The Carnival Lives!

The Carnival of Mathematics is still going strong.  This round – #76 – is hosted over at Walking Randomly and has, as usual, something for everyone, including a post from one my favorites: Language Log.  (Yes, they use math there.  Fairly often, in fact.)  Go check it out, and while you’re at it, contact Mike if you’d like to host one.

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.

Happy New Carnival!

It’s a new year, maybe a new decade (I’m a plebian), and the perfect day for a new Carnival!  Though I can’t help but feel guilty that I didn’t mention the previous one, and not because it wasn’t good either — it was.  So here’s a summary of the carnivals and a chance to start the New Year off on the right foot!

There was Math Teachers at Play #20 back on its original turf at Let’s Play Math, with it’s regular assortment of lots of fun math.  Speaking of Let’s Play Math, Denise has her annual New Year’s post with the 2010 Mathematics Game; I remember thinking last year that I should get a head start on that, and didn’t, but we’ve got some mathy company coming this weekend so it’ll provide some good entertainment.

Then there was the Carnival of Mathematics #60 over at Σidiot’s Blog (heheh — I just got that).  That carnival appeared back on December 4, and had some neat modular origami and puzzles and National Math Blog Writing month and a portrait of someone who isn’t a mathematician.

Next came Math Teachers at Play #21 at Math Mama Writes in mid-December (and Sue also has  a recent post exploring Pythagorean Triples, which seem to come back again and again as neat things to think about).

And now we’re at Carnival of Mathematics #61!  It’s up at Walking Randomly today, with puzzles and statistics and many other good things.  There’s a mention of calendars at the end, which reminded me of the printable dodecahedral one that TwoPi mentioned two years ago.  Not that that is a calendar or anything, but at least it’s a dodecahedron.

And there we have it.  Happy New Year!

Carnival of Maths #59 is up!

The Number Warrior is hosting this month’s carnival!  It’s up here, and I was impressed with the entries [both in number and quality].  Plus, there was even something on Bourbaki, though not the symbol I wrote on earlier.

I also really like the post right before the Carnival, about a possible case of cheating at the 2009 Philadelphia Inquirer Sudoku National Championship.  You can find some of the contest Sudoku puzzles at this pdf.

Now I want to try some Sudoku:  here’s one that’s a jigsaw puzzle (created by A.R. Nonenmacher and published under GNU-FDL)

Carnival Month! (past, current, and upcoming)

In celebration of the month of October Wait, you mean it’s October already? When did that happen? , here’s some belated Carnival News:

[picapp src=”0227/fda6d0ae-1865-438f-bdfe-747988e65087.jpg?adImageId=7027209&imageId=230872″ width=”234″ height=”350″ /]

[Hey, it’s the new PicApps!  I’m trying to decide if I like it — more pictures versus the less control thing.  And that little film strip.  Hmmm.]

Math Teachers at Play #16 appeared on October 3 over at  I Want to Teach Forever.  One of my favorite submissions was the Brain Games from mental_floss  Blog, but there’s plenty of other good stuff.    Then, two weeks later, there was Math Teachers at Play #17 over at mathrecrecreation. (who has a post on origami today!) with yet more interesting posts.  And now we jump ahead to Math Teachers at Play #19, over at Math Mama Writes [What happened to #18, you ask?  You’ll have to check it out and see!].  It’s got some cool stuff, including a post about using math to solve a murder case [but can they really neglect air resistance?  Wouldn’t that make a difference, and maybe make it possible to travel further in the x-direction?  HEY — it’s a project question for when I teach Diff Eq in the Spring!]

So there’s the way too late update!  Stay tuned for the Carnival of Mathematics next week over at The Number Warrior (who also has a cool problem-solving/communication  post currently up on the game Slitherlink).  The Carnival of Mathematics will now be appearing the first Friday of each month, with Math Teachers at Play moving to the third Friday of the month.  More details can be found here at Walking Randomly, who has taken over organzing the CoM.

Stay tuned for tomorrow:  the Mystery of the Fibonacci Pumpkin!

Carnivals Galore! Plus some Excel.

First off, there was a Math Teachers at Play (the second #15) just about two weeks ago.  It’s hosted by Maria Droujkova of the Math 2.0 Interest Group.    There’s the usual assortment of great stuff, including a computer game that I really want to play, and some stuff on Wolfram Alpha (which I know is totally old hat, but I gave two of my classes the homework assignment to play on W|A for 20 minutes and email me the neatest thing they found, and I think that’s been their favorite assignment so far.  Plus one of my Math for Liberal Arts groups cited it in a project when a pattern of numbers got too big for their calculator.  I love Wolfram Alpha) and sites for special needs students.

So that’s one carnival.

