Happy Birthday, Leonhard Euler

Sunday, April 15, is the 300th birthday of Leonhard Euler (pronounced "oiler"), one of the most important mathematicians ever to have lived.

Click the above link to read a wonderful description of his famous equation: e^iπ = –1

If you want to read some wonderful books, check out Paul Nahin's books: An Imaginary Tale and
Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills.

These books are worth reading and you'll learn about the mathematics of Euler.

The Mathematical Association of America has a wonderful column by Ed Sandifer entitled "How Euler Did It." Dr. Sandifer translates (I guess) some of Euler's original papers, tells you what Euler did, how he did it, and why that result is important.

Rotating polygons in space and in the lab

It was recently reported that there's a hexagonal rotating structure (see the image at left) at the North pole of Saturn.

We may not have found other life in our Solar System, but we have, it appears, found a polygon. An odd, six-sided, honeycomb-shaped feature circling the entire north pole of Saturn has captured the interest of scientists with NASA's Cassini mission.

NASA's Voyager 1 and 2 spacecraft produced images of the hexagon over two decades ago. The fact that it has appeared in the recent Cassini images indicates that it is a long-lived feature. A second hexagon, significantly darker than the brighter historical feature, is also visible in the Cassini pictures. The spacecraft's visual and infrared mapping spectrometer is the first instrument to capture the entire hexagon feature in one image.

Now others have seen the same phenomenon in the lab.


The unusual phenomenon in question involves rotating a bottom plate under a liquid in a circular (cylindrical) container. Bohr and his team of students at the Technical University and at the Niels Bohr Institute set up an experiment to find out whether or not such conditions would lead to stable deformations of a water surface into polygon shapes. The findings from their experiment were published May 3^rd in Physical Review Letters.

Bohr tells PhysOrg.com that a somewhat similar experiment took place eight years ago with a different team (including Clive Ellegaard and others). “We had fluid falling on a plane, like water from a faucet. We found that even if the rim of the plate is completely circular, the fluid surface can be shaped like a polygon.”

While the first polygon experiment Bohr did involved stationary polygons, the most recent effort shows rotating polygons. “Not only are these shapes rotating,” says Bohr, “but they are rotating at a different speed than the plate beneath them.”

This is a fascinating phenomena that is, apparently, unexplained as yet. Here's another site for a video and more links.


(Hat tip: Ilachina)

Are cellular phones killing bees?

Interesting article on how our cellular phones could be disrupting the navigation of bees.

Putnam Mathematical Competition Problems

Click on the link for the pdf file of the Putnam Mathematical Competition problems.

Good luck with them!

Planet of the Apes: Apes as People

In a ground-breaking case at the Mödling district court, just southwest of Vienna, Austria, a judge is to rule over "the humanness of a chimp"– specifically, over whether it deserves a legal guardian.

The chimpanzee in question is called Hiasl. He was born in the Sierra Leone jungle in 1981, captured by animal traders and illegally shipped to Austria, destined for a vivisection lab. Customs officials intercepted the crate and Hiasl was handed to an animal sanctuary. Now, years later, the sanctuary has gone bankrupt and Hiasl is to be sent to a zoo.

This is the most ridiculous legal item I've seen a long time. Of course the chimp is NOT a human. To say otherwise is to say that we, (you, me, your friends, etc.) are chimps. Clearly not the case.

Nonetheless, as an animal lover (dogs, in particular) I should think the court could see it's way to appointing a caregiver for the chimp without equating the chimp to a human. The caregiver would have certain rights as an owner and thereby take care of the animal. Anything more is an insult to humans.

Air traffic control, automatically

Fighter pilots will one day be able to control entire squadrons of uncrewed combat aircraft as well as their own plane, following successful flight demonstrations of a multi-aircraft remote control system in UK airspace.

In addition to cutting the number of pilots risked in military operations, the remote control system could one day also be used to auto-land hijacked planes. Or they might allow lone pilots to orchestrate complex search and rescue operations.

