Bianchi group
The Bianchi group is like a big group of very special toys that mathematicians like to play with. Imagine you have lots of different kinds of Legos, but these Legos are really special because they make a special pattern when you put them together in a certain way. This pattern is like a puzzle that the mathematicians try to solve.
Now, the Bianchi group is like a giant box of really cool Legos that only mathematicians who know a lot about numbers and shapes get to use. These Legos are made up of something called complex numbers, which is like a special way to write numbers using both real numbers and imaginary numbers.
When the mathematicians play with these special Legos, they create something called a hyperbolic plane. This plane is different from the plane you're used to because it has a curved shape. This means that lines on this plane bend and twist in ways that you can't always see just by looking at them.
The study of the Bianchi group and the hyperbolic plane is really important for a lot of other branches of mathematics, especially geometry and topology. By understanding how these Legos work and how they create this special plane, mathematicians can figure out all kinds of other puzzles and problems that are really hard to solve.
Now, the Bianchi group is like a giant box of really cool Legos that only mathematicians who know a lot about numbers and shapes get to use. These Legos are made up of something called complex numbers, which is like a special way to write numbers using both real numbers and imaginary numbers.
When the mathematicians play with these special Legos, they create something called a hyperbolic plane. This plane is different from the plane you're used to because it has a curved shape. This means that lines on this plane bend and twist in ways that you can't always see just by looking at them.
The study of the Bianchi group and the hyperbolic plane is really important for a lot of other branches of mathematics, especially geometry and topology. By understanding how these Legos work and how they create this special plane, mathematicians can figure out all kinds of other puzzles and problems that are really hard to solve.