Mathematicians Encrypt Images Using Mathematics of Sudoku - Technology Review

Mathematicians Encrypt Images Using Mathematics of Sudoku - Technology Review: "The number-placement puzzle, Sudoku, consists of a 9 x 9 grid which must be filled using the digits 1 to 9. 

However, there are several additional constraints. Each digit can only appear once in each column, once in each row and once in each of the nine 3 x 3 blocks that make up the grid. A Soduko solution grid is shown below. Players are given a number of digits from the solution to get the game started. 

Sudoku has thrown up a number of interesting challenges for mathematicians. Earlier this year, for example, we looked at how mathematicians had solved the 'minimum Sudoku problem' to find the smallest number of clues that leads to a unique solution (answer, 17).  

Today, Yue Wu at Tufts University in Medford and a couple of buddies use Sudoku to tackle a different problem--how to encrypt images before sending them. 

These guys say that the special properties of Sudoku grids lead to an entirely new type of matrix mathematics that they've exploited to scramble images. "

Wolfram|Alpha Blog : “Helm, Warp One, Engage!” Calculating Warp Speed Factors

Wolfram|Alpha Blog : “Helm, Warp One, Engage!” Calculating Warp Speed Factors: "Wolfram|Alpha’s goal is to cover all things computational, from mathematics and the sciences to movies and sports. But the set of all things computable encompasses areas outside of the real world as well. With the 25th anniversary of Star Trek: The Next Generation coming up, we can now compute the relationship between warp factors and the speed of light. Warp factors describe the speed for a spaceship, such as the Starship Enterprise, traveling faster than the speed of light within the Star Trek universe. In the real world, even approaching the speed of light is outside of our current capabilities. To get the sense of energies involved, we can start with the mass of the space shuttle. This comparatively small spaceship turns out to weigh about 81,000 kilograms. The kinetic energy of 81,000 kilograms at 0.99999c is 1.621*10^24 joules. This in turn is about 42 times the world’s estimated fossil fuel reserves as of 2003. So, for now, even fast subluminal velocities are outside of our reach. But in Star Trek, faster than light travel is a well developed technology. However, exact conversion of warp factor into multiples of the speed of light is somewhat complicated by the fact that the writers often neglected the established formulas in their scripts and that there are two versions of the formula used over the course of the various Star Trek series. The first formula was introduced in the original series’ writer’s guide by Gene Roddenberry, and was used for the original series. This the default formula used by Wolfram|Alpha when asked about warp factors such as warp factor 3."

iphone 4 4s case Spock Ear Design STAR TREK by Graphicpals

iphone 4 4s case Spock Ear Design STAR TREK by Graphicpals: "The prefect gift for the Star Trek fan turn you iphone 4/4s into a Vulcan inspired ear to make people look twice. Please let us know if you would like us to customize this case for you.

This image is printed to order in our shop using special heat activated inks that print to a high gloss permanent finish on special plates that are made in the U.S.A. that wont fade or peel off.

The case is made of a silicone rubber that conforms to the iphone for a nice snug fit which will not easily come off. We prefer the silicone style over the plastic style because the plastic cases tend to crack very easy, plus the rubber styles offer better protection from impact."

A wrinkle in space-time

A wrinkle in space-time: "Mathematicians at UC Davis have come up with a new way to crinkle up the fabric of space-time - at least in theory. 'We show that space-time cannot be locally flat at a point where two shock waves collide,' said Blake Temple, professor of mathematics at UC Davis. 'This is a new kind of singularity in general relativity.'"

Dolphins appear to do nonlinear mathematics - Technology & science - Science - DiscoveryNews.com - NBCNews.com

Dolphins appear to do nonlinear mathematics - Technology & science - Science - DiscoveryNews.com - NBCNews.com: "Dolphins may use complex nonlinear mathematics when hunting, according to a new study that suggests these brainy marine mammals could be far more skilled at math than was ever thought possible before. Inspiration for the new study, published in the latest Proceedings of the Royal Society A, came after lead author Tim Leighton watched an episode of the Discovery Channel's 'Blue Planet' series and saw dolphins blowing multiple tiny bubbles around prey as they hunted. 'I immediately got hooked, because I knew that no man-made sonar would be able to operate in such bubble water,' explained Leighton, a professor of ultrasonics and underwater acoustics at the University of Southampton, where he is also an associate dean.

