Hyperbolic volume (knot)
Hyperbolic volume is like counting how much space a special knot takes up. Imagine you have a really big ball of clay and you make a knot with it. That knot takes up some space inside the ball of clay, right? Well, hyperbolic volume is a way to measure how much space that knot takes up.
But here's the thing: this isn't just any old space. It's a special kind of space called hyperbolic space. This space is a bit unusual because it's really curved, like a wavy potato chip. It's so curved that if you tried to draw a straight line on it, the line would actually curve around and come back to where it started!
When you make a knot in hyperbolic space, it still takes up some space just like in regular space, but it's a bit different. The hyperbolic volume of a knot is the amount of hyperbolic space that the knot fills up.
So, in summary, hyperbolic volume is a way to measure how much space a knot takes up in a super curved space called hyperbolic space. It's like counting the amount of clay that a knot takes up, but in a space that's even more wiggly than the knot itself!
But here's the thing: this isn't just any old space. It's a special kind of space called hyperbolic space. This space is a bit unusual because it's really curved, like a wavy potato chip. It's so curved that if you tried to draw a straight line on it, the line would actually curve around and come back to where it started!
When you make a knot in hyperbolic space, it still takes up some space just like in regular space, but it's a bit different. The hyperbolic volume of a knot is the amount of hyperbolic space that the knot fills up.
So, in summary, hyperbolic volume is a way to measure how much space a knot takes up in a super curved space called hyperbolic space. It's like counting the amount of clay that a knot takes up, but in a space that's even more wiggly than the knot itself!