If you have watched lockdown math series by "3 blue 1 brown",
or if you are willing to watch this video, then I have a doubt.
At 38:02 of the video why is the number of years equal to the distance travelled on the circle?
How do we know that the full circle represents $\ 2\pi\ $ years?
I have asked the question in the video comments but don't expect any reply there so can anyone help me out here?
It really is only equal to the distance if you start with precisely 1 dollar on your bank account, because then the circle becomes the unit circle (radius 1). This means that the distance traveled along the edge of the circle has the same magnitude as the angle of the vector that rotates around origo (in this case z(t) describing the money as a function of time). For example, one whole rotation $z(2\pi)$ yields a circle with circumference $2\pi$. If you start with any other amount, the length traveled does not correspond to the time (years). It is the angle that corresponds to time. Watch the whole video and this should become clear (around he 55 min mark is when he presents the function z(t), where t is time). It might also be helpful to refresh radians in general. The wiki page on radians is sufficient.
If you wanted to visualize time in a graph, you would need to add another dimension to the graph. The result would be a spiral coming out of the screen as time increases.