I am trying to plot the contents of a circle, which include geometric elements and spirals, on a linear graph. For example, take a circle, take the beginning and the end and make it straight. What would it look like? For instance there are triangles in my circle that when plotted on a cartesian graph become something like an x^2 plot. My circle is a 360 degree circle around, but also contains radial degrees from center to edge with max 360 limit.
Here is my issue. The elements are not hard to plot, but My circle contains fibonacci spirals that i am trying to plot on a linear level as well, but cant seem to do it unless i get a ruler for every point i want to plot.
I know how to convert cartesian to polar and vice versa, i know my angles, but that is very tedious. I am looking for a formula that will give me r for every degree without using x and y. For instance, the x,y coordinate is 0,360. My spiral coordinate at that point is t,r = 0,360. Next i want the polar coordinate r for t=1, 0*=89, r=?, then t=2, 0*=88, r=? As it moves to the center of the circle around the spiral.
Again, i am not looking for x,y coordinates. I want a formula for this, is this posaible?
Most things i find are not limiting r but i am limiting r to 360.
I am studying cycles that is why r needs to be limited to 360. Like trying to fit a.circle in a square, if that makes sense
I have spent hours googling and brainstorming to no avail. Please note it has been about 7 years since my last calc class, but i do remember or catch on quickly, and learn best by an example.