Impossible figures brought to life in virtual worlds

Impossible figures brought to life in virtual worlds - New Scientist



Ever found a computer game truly impossible? If not, you soon might, thanks to Chinese computer scientists who have found a way to depict physically impossible figures in 3D virtual environments.

The endless staircases of the Dutch artist M. C. Escher appear impossible and possible at the same time, and able to go in all directions. Such visual trickery depends heavily on the observer's viewpoint – and that makes it difficult to animate Escher-type figures in games. If the viewpoint pans around a 3D computer depiction of such a staircase, "the impossibility is lost", says Tai-Pang Wu at the Chinese University of Hong Kong.

Now his team has found a way to make these images viewable from a useful array of angles. The trick is to take advantage of the image's strangeness; viewers scarcely notice if an Escher staircase becomes slightly distorted.

Observations: Three puzzles from Martin Gardner (1914-2010)

Observations: Three puzzles from Martin Gardner (1914-2010)

News of Martin Gardner's death began circulating on Saturday night. For those of you who are unfamiliar with his work, here's a taste of the kinds of puzzles he was famous for bringing to the world. You can read a profile of him here. Rest in peace, Martin.

1. Reversed Trousers
Each end of a 10-foot length of rope is tied securely to a man’s ankles. Without cutting or untying the rope, is it possible to remove his trousers, turn them inside out on the rope and put them back on correctly? Party guests should try to answer this confusing topological question before initiating any empirical tests.

2. Crazy Cut
This one looks much easier than it is. You are to make one cut (or draw one
line)—of course, it needn’t be straight— that will divide the figure into two identical parts.







3. Out with the Onion
Arrange four paper matches on a table as shown at right. They represent a martini glass. A match head goes inside to indicate the onion of a Gibson cocktail.

The puzzle is to move just two matches so that the glass is re-formed, but the onion—which must stay where it is—winds up outside the glass. At the finish, the glass may be turned to the left or the right, or even be upside down, but it must be exactly the same shape as before.

The figures below are not a solution, because the onion is still inside or because three matches have been moved.



Follow this link to see the solutions