one of my classes next year.

Here’s the idea:  Suppose you teach a course and you want to have 3 exams each worth 20% of your grade, homework worth 10%, and a final worth 30%.  One way to do this is to set the midterms at 100 points each, the final at 150 points, and homework scaled to 50 points for a total of 500 points in the class.

So far so good, right?  The problem with this is that if you offer extra credit you have to be careful not to give too much — you wouldn’t award 10 points for being the first to speak in class, right?  (OK, you might, but that would be pretty generous.)  So if you want to be able to offer smaller amounts but not have them sound small, you need to have a larger total number of points.

How large?  How about 1 trillion points!  That ties in nicely to the scale of the national debt, which you can tie together with mathematical literacy and/or an interdisciplinary math/political science activity.   Tests are now worth 200 billion points.  The final is 300 billion.  And now, if a student gives a good answer in class you can off the cuff award them one million points of extra credit!  The student feels good — who doesn’t like to receive a cool million points in extra credit? — and you don’t even have to bother remembering to enter it in your gradebook.  On the other hand, if there are little errors on an exam that you want to point out but don’t necessarily want to penalize (forgetting to write parenthesis, for example, so that 2·(3x+5) is written as 2 · 3x+5 ) you could take off 50 million points.  That’s enough to get anyone’s attention.

I think in some of our classes this would be intimidating, so it’s probably not the best scheme in general.  But in other classes, especially the upper level ones, I think our majors would see this as amusing and, perhaps, a help in internalizing the scale of some of these numbers.

Like I said, tempting.

Carnival of Mathematics #53 is up!

As promised earlier, the Carnival of Mathematics #53 is up at The Math Less Traveled.    It has a healthy number of posts on topics from brain exercises to hyperbolic models to Sangaku and GeoGebra.    The Carnival may be  a bit unpredictable these days, but it’s good to see that it’s just as fun to read!

Speaking of Carnivals, we went to one tonight — a real live one.  And we did the Cake Walk (and won some vivid cupcakes that might be interesting to view under a black light to see if they would glow), but before doing it I did a quick estimate as to whether it was better for four of us to play in a single 10-person game, or to spread it out over more than one game [two going in one round and two going in another].  This is similar to the Box Top problem, but has a different answer because the number of people per round is fixed:  the expected number of wins is the same whether or not we all go in the same round, but we’re more likely to win at least once if we all go at the same time.   In particular, although we lose the possibility of winning more than once by going in the same round, that’s offset by an increase in the probability that we’ll win at least once.  (I find it interesting that it has a different answer than the Box Top problem, which I still don’t feel 100% settled about.)

The 49th Carnival of Mathematics!

It’s the Carnival of Mathematics, here to brighten your weekend and chase any winter blues  or summer sadness away.  There are forty-nine eleven great posts, which we’ve interspersed with facts about the number 49.

Our very first post is Ethnicity, Religion, and War, courtesy of Fëanor at Jost a Mon, in which a statistical approach to history aims to show that if an Ottoman sultan’s mother was of European origin, the likelihood of him attacking Europe dropped by several percent.   Since “Religion” is part of the title, it might be worth mentioning that the period of “49 days” is significant in many religions:  the Buddha, for example, meditated for 49 days and in Christianity the Pentecost is 49 days after Easter.  [The 50 implied in the word Pentecost comes from inclusive counting.]

Next up, Rod Carvalho presents Distance between two words at Reasonable Deviations, which shows how to measure the distance between two words of the same length.  He introduces a graphical approach to make things more intuitive, and  includes Python source code so readers can generate word graphs.  We can trust Rod to be truthful about his Python (code), unlike the people who spread the story five years ago that an almost-49 foot Python snake was captured in Indonesia.  That would have been the largest snake ever found, but the python turned out to be only half that length.

It’s now time for a reading break.  If you were curious about the book Is God a Mathematician? by Mario Livio, you’ll be delighted to know that Arj reviews it over at Science on Tap!  Driving, like reading, is a leisurely activity and if you’re ever in San Francisco (maybe for the Joint Mathematics Meetings next January!) you might use 49 Mile Drive, a scenic route that winds its way through the city.

