Hyperbolic manifold

A hyperbolic manifold is like a special kind of playground with really curvy slides and bouncy floors.

When you walk on a normal playground with straight slides and flat floors, you can go forward, backward or sideways, and you stay on the ground. But on a hyperbolic playground, because of the curvy slides and bouncy floors, you might feel like you're bouncing back and forth or moving in circles, even if you're walking in a straight line.

This kind of playground is special because it has a unique shape that mathematicians call "hyperbolic geometry." Imagine drawing three straight lines on a piece of paper that meet at a point (like a triangle). On a normal piece of paper, those lines will always stay the same distance apart from each other. But on a piece of paper with hyperbolic geometry, the lines will spread apart and get farther and farther away from each other as they go.

In a hyperbolic manifold, there are lots of these kinds of shapes with curvy slopes and weird angles that can make you feel like you're moving in ways that don't seem quite right. But mathematicians study these shapes and find out really cool things about them, like how many sides they have or how far apart they are from each other. Overall, the hyperbolic manifold is a special kind of playground that lets us explore wild new shapes and forms, and see what kind of amazing things we can discover.