Welcome to the 23rd Carnival of Mathematics: Haiku Edition! First, I must apologize for the delay: I usually have very little trouble with my hosting provider, but of course it went down just when the CoM was supposed to be posted. But it’s free, so I can’t complain! It’s back up now, and will hopefully stay that way.

For this edition of the CoM, I decided to write a short seventeen-syllable haiku about each of the excellent seventeen submissions I received (along with additional commentary of the more prosaic variety). I’ve arranged the posts more or less in order of required mathematical background, but don’t stop halfway through because then you’ll miss the pretty pictures at the end. Enjoy!

*English pols want to*

make math more interesting.

It’s not already?

From Naomi Stevens’s Diary From England: a government bid to make maths more interesting.

*Neat, use perfect spheres*

to define the kilogram!

Off by just atoms…

Heather Lewis, of 360, writes about Australian scientists who are trying to make a perfect sphere. Pretty incredible stuff!

*Freshmen work in groups,*

and answer their own questions.

Effective? Discuss.

JackieB of Continuities explains the pedagogical approach she takes with her freshman. Be sure to read (or contribute to!) the fascinating discussion that ensues in the comments section.

*Multiple choice, now*

with bonus choice enhancement!

Hard tests, nice to grade.

Maria Andersen, at the Teaching College Math Technology Blog, shows off a new sort of multiple-choice test that’s easy to grade, but avoids many of the well-known problems with traditional multiple-choice tests. I wish I’d thought of this when I was teaching high school!

*Are you learning two*

languages—math AND English?

Great sites for you here.

Larry Ferlazzo presents a list of the best math sites for english language learners.

*Mathematics blogs*

are many; which are the best?

Here’s one opinion.

Denise of Let’s play math! writes about her favorite math blogs.

*I have not yet read*

“Letters To A Young Mathster”.

I’m not missing much.

Andrée has written a (not-too-favorable) review of Ian Stewart’s book “Letters to a Young Mathematician”, over at her blog meeyauw.

*Albatrosses fly*

in fractal patterns! Oh wait–

experiment sucked.

Julie Rehmeyer discusses how scientists are revisiting some research on fractal patterns in the flight patterns of albatross at MathTrek. Apparently, just because an albatross’s feet are dry doesn’t necessarily mean it’s flying. Who knew?

*Eight ninety-eight, eight*

ninety-nine, nine hundred… sigh…

infinity yet?

Thad Guy has a funny comic about infinity. Check out some of his other comics, too—I’m a (new) fan!

*Need socks in the dark?*

The pigeonhole principle

comes to your rescue!

Mary Pat Campbell (aka meep) presents a cute video explaining the pigeonhole principle. Did you know that at least two people in the US have the exact same number of hairs on their body? You can’t argue with math!

*A counting problem:*

how many bracelets are there?

Harder than it looks…

MathMom came across an interesting MathCounts problem involving beaded bracelets, which generated some great discussion. How would you solve it?

*List of rationals,*

both elegant and complete?

Is it possible?

Yours truly has posted the first in a planned multi-part series explaining a particularly elegant way to enumerate the positive rational numbers.

*Koch snowflake fractal:*

Area? Perimeter?

Fractals are so strange…

Over at Reasonable Deviations, rod uses geometric series to calculate the area and perimeter of the Koch snowflake. The result is rather surprising!

*Twelve Days of Christmas?*

How many presents is that?

Let’s figure it out!

Over at Wild About Math!, Sol Lederman presents a seasonally-appropriate exploration in counting presents. Fun!

*A tricky puzzle:*

rectangles and angle sums.

I solved it, can you?

JD2718 shares a gem of a puzzle involving the sum of some angles. It’s tricky—are you up to the challenge? I would especially encourage would-be solvers to come up with a nice

*geometric*solution (I couldn’t)!*Pascal’s Triangle:*

writing it out is a chore.

How fast does it grow?Foxy, of FoxMaths! fame, presents an interesting two-part analysis of the asymptotic growth of the rows of Pascal’s triangle—not the growth of the actual values in the rows, but of the space needed to write them!—making use of some clever algebraic gymnastics and asymptotic analysis.

*In how many ways*

can the Nauru graph be drawn?

The answer: a lot!David Eppstein of 0xDE presents The many faces of the Nauru graph: a collection of diverse ways to visualize a particular graph which he dubs the “Nauru graph”, due to the similarity of one of its drawings to the flag of Nauru. Planar tesselation, hyperbolic tesselation, embedding on the surface of a torus… all that and much more, with, yes, pretty pictures for everything! Even those who don’t understand the article itself should still go take a look, solely for the sake of the pictures. =)

Thanks to everyone for the great submissions, I had a fun time reading them and putting this together. The next CoM will be hosted at Ars Mathematica. As always, email Alon Levy (including “Carnival of Mathematics” in the subject line) if you’d like to host an edition.

Wait! Before you go, in honor of the new year, here’s one last link from Mike Croucher at Walking Randomly, who wants to know: what is interesting about the number 2008?

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The great Carnival

Many flock to see it here

We all read it now

Really great job. One detail: Andrée is a she.

Jonathan

Oops! My apologies! Thanks for the catch, Jonathan.

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Hey, Brent, I’m impressed

At your haiku-making skill.

You made no mistakes.

Then again, it’s not

Often that “interesting”

Has four syllables.

That word’s often said

with three syllables, but it’s

technically four.

Yes, “technically”

is another of those words.

Refrigerator.

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Ars Mathematica is hosting the next Carnival. I reminded Alon, who updated the Carnival site with the information. I would appreciate it if you could also put something up to that effect.

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On point 15, the angle puzzle, there is a nice geometric solution, though the analytic one with complex numbers might be easier to find. I don’t remember where I’ve read it, maybe it was an IMO task or something. Anyway, it’s this.

As in the task, define the points A=(0,0), D=(3,0), E=(3,1), F=(2, 1), G=(1, 1). Also, take the point T=(2,-1). Then, segment AT is equal to segment ET and they are perpendicular, so the triangle ATE is an isosceles right triangle. Thus, the TAE angle is equal to the TEA angle. Also, obviously, the DAT angle is equal to the DAF angle, so the TAE angle is equal to the DAE angle plus the DAF angle. Finally, the DAG angle is obviously half a right angle.

My name is Kevin.

History is my true love,

Math is close second.

Draw a polygon.

Any sided shape will do.

Do not be a square.