Re:Topology 101: The Hole Truth
by thunderbong on Tuesday January 26, 2021 @04:15PM
(#25921144)
This is how I understood the comment -
In a torus, there are effectively two holes -
1. the center hole around which there is a cylindrical ring
2. the whole inside the cylindrical ring, which is hidden and connected.
When we cut along the length of the cylindrical ring, we are effectively creating two edges, just like if we were to cut a circular ring of wire, we would end up with two points at the end.
The two edges then open up, effectively forming another cylinder, which has to be cut again.
Any other object which has only a single hole, would require only a single cut to flatten out.
In a torus, there are effectively two holes -
1. the center hole around which there is a cylindrical ring
2. the whole inside the cylindrical ring, which is hidden and connected.
When we cut along the length of the cylindrical ring, we are effectively creating two edges, just like if we were to cut a circular ring of wire, we would end up with two points at the end.
The two edges then open up, effectively forming another cylinder, which has to be cut again.
Any other object which has only a single hole, would require only a single cut to flatten out.