Deep math of the folded pizza slice

from Boing Boing:

Why does a flat pizza slice flop over unless you bend it into a curve? Thank Gaussian curvature, the 19th century mathematical principle that underpins everything from corrugated cardboard to eggshells to Pringles chips.

Wired's Aatish Bhatia uses the pizza-slice as a jumping-off point to explain one of the most elegant and fascinating parts of geometry, and once you read his work, you'll never be able to look at a curved surface again:

Well, the pizza slice was flat before you picked it up (in math speak, it has zero Gaussian curvature). Gauss’s remarkable theorem assures us that one direction of the slice must always remain flat — no matter how you bend it, the pizza must retain a trace of its original flatness. When the slice flops over, the flat direction (shown in red below) is pointed sideways, which isn’t helpful for eating it. But by folding the pizza slice sideways, you’re forcing it to become flat in the other direction – the one that points towards your mouth. Theorema egregium, indeed.

By curving a sheet in one direction, you force it to become stiff in the other direction. Once you recognize this idea, you start seeing it everywhere. Look closely at a blade of grass. It’s often folded along its central vein, which adds stiffness and prevents it from flopping over. Engineers frequently use curvature to add strength to structures. In the Zarzuela race track in Madrid, the Spanish structural engineer Eduardo Torroja designed an innovative concrete roof that stretches out from the stadium, covering a large area while remaining just a few inches thick. It’s the pizza trick in disguise.

How a 19th Century Math Genius Taught Us the Best Way to Hold a Pizza Slice [Aatish Bhatia/Wired]

What we really feel when we feel "cold"

Temperature is just a measure of jigglyness, says Henry Reich of Minute Physics. Not in the "I don't think you're ready for this jelly" sense, but at the scale of atoms. And it's this jiggle that can help explain why two things that are, technically, the exact same temperature can feel totally different when we touch them. Great science for a cold day!

Thanks, BoingBoing

Staying Dry In The Rain: Should You Run Or Walk?

from BBC news

Staying dry in rain: run or walk?
By Jason Palmer
Science and technology reporter, BBC News

A physicist has put forth new ideas in the long-running question of how best to keep dry when moving in the rain.

If you run, you are out in the rain for less time, yet you run into more drops - so what is the optimal speed?

Franco Bocci, reporting in the European Journal of Physics, now asserts that both wind direction and a person's stature figure into the answer.

In most cases, the general answer is to run as fast as possible; but the answer changes in a tailwind, or for the thin.

Prof Bocci is by no means the first person to address the problem, which is far more mathematically complex than it seems on the surface.

In the 1970s, a number of papers came out in mathematics magazines debating the question, each more fully exploring the issues at hand.

The battleground for this bit of hobby mathematics now seems to be the UK's Institute of Physics publication the European Journal of Physics.

In 1987, another Italian researcher asserted in the journal that changing strategies did not make a substantial difference.

In 2011, a textile expert and a physicist used the same publication to suggest that an optimal speed existed, depending on the wind direction.

"For the most part in the previous work, there was a simple answer, but I found that the problem is much more complicated," Prof Bocci told BBC News.

What complicates the question is the human shape; for simplicity, previous attempts to crack the thorny problem assumed people to be thin sheets or upright, rectangular boxes.

When Prof Bocci considered a more general case - likely to be the case you would face in the rain - he found that the answer may depend on an individual's height-to-breadth ratio as well as wind direction and raindrop size.

Luckily there are a few generalisations in the analysis, to spare you having to calculate the cosine of the angle between your path and the wind direction.

"Let's say that in general, the best thing is to run, as fast as you can - not always, but in general," said Prof Bocci.

"If you're really thin, it's more probable that there will be an optimal speed. Otherwise, it's better to run fast."

As for wind direction - and again, in general - you should run as fast as you can unless the wind is behind you, in which case the optimal speed will be exactly the speed of the wind.

Prof Bocci said that the problem promises to get even more complicated as more factors are taken into account, but that for now he is drying his hands of the question.

Dark energy: No, seriously, what the heck is it?

from BoingBoing

The fun thing about the Nobel Prize in Physics is watching pundits try to explain to the public the research that won. It doesn't always go well. Physics is not, shall we say, the public's best subject. (And I include myself in that "public".) Beyond that, words that describe legitimate concepts in physics have taken on new, more fantastical meanings in science fiction, which only serves to confuse people further.

That's why I like this video produced by KQED Science. It features Lawrence Berkeley Lab astrophysicist Saul Perlmutter, one of the winners of this year's Nobel Prize in Physics, and does a nice job of explaining what "dark energy" really is, why work with dark energy is worthy of a Nobel, and what Perlmutter and his colleagues have contributed to the expansion of human knowledge.