And the next is the Carnival of Mathematics #58 at Walking Randomly, up this past weekend, with near integers and binary in baby toys and maps.  (And now the 9-year old is wondering why I’m listening to  Men at Work).   Even though it’s not in the Carnival, also check out the post about (-1)*(-1)=+1.]

This has nothing to do with the Carnivals, but do you want to know what I learned how to do on Excel this weekend?  Conditional formatting!  I use Excel for my gradebook and I usually highlight if a student gets below 70% on exams or projects.  In the past I’ve done this by hand — which isn’t too time consuming because we’re not talking loads and loads of people — but it turns out that you can highlight a group of cells, go to Format, and then Conditional Formatting, and then set it up.  I even got lazy and for a 32-point assignment I set it to highlight scores less than “=70%*32”.    I expect this isn’t news to many people, but since the first person I mentioned it to hadn’t heard of it, I figure that’s good enough reason to bring it up.  Thanks for showing me this Nicole!

Carnival of Mathematics #57

Welcome to the 57th Carnival of Mathematics!  This particular carnival is sponsored by the numbers 57 and 2:  the first for the obvious reason and the second because it turned out that each contributor has two blog posts (though in some cases that will come as a surprise to the contributors).

The number 57, while not actually prime, is known as a Grothendieck prime in honor of Alexandre Grothendieck.  According to legend:

In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”

This story is not implausible, because Grothendieck didn’t normally think in terms of numbers and actual examples (according to the rest of the article above).  Indeed, abstractness was a characteristic of his.  Speaking of characteristics, Akhil Mathews at fellow group blog Delta Epsilons has a post on Hensel’s lemma and a classification theorem for complete Discrete Valuation Rings with a residue field of characteristic zero.  (It’s actually part of a longer series, which I think starts here and continues over the next few days.)

The number 57 also occurs in the ketchup Heinz 57.  When they introduced their catsup, they had roughly 60 products of various sorts on the market.  57 sounded nice, so they called the catchup their 57th product.  In this case, they were just using the numbers to count, but another thing that you can do with numbers is to combine and permute them.  However, as John D. Cook shares over at The Endeavor,  a misunderstanding of those processes can (almost) lead to blows:  see Classroom Violence, Combinations, and Permutations for the full story. He also write about Gilbreath’s conjecture in Easy to Guess, Hard to Prove, which provides a great example to share with students about a math problem that seems simple but, as the title suggests, isn’t.

Rod Carvalho wrote two posts on optimal debt allocation over at Reasonable Deviations:   Part I is here and Part II is here.  The articles, inspired by real-life bill-splitting at dinner, pose some interesting questions that I hope are solved soon.  Something else that is solved — well, really, solvable — is any group of order 57.  (There are several reasons for this, the simplest being that 57 is the product of two odd primes.)

Both TwoPi and I started our life in California, which has 58 counties.  (Yes, that’s not 57.  No state has 57 counties, though Montana would win the Price is Right prize with 56).  Speaking of life, Nathaniel Johnston shares a post on generating sequences of primes in Conway’s game of life .  Also check out today’s post about how primes with millions of digits aren’t useful for cryptography.

And last but not least, Pat Ballew of Pat’sBlog wrote about samuri and mathematics in Pi and the 47 Ronin, with a request for any photos that might be available of the tomb of Matsumura.    He also explored an exploration by Leibniz in Limits as x→Infinity.  Something that isn’t infinite is the list of Idoneal numbers:

An idoneal number, also called a suitable number or convenient number, is a positive integer D such that any integer expressible in only one way as (where x² is relatively prime to Dy²) is a prime, prime power, or twice one of these.

There are only 65 of them, or maybe 66 if the generalized Riemann hypothesis holds.  The number 57 is one of those Idoneal numbers.  Isn’t that Convenient?

The next Carnival of Mathematics will be hosted by Michael Croucher over at Walking Randomly!  See you there in two weeks!

Recent MTaP #15 and Upcoming Carnival of Math #57

The most recent Math Teachers at Play, #15, is up at the Homeschool Math Blog.  I got completely distracted by the first post about some math for kindergarteners, and several clicks later I was listening to binary music.  As usual the rest of the Carnival is full of great stuff as well.

Speaking of Carnivals, assuming I don’t lose track of the days we’re hosting the next Carnival of Mathematics here on Friday!  You can email submissions to hlewis5#naz.edu [except replace that # with a @], ideally putting something like “Carnival” in the title, or post a link here or with the previous announcement.  And since I’m a procrastinator, I’d say you safely have through Thursday night to submit.

On an unrelated note, but just because it’s fun, here’s what a colleague wrote on the whiteboard of my office:

111,111,111×111,111,111

(I think it’s more fun to do by hand than on a calculator, but it’s neat however you find the answer.)

Carnival of Mathematics #56 is up!

