The Euler Spiral Map Projection

H5N1 Euler spiral is a bend whose curved sort changes linearly amongst its bend length. H5N1 Euler spiral tin hence move used to exercise a map projection yesteryear projecting a curved footing onto a apartment spiral. The interesting indicate for cartographers is that the to a greater extent than spirals used inward a Euler spiral map projection the less distortion at that spot is.

Now for the math. By cutting a sphere along a spiral amongst width i / northward together with flattening out the resulting sort nosotros exercise a Euler spiral when northward tends to the infinity. In other words nosotros tin exercise a map projection whose distortion tends to zippo equally northward tends to the infinity.

If this sounds a petty confusing together with so it mightiness aid to play amongst an interactive Euler spiral map. This interactive Euler Spiral Map allows you lot to conform the lay out of spirals used inward the projection yesteryear changing the thickness of the spirals. By reducing the thickness of the spirals you lot tin growth the lay out of spirals used inward the map projection. The to a greater extent than spirals you lot exercise together with so the less distortion inward the projection.

Unfortunately for cartographers a Euler spiral map projection is non really useful for navigating with. If you lot are even so confused together with so this first-class Numberphile video explains the projection far to a greater extent than clearer than I can: