Thursday, March 4, 2010

Carnival of Mathematics 63


Welcome to the 63rd Carnival of Mathematics. Here's a property of the number 63, courtesy of Number Gossip:
Consider two functions $f$ and $g$ where
- $f$ maps a natural number onto its Roman Numeral (a string of letters);
- $g$ maps a word onto the sum of the numerical values of its letters (the value of a letter is its position in the alphabet).
It turns out that our number 63 is a fixed point of the endomorphism $gf$, ($63 \mapsto LXIII \mapsto 12+24+9+9+9 = 63$). Number Gossip assures us that there are not too many fixed points of this map.

What is a math(s) carnival? Please see this post by Mike Croucher at Walking Randomly. Want to see more mathematics carnivals? Check out the list of past incarnations of Carnival of Mathematics here, along with past Math Teachers at Play carnivals here (if nothing else, be sure to check out the most recent MT@P!).

The images appearing in this edition of the blog carnival are courtesy of Jeff Miller's mathematicians (and mathematics) on postage page.


Bryan of Soul Physics, presents two recent posts: How to time-reverse a quantum system and Unitary operators and spacetime symmetries.

John Baez and Mike Stay have both blogged about their recent paper Algorithmic Thermodynamics at the n-Category Cafe and reperiendi, respectively.

At bit-player, Brian Hayes has written an interesting post about someone who may have been the first proto-blogger on computational topics (circa 1970) in his post Gruenberger’s prime path.

Charles Siegel proves a big theorem in his post Monodromy and Moduli posted at Rigorous Trivialities.

Martin wonders where zero might be pointing in Zero's signs posted at Enigmania


Peter Rowlett's post Truchet, Braille and Euler from Travels in a Mathematical World provides us with a whole new way of seeing a familiar identity.

Fëanor presents Common Errors (31): Pythagoras posted at New at LacusCurtius & Livius.


International Women's Day is coming up next Monday (March 8th). Suzane Smith reminds us of 15 Female Scientists Who Changed the World posted at EKG Classes. Reading through this list reminded me of an excellent article, Not good with numbers, posted by Izabella Laba at The Accidental Mathematician.

On his new math blog, Puzzle Zapper Blog, Alexandre Muñiz presents Holy Hyperbolic Heptagons!. The neat hyperbolic diagrams there reminded me of M.C. Esher's hyperbolic tilings.

Coincidentally, Chaim Goodman-Strauss of the Math Factor recently blogged (and pod-casted) about the largest Escher exhibit ever.


A Twitter discussion about the relative merits of MathType and Latex has prompted Robert Talbert of Casting out Nines to blog about Five reasons you should use LaTeX and five tips for teaching it.

Inspired by the same tweets, Kate Nowak gives us a demonstration of how well MathType can work for those who've mastered their keyboards in MathType Challenge at f(t).

Keeping with the 'tools of the trade' theme, Mike Croucher proves that Mathematica does not suck by teaching us about Integrating Abs(x) with Mathematica posted at Walking Randomly.


And now, some introductions...

Jamie introduces his two new math blogs with What is Daily Mathercise? posted at Daily Mathercise, and What is Math Factoid? posted at Math Factoid.

Nancy Goroff introduces us to George Hart's work at Make Magazine's Math Mondays with Make: Online : Math Monday: Sierpinski tetrahedron posted at MAKE Magazine.


Following John Allen Paulos, students from the University of Leicester comment on mathematics in the media on their blog, Math Students Read the Newspaper.

John Cook presents his latest post on laws of numbers - large, small, and now medium in The Law of Medium Numbers — The Endeavour posted at The Endeavour.

Inspired by a recent essay by Micha Gromov, T of Meteoroids from Mindspace takes us on a tour of mathematical platonism in a context for Gromov's program.

Is there really such a thing as a coincidence in mathematics? By chance or by design, Pat Ballew has written about A Serendipitous Coincidence? The First-Ever Pursuit Problem. posted at Pat'sBlog.


Jason Dyer reprises a worthy, and surprisingly heated, topic in Multiplication is Not Repeated Addition? Revisited posted at The Number Warrior.

Jason's post prompted Sue VanHattum to ask What is Multiplication? posted at Math Mama Writes....

All the ensuing discussion on both blogs reminded me of 360's classic series of posts on the various ways we can multiply (warning for those with strong feelings: repeated addition is on the list).


Thanks to everyone who submitted, and to everyone who has visited. Be sure to submit your preK-12 math posts to Math Teachers at Play, and your everything-but-the-kitchen-sink math posts to the next Carnival of Mathematics. Be on the look out for the 64th edition of CoM, coming next month at Teaching College Math.

4 comments:

  1. Actually, I think Jason and I were both inspired by the discussion at Michael Paul Goldenberg's blog, Rational Mathematics Education.

    I love the stamps! The Liberian one, showing the 'Pascal' Triangle, is my favorite. Wikipedia says "Pascal's triangle is called Yang Hui's triangle in China." And the textbook I used when I taught math for elementary teachers said that there's a mistake in it. Here's a bigger picture. Can you find it?

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  2. Fantastic carnival Dan - thanks for hosting. I'm loving the postage stamp theme! One of my guilty secrets is that I am a stamp collector and I have a little sub-collection of maths on stamps including some of the ones you show here.

    Cheers,
    Mike

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  3. Sue VanHattum,
    That's a great puzzle! My eyes weren't sharp enough to spot it by just comparing symbols, but once I figured out the notation I finally found the mistake in the next-to-last row.

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  4. Thanks! Make sure you check out the rest of Jeff Miller's collection :)

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