Yay, it’s another Carnival of Mathematics (This one #56)!  It’s up at Reasonable Deviations, and includes computers, statistics, geometry, primes, and even tinkertoys [which match the previous post on RD about a marble adding machine].   Thanks, Rod, for putting together so many posts!

(Incidentally, we’ll be hosting the Carnival of Math #57 in two weeks time.   Would anyone like to volunteer for #58?)

Current Math Teachers at Play and upcoming Carnival of Math

Yup, the title pretty much sums it up!

Math Teachers at Play #14 is up at Math Mama Writes… and, as always, is full of great posts.  One of my favorite is  a chart illustrating how few quadratics have integer roots.  It’s a little daunting (although I suppose you can increase the number by considering negatives).

Speaking of Carnivals, there will be a Carnival of Mathematics #56 next Friday up at Reasonable Deviations.  The official Carnival submission page doesn’t seem to work anymore, but there are instructions at the link above to email or post a submission.

Math Teachers at Play #13 is up

Last Friday, right on schedule, Math Teachers at Play #13 appeared at Blog, She Wrote, the blog of homeschooler, science lover, scrapbook lover Heather.    As usual, there is a great collection of materials, including one of my favorite card tricks.  😀

Carnival of Math #55 is at SBHS!

Yay — we’re home!  And despite the fun of hanging out at beaches (Oregon) and cities (Cincinnati, Chicago) with a total of three dozen family and friends over the past month, it feels mighty good to be home.  But our classes start in just over three weeks (wait, really?  Somehow it feels like it should be a lot further away than that), so it’s back to work sooner rather than later.  As in, tomorrow.

However, there’s no better way to get into the work spirit than with a Carnival!  The Carnival of Maths #55 is over at Maths at SBHS, the Class blog for Maths at Sowerby Bridge High School, UK.   One of the things I really like about this edition is that I didn’t recognize several of the blogs with contributing articles, so there are a whole bunch of new places to check out.  Woo hoo!  (Plus, the post below it was pretty funny, about estimating the general shape of a graph of the number of bras left on a fence over time in New Zealand.)

The next Carnival of Mathematics will be hosted by Someone at Some point in the future.   Stealth Carnivaling at its best!

Carnivals Galore

As part of our limited-internet limited-posts July, we fell behind on all the Carnivals.  Rather than skip them completely, which would be sad, we’ll do a quick summary.

We missed the Carnival of Mathematics #54 at Todd and Vishal’s Blog (Topological Musings), but there is a lot of good info there, including links to a couple of new blogs.

Earlier this month was Math Teachers at Play #11, hosted by Sue Van Hattum at  Math Mama Writes….  (Incidentally, her current post on Myths about Math is also interesting to think about.  I see a lot of those beliefs when I teach our Thinking Mathematically course, which is one of my favorite classes to teach [usually taken only to satisfy the general ed requirement]).

Finally, today is Math Teachers at Play #12, hosted by Jason Dyer over at The Number Warrior.   (I love the photo in one of the links of an elevator in Serbia with negative numbers!)

This is unrelated to Carnivals, but we were thrilled to be included on Online Universities’ list of the 100 best websites for Mathletes.    They have several groups of info, including major math organizations [primarily in the US],  a list of contest sites, and a section on Career Tools and Guides.  Thanks!

Balloon photo from wwskies.

Math Teachers at Play #10 and Time Savers

On Friday, right on schedule, Math Teachers at Play #10 was posted at Homeschool Math Blog.  There’s good information on Wolfram Alpha and homework and optical illusions and a host of other interesting things.

The discussion on homework had me remembering one of my favorite Teaching Time Savers.  Jane Murphy Wilburne explained here how she dealt with homework.

As the students entered class the next day, they would list the page number and problem number of the problems they could not solve, on the front board in a designated area. If the problem was already listed, they placed a check (√) next to it. Once the class started, they were not allowed to record problem numbers at the board. Other students, who were successful in solving these problems, immediately went to the board when they entered the class, indicated that they would solve one of the listed problems, and worked it out in detail. When they finished they signed their name to the problem.

I tried this out in calculus, a course where I assign homework every day, and it worked fabulously.    It didn’t eliminate grading, but it did cut way down on how much time I spent going over homework in class.  The only change I’ve made is that I now  insist that people write down what they had trouble with, so instead of writing just #23 they’d write “#23:  couldn’t get started” or “#23:  what do you do after [this step]?” or “#23:  I got x² but the book says x³.”  And I count answering the questions correctly as extra credit.  (In perspective, homework is 10% of a person’s grade in calculus; usually each assignment gets 5 points, and there are probably 35 assignments over the semester.  I’ve ended up giving 1 extra credit point for each time a person added correctly, with a cap of earning 100% total for homework.)

I haven’t done this in all courses, but I do use it in every calculus-type course (where the problems tend to be shorter) and it’s gone really well.  So that’s my two cents.