'These dolphins were either 'blinding' their most spectacular sensory apparatus when hunting — which would be odd, though they still have sight to reply on — or they have a sonar that can do what human sonar cannot. ... Perhaps they have something amazing,' he added. Leighton and colleagues Paul White and student Gim Hwa Chua set out to determine what the amazing ability might be. They started by modeling the types of echolocation pulses that dolphins emit. The researchers processed them using nonlinear mathematics instead of the standard way of processing sonar returns. The technique worked, and could explain how dolphins achieve hunting success with bubbles. The math involved is complex. Essentially it relies upon sending out pulses that vary in amplitude. The first may have a value of 1, while the second is one-third that amplitude. 'So, provided the dolphin remembers what the ratios of the two pulses were, and can multiply the second echo by that and add the echoes together, it can make the fish 'visible' to its sonar,' Leighton told Discovery News. 'This is detection enhancement.'"

“Game of Thrones” For Mathgeeks

“Game of Thrones” For Math Geeks - SF Signal – A Speculative Fiction Blog: "I loves me some charts…especially when they applied to genre shows.

Here are some interesting stats on Game of Thrones, both book and film, that give one an interesting perspective…"

Harmony 'driven by mathematical ratios'

Harmony 'driven by mathematical ratios' - The Irish Times - Mon, Jul 16, 2012: "It was apparent to mathematicians going back to Ancient Greece that musical harmony was fundamentally driven by mathematical ratios.

The public are generally unaware that the ‘three chords trick’ which is the basis of all popular music is an idea going back to the father of geometry Pythagoras.

The Greeks established that the first note in the scale and the fourth and fifth are the most harmonious together and they are governed by ratios.

For instance a standard A has a pitch of 440hz, the fourth note a D has a pitch which is three-quarters of that at 330hz and the E note or fifth is two-thirds of the pitch of the A at 293.33hz. The higher A at the end of the octave is at 220hz half that of the lower A.

The ratios remain as important today as they were in Greek times."

Huge old-school video game collection sells for $1.2m

Huge old-school video game collection sells for $1.2m | Hot Topics | a Chron.com blog: "A collector of old school video games has sold a collection of thousands of games for $1.2 million.

The French video game collector named Andre had amassed a collection that included all games for most of Nintendo’s consoles, all of Sega’s and NEC’s games, which included some 7,000 individual games."

Space Images: 'Greeley Panorama' from Opportunity's Fifth Martian Winter

Space Images: 'Greeley Panorama' from Opportunity's Fifth Martian Winter (False Color) - NASA Jet Propulsion Laboratory: "This full-circle scene combines 817 images taken by the panoramic camera (Pancam) on NASA's Mars Exploration Rover Opportunity. It shows the terrain that surrounded the rover while it was stationary for four months of work during its most recent Martian winter.

Opportunity's Pancam took the component images between the 2,811th Martian day, or sol, of the rover's Mars surface mission (Dec. 21, 2011) and Sol 2,947 (May 8, 2012). Opportunity spent those months on a northward sloped outcrop, 'Greeley Haven,' which angled the rover's solar panels toward the sun low in the northern sky during southern hemisphere winter. The outcrop's informal name is a tribute to Ronald Greeley (1939-2011), who was a member of the mission team and who taught generations of planetary scientists at Arizona State University, Tempe. The site is near the northern tip of the 'Cape York' segment of the western rim of Endeavour Crater.

North is at the center of the image. South is at both ends. On the far left at the horizon is 'Rich Morris Hill.' That outcrop on Cape York was informally named in memory of John R. 'Rich' Morris (1973-2011), an aerospace engineer and musician who was a Mars rover team member and mission manager at NASA's Jet Propulsion Laboratory, Pasadena.

Bright wind-blown deposits on the left are banked up against the Greeley Haven outcrop. Opportunity's tracks can be seen extending from the south, with a turn-in-place and other maneuvers evident from activities to position the rover at Greeley Haven. The tracks in some locations have exposed darker underlying soils by disturbing a thin, bright dust cover."