Riemannian circle
Okay kiddo, imagine a big round circle like a pizza. Now let’s play a game called "walking on the circle." To play this game, we need to pretend that we are walking around the edge of the circle.
Now, let's say we want to measure how far we've walked on the circle. We can measure distance on a flat surface, like a piece of paper, by using a ruler. But the circle is not flat, it's curved like a ball. So we need to use a special ruler that can measure distances on a curved surface. This type of ruler is called a Riemannian ruler.
A Riemannian ruler is a special tool that helps us measure distances on a curved surface like a circle. It’s like using a different type of ruler that can measure things on a curved surface instead of a flat one.
When we use a Riemannian ruler to measure distances on the circle, we find out that some distances are shorter than others. For example, if we start walking from one point on the circle and walk halfway around the edge to another point, the distance we've traveled is shorter than if we walked all the way around the edge. This is because the circle is curved, and distances change depending on where you start and end up.
So, a Riemannian circle is a special kind of circle where lengths and distances are measured using a Riemannian ruler, which takes into account the curved shape of the circle. It allows us to measure distances in a way that makes sense on a curved surface like a ball or a circle.
Now, let's say we want to measure how far we've walked on the circle. We can measure distance on a flat surface, like a piece of paper, by using a ruler. But the circle is not flat, it's curved like a ball. So we need to use a special ruler that can measure distances on a curved surface. This type of ruler is called a Riemannian ruler.
A Riemannian ruler is a special tool that helps us measure distances on a curved surface like a circle. It’s like using a different type of ruler that can measure things on a curved surface instead of a flat one.
When we use a Riemannian ruler to measure distances on the circle, we find out that some distances are shorter than others. For example, if we start walking from one point on the circle and walk halfway around the edge to another point, the distance we've traveled is shorter than if we walked all the way around the edge. This is because the circle is curved, and distances change depending on where you start and end up.
So, a Riemannian circle is a special kind of circle where lengths and distances are measured using a Riemannian ruler, which takes into account the curved shape of the circle. It allows us to measure distances in a way that makes sense on a curved surface like a ball or a circle.