Scientists have invented new ways of cutting pizza

Mathematics from the University of Liverpool in his new job published several previously unknown ways Partitioning equal parts. This work belongs to the section geometry, the so-called student паркеты - tiling polygons plane without gaps and overlaps. At work inspired scientists searching for ways to cut the pizza - most of us are familiar procedure.

When tiling the plane geometric figures (tiles) can be set and solve different problems. One of the most interesting problems - the use monoedricheskih tiles. In this case, all the tiles have the same shape, or more precisely, are congruent. This means that any two tiles can be combined using translation, rotation or mirroring.

Set the form of tiles used for the replacement of the plane, called protoplitkami. Interestingly, there is no mathematical method to say in advance whether it is possible using the specified protoplitok replace the plane. For example, it is known that from the следующих 24 geptamondov (shapes composed of seven equilateral triangles), only one is not suitable for tiling monoedricheskogo plane. But what exactly?



In this case - V-shaped. But the proof of this - a rather trivial task.

However, Liverpool mathematics instead of the entire disk plane limited and seek monoedricheskih protoplitok suitable for dividing the disk. One version of such protoplitki known to all. In the standard method of cutting the pizza, it is divided into equal slices a triangular shape, the tops of which converge in the center. Scientists also decided to answer the question - whether there are dividing the disk into equal pieces, in which not all of these figures relate to the center Disk?

That is, is it possible to cut the pizza into equal parts so as to please both those who like a little more filling, and for those who like a little more brown? It turned out that you can. Moreover, one embodiment of such a cutting is known for a long time, and is located on the logo community, the University of Pennsylvania , organize seminars math for students:



The shaped slices can be divided in half, and all parts are obtained congruent with only half of them will touch the center.

Mathematicians have developed this idea and offered the ways of dividing the drive to an almost infinite number of equal parts.







As often happens in mathematics, the possibility of applying the ideas work in practice is not entirely clear - perhaps, the use of non-standard cutting pizzeria pizza as a competitive advantage. On the other hand, to predict how the mathematical discovery will be useful in the future, it is also impossible.

Source: geektimes.ru/post/269082/