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<\/div>There\u2019s a mathematical trick to get out of any maze<\/p>\n
Klaus Vedfelt\/Digital Vision\/Getty Images<\/p>\n<\/div>\n<\/figcaption><\/figure>\n<\/p>\n
It will soon be 14 March and that means pi day<\/a>. We like to mark this annual celebration of the great mathematical constant at New Scientist\u00a0<\/em>by remembering some of our favourite recent stories from the world of mathematics<\/a>. We have extracted a list of surprising facts from them to whet your appetite, but for the full pi day feast click through for the entire articles. These are normally only available to subscribers but to honour the world\u2019s circumferences and diameters we have decided to make them free for a limited time.<\/p>\n There is a shape called \u201cthe hat\u201d that can completely cover a surface without ever creating a repeating pattern. For decades, mathematicians had wondered whether a single tile existed that could do such a thing. Roger Penrose<\/a> discovered pairs of tiles in the 1970s that could do the job but nobody could find a single tile that when laid out would have the same effect. That changed when the hat was discovered last year.<\/p>\n <\/p>\n You are one in a million. Or really, it should be 1 in a 1010^68.\u00a0 <\/sup>This number, dubbed the doppelg\u00e4ngion by mathematician Antonio Padilla, is so large it is hard to wrap your head around. It is 1 followed by 100 million trillion trillion trillion trillion trillion zeroes and relates to the chances of finding an exact you somewhere else in the universe. Imagining a number of that size is so difficult that the quantum physics required to calculate it seems almost easy in comparison. There are only a finite number of quantum states that can exist in a you-sized portion of space. You reach the doppelg\u00e4ngion by adding them all up. Padilla also wrote about four other mind-blowing numbers for New Scientist<\/em>. Here they all are.<\/p>\n There is a simple mathematical trick that will get you out of any maze<\/a>: always turn right. No matter how complicated the maze, how many twists, turns and dead ends there are, the method always works. Now you know the trick, can you work out why it always leads to success?<\/p>\n There is a sequence of numbers<\/a> so difficult to calculate that mathematicians have only just found the ninth in the series and it may be impossible to calculate the tenth. These numbers are called Dedekind numbers after mathematician Richard Dedekind and describe the number of possible ways a set of logical operations can be combined. When the set contains just a few elements, calculating the corresponding Dedekind number is relatively straightforward, but as the number of elements increases, the Dedekind number grows at \u201cdouble exponential speed\u201d. Number nine in the series is 42 digits long and took a month of calculation to find.<\/p>\n There is a number so big that in can\u2019t fit in the universe<\/a>. TREE(3) comes from a simple mathematical game. The game involves generating a forest of trees using different combinations of seeds according to a few simple rules. If you have one type of seed, the largest forest allowed can have one tree. For two types of seed, the largest forest is three trees. But for three types of seed, well, the largest forest has TREE(3) trees, a number that is just too big for the universe.<\/p>\n There is a system of eight-dimensional numbers called octonions that physicists<\/a> are trying to use to mathematically describe the universe. The best way to understand octonions is first to consider taking the square root of -1. There is no such number that is the result of that calculation among the real numbers (which includes all the counting numbers, fractions, numbers like pi, etc.), so mathematicians add another called i.\u00a0<\/em>When combined with the real numbers, this gives a system called the complex numbers, which consist of a real part and an \u201cimaginary part\u201d, such as 3+7i. In other words, it is two-dimensional. Octonions arise by continuing to build up the system until you get to eight dimensions. It isn\u2019t just mathematical fun and games though \u2013 there is reason to believe that octonions may be the number system we need to understand the laws of nature.<\/p>\n Mathematicians went looking for solutions to the three-body problem and found 12,000 of them. The three-body problem is a classic astronomy problem of how three objects can form a stable orbit around each other. Such an arrangement is described by Isaac Newton\u2019s laws of motion but actually finding permissible solutions is incredibly difficult. In 2007, mathematicians managed to find 1223 new solutions<\/a> to the problem but this was greatly surpassed last year when a team found more than 12,000 more.<\/p>\n Topics:<\/p>\n<\/section><\/div>\nThe world\u2019s best kitchen tile<\/h2>\n
Why you\u2019re so unique<\/h2>\n
An amazing trick<\/h2>\n
And the next number is<\/h2>\n
Can\u2019t see the forest for the TREE(3)<\/h2>\n
The language of the universe<\/h2>\n
So many new solutions<\/h2>\n