It’s almost March 14th, or Pi Day. We celebrate this annual celebration of the great mathematical constants by new scientist Let’s recall some of our favorite recent stories from the world of mathematics. To whet your appetite, we’ve extracted a list of amazing facts from it, but if you want to indulge in Pi Day, click through for the full article. These are normally only available to subscribers, but to respect the circumference and diameter of the world, we have decided to make them free for a limited time.

The world’s best kitchen tiles

There are shapes called “hats” that can completely cover a surface without creating a repeating pattern. For decades, mathematicians have wondered whether a single tile exists that can do such a thing. Roger Penrose discovered a pair of tiles that could do the job in his 1970s, but no one could find a single tile that had the same effect when placed. Things changed last year when this hat was discovered.

why are you so unique

You are an irreplaceable person.Or actually he should be a tenth^{10^68.} Called the doppelgängion by mathematician Antonio Padilla, this number is so large that it’s difficult to wrap your head around it. This is a 1 followed by 100 million trillion zeros, and has to do with the possibility of finding exactly the same person somewhere in the universe. It is so difficult to imagine numbers of this size that the quantum physics required to calculate them seems almost trivial in comparison. There is a finite number of quantum states that can exist in the same size part of the universe. Add them all up and you arrive at Doppelgängion. Padilla also wrote about four other surprising numbers of his. new scientist. We’re all here.

amazing tricks

There is a simple mathematical trick to get out of any maze. That means always turning to the right. This method always works, no matter how complex the maze, no matter how many twists and turns and dead ends there are. I got the trick. Can you see why it always leads to success?

and the next number is

There may be a sequence of numbers that is very difficult to calculate, and the mathematician has just found number 9 in the sequence, and it may be impossible to calculate number 10. These numbers are called Dedekind numbers, after the mathematician Richard Dedekind, and represent the number of ways a set of logical operations can be combined. When a set contains a small number of elements, it is relatively easy to calculate the corresponding Dedekind number, but as the number of elements increases, the Dedekind number grows “at twice the exponential rate.” His number 9 in this series was 42 digits long and took him a month to find.

You can’t see the forest for the trees (3)

There are numbers too large to fit in the universe. TREE(3) comes from a simple math game. The game involves generating a forest of trees using different combinations of seeds according to some simple rules. If there is one type of seed, then the maximum allowed forest can contain one tree. For two types of seeds, the largest forest will have three trees. But for three types of seeds, the largest forest has TREE (3) trees, which is too large a number for the universe.

language of the universe

There is an eight-dimensional number system called the octanion that physicists use to try to describe the universe mathematically. The best way to understand octonions is to first think about taking the square root of -1. Among the real numbers (including all counting numbers, fractions, pi, etc.) there is no such number that is the result of its calculation, so mathematicians add another number called . I. When combined with real numbers, we get a system called complex numbers, which consists of a real part and an “imaginary part,” such as 3+7i. That is, it is two-dimensional. Octonion occurs by continuing to build systems until you reach the 8th dimension. However, this is more than just mathematical fun and games. There is reason to believe that octonions may be a necessary number system for understanding the laws of nature.

so many new solutions

Mathematicians went looking for solutions to the three-body problem and found 12,000 solutions. The three-body problem is a classic astronomical problem that asks how three objects can form stable orbits around each other. Such an arrangement is explained by Isaac Newton’s laws of motion, but finding a solution that is actually acceptable is incredibly difficult. In 2007, mathematicians were able to find his 1,223 new solutions to this problem, but this was significantly surpassed last year when the team discovered more than 12,000 more solutions.