Break’s over!  Rémy Oudompheng now treats us to a post on computer assisted computations in algebraic geometry with Experimental Algebraic Geometry I:  the Grassmanian over at Embûches tissues.  Speaking of computations, the fraction 1/49 can be written as 0.02+0.0004+0.000008+… .  For that matter, the number 49 can be written as the geometric series 0.98+0.98²+0.98³+…

Next, David asks the question, “Is it possible to make a toroidal polyhedron in which all faces are equilateral triangles and all vertices have six incident edges?” The answer appears to be no, but in Flat equilateral tori? at 0xDE he shows a colorful model that comes close.   These might look good in a motion picture — perhaps one put at by Dreamworks Animation, the  company founded by the 49^th richest American (David Geffen).

Mike Croucher now presents Quadraflakes, Pentaflakes, Hexaflakes and more from  Walking Randomly, which shows lots of different fractal flakes.  These flakes won’t make you cold like the snowflakes that have been covering a lot of the northern hemisphere lately, including Alaska, the 49^th state in the US.

The fractal flakes above aren’t the only thing that blend the familiar with the unusual.  The calculus of finite differences has remarkable similarities to ordinary calculus, but yields a few surprises itself, as illustrated by John Cook in  Finite differences at The Endeavour.     The number 49 is (4+3)², a familiar fact, but it’s also the 4^th smallest number with 3 factors.

Le’ts move on to games!  Burak Bilgin shows how game theory applies to economics, and how you can benefit from a simple rule derived from it, in The Simple Rule of the Economics Game from Distiller’s Corner.   A simple fact about 49 is that it is 23 base 23.

Next there’s  Math: A Different Perspective at Foxmaths! 2.0, in which Foxy derives some nice approximations for a complicated summation; these prove to be rather nice approximations indeed. The moral is to really stop and think about the math, do the math, rather than treating math as an abstract object.  With sums in mind, it’s pretty simple to verify that 49 can be written as 1/24+2/24+3/24+…+49/24.

Now we hit a snag:  this next post was submitted by Dave Richeson, but it’s on the blog bit-player that seems to be by Brian Hayes.  Are secret identities being revealed?  Whatever the case, the post Long division has lots of neat division.  Not the “4 goes into 12” kind, but the kind that divides an entire continent — in this case, North America.   There are pictures included that look like they were based on photos taken from out in space.  Space is where the space shuttle Endeavor might be in mid-May; its first flight was STS-49.

Finally, we end with vlorbik’s Section 5.5: A Manifesto, which he refers to as a “lengthy rant about pre-calc text” on Vlorbik on Math Ed.  And we’ll end the 49 trivia by noting that 49 has an interesting connection with the numbers π and e:
The sum of the first ten decimals of π^e is 49.
The sum of the first ten decimals of ln(π) is 49.

With that, our Carnival comes to a close.   Thanks to all who submitted!

Balloon photo by wwskies.

Carnival of Mathematics #48

You blink your eyes and all of a sudden two weeks have passed, and it’s time for another Carnival of Mathematics!  This one, the 48th edition, is being hosted by the group blog Concrete Nonsense.   As usual, there is a whole bunch of great stuff there, from models of how long people spend in coffee shops to integrals, cabbages, music, and the US Constitution.

(Concrete Nonsense also has a recent post I particularly enjoyed, called “Wood, glue, and the Octahedral Axiom”.  It’s not my area of math, the post and looking at the model were still really interesting!)

Happy reading!

[Incidentally, we’ll be hosting the next Carnival, on Friday the 13th!]

Carnival of Math #47: The Star Trek Edition

The 47th Carnival of Mathematics is up today, courtesy of regular host jd2718.  The number 47 appears a lot in Star Trek (particularly Star Trek:  The Next Generation), so this Carnival is written with a Star Trek theme in mind.    Now I’m torn between reading more of the math posts and reminiscing about ST:TNG, which I used to watch every week in college.  But fortunately the weekend is only half over, so there is plenty of time for both.   Enjoy!

The photo of George Takei is by Zesmerelda, licensed here under Creative Commons.  And OK, he’s in a parade, but that’s LIKE a Carnival.

