i see your very valid point my good sir.. but all i see is a straight line so that would be my answer to this post.. :) but your thought cleared a lot up for me so thx for that!
Make a circle and set r to infinity. What do you have? A line which is infinitely distant from a point.
On the left is a circle, with two radial lines, which are defined as being perpendicular to the point at which they intersect the circle on its edge. the angle between them is always non-zero, so there's curvature. On the right is an infinitely large circle. Any two points which are perpendicular to where they intersect also happen to be parallel to one-another. A line is defined in this exact way, as is shown in the circle to the right.
I couldn't understand alot of it since it had alot of hard words in it (i'm not english) a circle with a radius of inifinite would have that line on the right left and the bottem aswell, this one only has one and it doens't go to the right or left to infinity. I'm not sure if this is a a respons to what you said but i tried
I see what you mean, but things can "exist" without really existing, but their form would take on another shape. In this case, an infinite circle can exist, but in doing so it would become a line due to the limitations of finite space.
In this sense, such a circle can only exist as a line facing in one direction if it were to appear in our Universe.
...Sorry for difficult language, but it's hard to explain using simple words.
Let's break this down: Portals operate by connecting two points in space together, each side connected by a wormhole of some sort. Now, you can go into hugely convoluted technobabble and talk about how the wormholes possibly connect all points in the universe, bend time, etc etc, but what it all comes down to is this: How the **** is it staying in the air?
it would just act as a stiff rod and fall down until it got to the bottom of the portal, and depending on how portals act it would either stop falling or the end would get cut.
Nope. The rope can only exert tensional force horizontally whilst gravity acts on it vertically. The rope has no way of exerting a vertical force so it would accelerate downwards.
This could only be the case if you were still holding it because your hands provide the upward force. Once you tie it off and let go you remove the component upwards so the arrows in your picture would go back to being horizontal.
The knot itself can't 'save' and apply the upward force because it's effectively just bonding the two ends together so any shear force that could be generated would apply in equal and opposite directions on either side of the cut, even with the additional application of gravity.
Then it'd look awesome because it'd look like a badly looped GIF as the knot appeared to travel down the rope and then suddenly pop up at the top again.
I made a quick pic to show the forces acting on an imaginary cut through something. In our case it represents the knot because the rope has literally been split but it's been joined back together so the same theory can be applied to it.
The top shows the cut with S being the shear force and T being the tension. Everything has to balance out regardless or external forces else the structure would tear itself apart. The tensional and shear forces can't effect each other at all.
The bottom is a small element of the rope, x meters long. The weight of the rope can be modeled as a single force in the middle. You might think that the shear forces could act upwards at both sides but then the next element along would have an even larger downward force and the next a large upward etc. The forces cannot flip flop like this. So the knot cannot exert an upward force to balance the effect of gravity.
It still won't make a difference. Any horizontal force is unable to have any effect in the vertical plane and the same restriction applies to shear forces in the rope.