This is a brief description on an idea that I have been tinkering with for a few months.
As we saw in the previous work, the do nothing machine actually is an orbital calculator. We should apply this knowledge to different curves, including 3D. But what happens if we try to draw “the inner path” of an orbit that is increasing such as with the case of a logarithmic spiral.
Well if the radius was following along a logarithmic spiral curve that is one-half the size as the main logarithmic spiral we see the continuation of the shape is formed by the shape itself plus some radius.
But what if we took a different approach to draw the “inner path” of the arms that form the given spiral? If there was a “pivot” or movement of one of the arms from the first track to the second we could draw a logarithmic spiral.
But what if we wanted a path without “sliding” of the arms? We could take the inverse of interconnecting half circles. More simply put, we could take the bottom half of the circle and use it as our top path. Then connect the upper half of the circle and use it as a connection to the bottom of our path.
So the path would be alternating connects of the bottom and top halves of a circle.
Why go to so much trouble. Well picture the following: You have a vehicle that is magnetic and can travel short distances in through the air. It sticks from point to point. And the points are positions of a logarithmic spiral. Put the point it sticks to (let’s call them tracks) can move. So as the magnetic vehicles shoot from track to track we can shoot to a predetermine position anywhere along the logarithmic spiral.
Why would you do such a thing? Even though we don’t have the technology we could apply this to orbits of space craft. But for the mathematician this gives him a way to shoot to different numbers!