Edited 1/18 to add: This post was actually written by Ξ, not TwoPi — I wrote it before realizing that TwoPi was logged in, and am not sure how to change the authorship.  Whoops!  And this wouldn’t be a big deal, of course, except that TwoPi is a fan of the original Star Trek, not so much TNG.

The Last Carnival…

Don’t worry, it’s just the last Carnival of the year, not forever!  The 46^th Carnival of Mathematics is up at Walking Randomly, one of our favorite blog reads.

This was a short carnival since some people (insert embarrassed face here) got all distracted with sending out Christmas cards New Year cards Happy Winter cards, and forgot to submit anything.  But fortunately those submissions are good reads, and Mike supplemented the Carnival by adding 12 additional posts of his own choosing, one for each month of the year.

Happy Reading!

Carnival of Mathematics #44

It’s two months before the 44^th president will be in the White House, but the 44^th Carnival of Mathematics is already here!  It’s got everything from controversy and fraud to games and a request to include some good mathematics in the list of 1,000,000 good things!

This carnival is being hosted by Maxwell’s Demon, the blog of Edmund Harriss, who does both mathematics and art.    On his blog he has a neat post on rep-tiles here (which leads to fractal dragons, on which is based the crocheting project Here Be Dragons at Woolly Thoughts), and on his homepage he shows some of his artwork here and here, including the Octagonal Gasket (like Sierpinski’s Triangle, but with octagons)

and these wooden fractal puzzle pieces that can be put together in different ways

(Both are licensed under Creative Commons)

Enjoy!

Carnival of Mathematics #43, Warrior Style!

Lots of good stuff here at the 43rd Carnival of Mathematics! It’s being hosted by The Number Warrior, who also hosted the 30th Carnival of Mathematics. There are quite a few puzzles to ponder in this Carnival, and computers, and quivers, and costs, and all sorts of other cool things.

Blog author Jason Dyer has plenty of other good entries on his blog (plus a neat article on ten different ways to write the equation of a line over at Invisible Math). In this one he talked about classroom setup on the first day and mentioned doing a little math in the news each day. This reminds me of a colleague who, after each test, would spend a little bit of time introducing students to different areas of math: möbius strips, clock arithmetic, etc. just to get students seeing how broad the area of Mathematics is.

Carnival of Mathematics #42

It’s time for the answer to life, the universe, and everything in Carnival Form:  Carnival of Mathematics #42 is up over at The Endeavour, a blog by John D. Cook.    His blog has neat articles like how to convert files to .pdf and Jenga Math (weakening the hypothesis of a theorem without causing the whole thing to collapse).   The Carnival has lots of neat articles on logic, computer science, and how the check-sum digit works on credit cards.  So pull up a chair and Enjoy!

The 41st Carnival of Mathematics

Welcome, one and all, to the 41st Carnival of Mathematics! Step right up and marvel at the amazing, the astounding, the prime number 41! It is, of course, the 41st natural number, and is equal to the product of itself and 1!

Perhaps more interesting is the fact that 41 is a twin, supersingular, Germain, Eisenstein, Proth, and Newman-Shanks-Williams prime (which has to be some kind of record). It is also a centered square number.

We begin with a very accessible discussion of infinite sets, and the difference between countable and uncountable, by Carnival XL host Barry Leiba, in Countable and uncountable sets, part 1, at Starting at Empty Pages. (There’s also a part 2.)

How cool would it be to have a Mathematician for President? Denise tells us all about James Garfield and his proof of the Pythagorean Theorem over at Let’s Play Math.

The Central Limit Theorem is a well-known result in statistics, but in order to use it, one must assume a sufficiently large number of samples. John Cook, from The Endeavor, wants to know about quantifying the error in the central limit theorem, and how close an approximation we can really get. He also compares three methods of computing standard deviation – turns out they’re not all equally good.

Motivated by a confusing chapter in a book on game theory, Rod Carvalho decided to analyze the “Tragedy of the Commons” in Bandwidth-Sharing Games, over at Reasonable Deviations. In his words:

Suppose that n players would like to have part of a shared resource: each player wants to send information along a shared channel of known maximum capacity. I analyze this problem using a game-theoretic approach.

