The Light Side: Cutting a Round Cake on Scientific Principles
June 27, 2014
It's an office party for a co-worker's birthday, and the cake has arrived. What happens next is familiar: No one dares to step up and cut the cake, not even after someone finally steps in and cries out for a volunteer. Who wants the mission-critical responsibility of cutting equal slices and making sure every single person gets a piece of cake to avoid an Office Space catastrophe?
But thanks to a letter to the editor of Nature more than 100 years ago, written by British scientist Francis Galton and recently dug up by The Guardian's math and science contributor, Alex Bellos, now we can completely avoid the awkwardness of cutting perfect wedges in front of a bunch of staring, hungry eyes.
Galton's method involves cutting a round cake by its diameter to make long, thin slices, as shown in the video below. Keep in mind that more than a century ago, before refrigerators, plastic wrap, and Tupperware existed, it was important to find ways to keep food lasting when there were leftovers. The conventional way of cutting a cake leaves its interior exposed to dry up and harden, preventing maximum gastronomical pleasure.
Galton wrote, "The ordinary method of cutting out a wedge is very faulty in this respect." Galton's method, on the other hand, allowed cake lovers to take as many longitudinal slices as desired and then press the remaining leftovers together in order to keep moisture in and prevent air from drying the cake out before the next sitting -- as you'll see in Bello's video.
Admittedly, Galton did not devise this century-old, cutting-edge science to ensure that everyone got an equal helping of cake -- as one makes diameter-length cuts from the middle out, the slices become shorter. However, one can get around this conundrum by dividing the first several slices (Bellos calls the first slice the "T-bone slice") to make sure no one unfairly gets an oversized portion.
So say goodbye to stale cake and office politics.
Aston Martin, perhaps best known as the maker of James Bond’s car of choice, is looking for any edge it can give to its race cars. The automaker thinks that solar power may provide that edge.
All cars participating in the FIA World Endurance Championship are required to have air-conditioning to keep a driver’s ambient air temperature at or below 90oF. But the AC decreases fuel efficiency and reduces a car’s performance. To solve those problems, Aston Martin is teaming up with Hanergy Global Solar, a manufacturer of thin-film photovoltaics (PV). They hope to make a PV system that can directly power the car’s air-conditioning, freeing the engine to do what Aston Martin engines were designed to do: go fast!
A typical car roof can accommodate a 300 watt thin-film PV panel. Add one to the spoiler and you’ll get about 500 watts total, assuming full sun and ideal conditions. It’s difficult to find exact power specifications for car AC units, so I used typical numbers based on a Nissan Leaf and calculated that its AC system uses about 2.5 kilowatts. If Aston Martin wants the AC driven entirely by PV panels, its engineers have quite a challenge on their hands. The company may have to recruit "Q" from MI6 to work a little magic.
If nothing else, the power from the PV panels could at least provide some of the energy needed to run the AC, which will improve performance and fuel economy -- even for those of us with more modest vehicles. PV panels can also run a fan to help keep the car cool when it’s parked in the sun. Toyota offers that option on its Prius.
Two things might become slightly more efficient through the Aston Martin-Hanergy Global Solar partnership: thin-film PV cells and air-conditioners. Even so, I doubt that the auto industry will be shaken by rooftop PV panels. It might, however, get a little stirred.
Researchers Develop Camera That Sees Around Corners
Researchers at the University of Bonn in Germany have developed a camera that can image objects around corners without the use of mirrors or telescoping lenses.
While cameras have been able to influence the way we see the world, they’ve only been able to see what’s directly in front of their lenses. That may be changing.
According to Bonn researchers, their camera could see objects around blind corners through the use of a single-beam of laser light. Rather than allowing light to flood into its lens, the new camera would collect the diffuse light of a laser bounced off a wall opposite its target. After enough laser light has been collected on the camera’s CCD image sensor, complex mathematical algorithms are used to determine how the laser light diffused and then reconstruct those photonic paths to form an image of the hidden object.
“We are recording a kind of light echo, that is, time-resolved data, from which we can reconstruct the object," said computer science professor Matthias Hullin. "Part of the light has also come into contact with the unknown object, and it thus brings valuable information with it about its shape and appearance."
Though the technological complexity of this new camera is quite low, cameras with adequate CCDs have been on the market for years. The mathematics behind this camera’s unique abilities are quite complex and still a limiting factor.
"The accuracy of our method has its limits, of course," Hullin admits, as the Bonn camera’s current incarnation only produces rough outlines of its target. However, researchers are confident that as mathematical models and technical components become more sophisticated, the camera’s ability to create a clear image will sharpen, as well.This article and the preceding article were originally published on Engineering.com and are adapted in their entirety with permission. For more stories like this please visit Engineering.com.
Edward Gamson would probably buy a vowel for British Airways if he wins his lawsuit against the airline for taking him and his companion to the Caribbean destination of Grenada instead of the Spanish city Granada.
The American dentist is suing BA for $34,000 after a booking agent at the carrier botched his reservation and itinerary and he wound up on the southeastern Caribbean island just off Venezuela. Gamson, who is based in the Washington, D.C. area, planned to vacation in Granada before attending a dentists' conference in Lisbon, Portugal, and then flying back to D.C. But after a connection in London, the plane Gamson was on headed west rather than toward southern Spain.
According to an AP report, Gamson said he didn't notice this until the flight was airborne and he looked at the in-flight map on his TV screen. He claimed that his first-class electronic ticket referred to "Grenada" but didn't list the country, airport code, or flight duration. Instead of enjoying a two-hour flight from London, Gamson underwent a nine-hour ordeal in first class with his teeth clenched. Let's hope he's not as careless around the dentist's chair.
BA did eventually fly Gamson back to Lisbon for his conference, but the Alhambra will have to wait for another time. The airline offered him and his companion several hundred dollars as well as a total of 100,000 miles, but he had used roughly 376,000 frequent flyer miles and a companion voucher to book his ticket and didn't think the offer was acceptable. He also declined an offer of new flights to Granada or complimentary flights to a different destination, according to a BA statement.
The AP story points out that BA passengers are often misrouted to Grenada, noting that a member of the ground crew told Gamson that "the exact same situation" had happened the week before.
These mix-ups are not isolated to the Spanish city and Caribbean island, obviously. The clothing racks of tourist shops in Vienna, Austria, are filled with T-shirts declaring, "No Kangaroos Here!"