This is not as new as it would seem. Just today I was in a meeting discussing how we might see unmanned aerial vehicles flying in U.S. airspace and how cargo planes could become pilotless. This demonstration is one step to seeing those ideas become a reality.

Wheat at risk

"This thing has immense potential for social and human destruction." Startling words - but spoken by the father of the Green Revolution, Nobel laureate Norman Borlaug, they are not easily dismissed.

An infection is coming, and almost no one has heard about it. This infection isn't going to give you flu, or TB. In fact, it isn't interested in you at all. It is after the wheat plants that feed more people than any other single food source on the planet. And because of cutbacks in international research, we aren't prepared. The famines that were banished by the advent of disease-resistant crops in the Green Revolution of the 1960s could return, Borlaug told New Scientist.

The disease is Ug99, a virulent strain of black stem rust fungus (Puccinia graminis), discovered in Uganda in 1999. Since the Green Revolution, farmers everywhere have grown wheat varieties that resist stem rust, but Ug99 has evolved to take advantage of those varieties, and almost no wheat crops anywhere are resistant to it.

Not only is Ug99 a threat in itself, but even if we have resistant wheat, we have still another problem:

However, Ug99 has another ace up its sleeve. The spores blowing in the wind now are from the asexual stage that grows on wheat. If any blow onto the leaves of its other host, the barberry bush (Berberis vulgaris), they will change into the sexual form and swap genes with whatever other stem rusts they find. Barberry is native to west Asia. "As if it wasn't challenging enough breeding varieties that resist this thing," laments Ward. "All I know is that what blows into Iran will not be the same as what blows out."

One solution is to apply fungicide to the crops which for many countries will work until new wheat can be developed that's resistant. But for poor countries fungicide is too expensive.

If you like to gamble, maybe it's a good time to go long on wheat futures?

The food cycle in the ocean

A shortage of big sharks along the U.S. East Coast is letting their prey flourish, and that prey is going hog wild, demolishing bay scallop populations.

That's the conclusion of researchers led by the late Ransom Myers of Dalhousie University in Halifax, Nova Scotia, who died this week. Combining census surveys from the past 35 years, Myers' team found shrinking populations of big sharks and shellfish and increasing numbers of smaller sharks and rays.

"Affecting something at the top [of the food web] is going to have huge consequences as effects ramify through the system," says study collaborator Charles H. Peterson of the University of North Carolina's Institute of Marine Sciences at Morehead City. As part of the new study, he and his colleagues explored some of those effects by protecting bay scallops from the cownose ray (Rhinoptera bonasus), one of the flourishing midlevel predators.

So, the cownose rays have multiplied and are eating more of the delicacies of scallops. What to do? Should we hunt down the rays now or, as the article later suggests make the rays a delicacy themselves?

Cownose rays have grown so abundant along the U.S. East Coast that fisheries managers are trying to promote them as a seafood delicacy. TV cooking-show host Emeril Lagasse has even developed some recipes. (Picture caption)

I have never eaten a ray and have no desire to ever do so. But if people like them, why not hunt them and eat them? They are part of the food chain, as are we, and we should look at them as food just like we do for a cucumber.

Bon apetit!

Sunspots erupt out high!

From the Astronomy Picture of the Day:

Why are there dark spots on the sun? Although noted for thousands of years, sunspots have been known for decades to be regions of the Sun that are slightly depressed and cooled by the Sun's complex and changing magnetic field. High resolution pictures like the above image from Japan's new Sun-watching Hinode satellite, however, are helping to increase modern understanding. In the center of the above image is a sunspot, but not seen in the usual orientation --this sunspot is seen sideways. Of particular interest is erupting glowing gas that shows how the Sun's magnetic field comes right out of the spot center, but curves markedly around the spot edges. Better understanding of how the Sun ejects particles into space may result in more accurate predictions of solar storms that affect satellites, astronauts, and even power grids on Earth.