Barry Wright III, at 3 Style Life, goes in depth on elections in Facts about the Copeland Score (with PDF continuation), a way to generalize the Condorcet winner to elections that don’t have a Condorcet winner.

Music and math often go hand in hand, and David Stutz gives us a lot to think about in more musical Turing machines, at the synthesist. Inspired by Neal Stephenson’s new book Anathem, Stutz led a choral performance of a 3-state, 2-symbol Turing machine that performed binary addition. From there, things really take off!

Mike Croucher, 2-time Carnival host and owner of Walking Randomly, and a Mathematica power user, shows us how to Simulate Harmonographs. (A harmonograph is the result of letting a pendulum with a pencil attached to it swing over a piece of paper, like a Spirograph, but cooler.) Then he asks the question: NAG – The Ultimate MATLAB Toolbox? Read to find out if the Numerical Algorithm Group has hit a home run.

Looking for help with your math homework? Visit VideoJug’s math repository for a collection of advice videos on math.

Technology can be a great tool in teaching, and Maria, from Teaching College Math Technology Blog, demonstrates How Tablets Enhance the Math. Derivatives have never looked better.

Last, but certainly not least, how would you get a computer to use ordinal numbers? Mark Dominus tackles the question in Representing ordinal numbers in the computer and elsewhere, over at The Universe of Discourse.

An accidentally missed submission (sorry Jason!) comes from Jason Dyer. His entry, Visual Clarity in the Naming of Variables, examines how using similar letters for different variables can be confusing to students, and he offers several alternatives.

That’s it for #41, but tune in on October 24 for the next edition, hosted by The Endeavor.

The XL Carnival of Mathematics

The long-awaited 40^th Carnival of Mathematics has arrived, courtesy of Barry Leiba over at the blog Staring at Empty Pages. When I was looking over the blog earlier this week I thought, “Hey, I’m going to link to his series on Paradoxes, because I like the explanation and examples of the different kinds of paradoxes, but then it turned out that the series appeared in Carnival #40 anyway. And so did a description of Euclid’s Elements that has a directed graph showing what is needed to prove what (which I’ll certainly be showing to my Geometry students in the spring!) and plenty of other neat posts. So go check it out!

While we’re on the subject of Carnivals, the next Carnival is being hosted right here on Friday, October 10. You can submit via a link in the comments, through the official BlogCarnival link, or by sending an email. (To send an email: the last part is @naz.edu and before the @ you can type either “mkoetz1” or “hlewis5”. Put something like “Carnival” in the title for easy identification.)

Carnival of Mathematics #39

The Carnival is here again! Celebrate the nearing end of August by visiting the 39^th Carnival of Mathematics over at It’s the Thought that Counts, a blog by A and Z about “politics, society, science, morality, religion, and whatever else comes to mind”. (One post of theirs from earlier this month that I particularly enjoyed: Gallons per mile, which examined whether miles per gallon is the most appropriate way to measure a car’s efficiency.)

Returning to the carnival, this edition features a neat problem about the number 39 (If 39 people are sitting around a circular table and no one is in the correct place, prove that there is some rotation with at least two people in the correct place. Only they said it with more storytelling flair.), and a great collection of other posts. Enjoy!

Carnival of Mathematics #38 at CatSynth

The 38^th Carnival of Mathematics is being hosted by CatSynth, the same folk who hosted the 35^th Carnival and who have a great picture of a cat looking at a Lissajous curve (along with an explanation of the curves themselves).   This Carnival features facts about 888 (the date of posting), then a stories on epsilonica all the way down to coloring a plane, with a possibility of more posts to come this weekend.  Enjoy the read!

Carnival of Mathematics #37 at Logic Nest

The 37^th Carnival of Mathematics is up over at Logic Nest. It features prime-generating functions and integrals all the way to cats and Fourier series, with lots of interesting posts in between!

The host, Logic Nest, is the personal blog of Systems Analyst and family guy Ian Luke Kane.   Carnival aside, there are several posts on his front page that caught my interest, like the Pirahã in Brazil who have no concept of precise numbers, and a link to a story about why tape tears.