Carnival of Mathematics 108

Welcome to this months Carnival of Mathematics!

I thought it was auspicious that this is 108, a number closely connected with the Golden Ratio, because of its appearance in the regular pentagon. (I am also Golden, if you can't see the auspices.)

108 is pretty interesting in other ways, too. I got wondering if many other numbers are multiples of the same number with zeroes removed. (What about other digits?) New to me was the idea of a refactorable number: a number divisible by the count of its divisors. They are rarer than I would have first expected; also called the tau numbers. 108 is the 18th tau number. Can you find all 17 prior?

Let's get to the submissions! Where I could find them, I linked the author's twitter account as well.

There are many states with a Highway 108, but Kansas gets the picture, since they use a sunflower (their state flower), which is also - of course - associated with the Golden Ratio. 






Patrick Honner asks who has done a billion dollars worth of work? Wages, worth and gender bias all figure in.

Cav has a post trying to make sense of maths testing. Maybe separating it out into two different subjects... On a more personal note, he looks at amusing, infuriating and worrying answers on his own students' exams.

Jennifer Silverman shares her visual approach to the quadratic formula at her tumblr. College math majors often are missing this connection between completing the square and the QF.

Malke Rosenfeld writes about Beautiful Objects at Math in Your Feet. The objects in consideration are lovely group symmetries from Christopher Danielson.

Mike Lawler got great reasoning out of Fawn Nguyen's bridge problem. Inspired me to try it with freshmen and grad students to great effect. And now on to the grad students classrooms, too!

Sue Van Hattum makes an argument that optimization is the best application topic in standard math classes, and uses her recent calc lesson as an example.

This graphic designer, Jack Hagley, made a neat logo based on his research at Wolfram-Alpha. He thought 108=1x2x2x3x3x3 was beautiful in its own right. (I agree!) These are hyperfactorial numbers.


Edmund Harriss has several threads converging in his post at Maxwell's Demons about Rational Parameterisation of the Circle. Very novel idea, connections with stackexchange, and beautiful images from Lissajous variations. He also has some very mathy fun with generating "huge worlds of potential logos" for Twitter Math Camp 14. (Full, but there is a wait list.)

John D. Cook accesses Category Theory to determine whether the stars go up or down at his blog, the Endeavor. Hint: yes.

Dan McQuillan writes about induction in the Unreasonable Efficiency of Mathematical Writing. I love his advice: "focus on the beautiful idea."

At the By Way of Contradiction blog, there is a probability post on how to pick odds in the most favorable way. Includes this sentence: "Satisfied with your math, you share your probability, he puts 13.28 on the table, and you put 2.72 on the table." This is, I think, the pub for me.

In some Hindu and Buddhist practice, a mantra is recited 108 times. This leads to malas (prayer beads) often having 18, 27, 54 or 108 beads. This may be connected to the Sri Yantra, which has "9 interlocking triangles forming 43 smaller triangles."

Cool geometry, regardless.

Edward Frenkel, author of the recent hit Love and Math, had a much talked about editorial in the LA Times: How our 1000 year old math curriculum cheats America's kids. (That's what we get for buying an 800 year old curriculum when we started, I say.)

Askhat Rathi at the Conversation has my favorite recent math in the news story, the discovery of a new class of polyhedra. Yeah!

108 figured prominently on LOST. (Here's some of the connections from the show.) Most significantly, it was the sum of the numbers 4 8 15 16 23 42. Never sufficiently explained, I think, and I'm still mad about the ending. So there.



Evelyn Lamb digs into the history of the Parallel Postulate at her Scientific American blog Roots of Unity. Triangles with angle sums of 0 degrees, rectangles held hostage - exciting stuff. Evelyn also has a post at the AMS (her Blog on Math Blogs) looking at Michael Pershan's Math Mistakes site and contemplating SBG. (Go for it, Evelyn!)

Fiona Keates, who blogs in The Repository at the Royal Society, has a piece on a mathematician in the movies. Yes, Ramanujan is coming to a theatre near you!

Shecky Riemann interviews the  fascinating Cathy O'Neil, author of the Mathbabe blog, at Math Tango. (Cathy's on Twitter, too.)





The oddest 108 connection I found was 108 Rock Guitars. Since Math Rocks!, they get a link. (Maybe I meant Math Rock?)







Antonio Chinchón has a post on the sound of the Mandelbrot Set. A neat combination of pretty, computation and sonification of data. He also has a post about Warholing data (after the pop artist), which he does to Grace Kelly.

Mike Croucher at Walking Randomly has several different mathematizations of the heart that go far beyond the standard cardioid.

Sam Shah derived the curve found in string art as he did Doodling in Math Class.

Hopefully you got a chance to see Carnival 107 at White Group Mathematics. Next month's 109 is at Tony's Maths Blog. Be sure to check out Sue Van Hattum's hosting of the Math Teachers at Play carnival 71 (with 71 links). You can submit a post at the Carnival's homepage at the Aperiodical. Katie Steckles makes these happen, and submitted several interesting items above; Thony Christie also made some nice picks. Gracias!

108 Eyes by playful_geometer

There were some posts I wasn't sure what to make of... John Gabriel arguing that no valid construction of the reals exists. Katie submitted a Windows 8 math game app called Equations. I haven't been able to test it out, though. The reviewer dislikes it for pretty valid sounding reasons.