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Drawing plane curves
- Thread starter odyssey
- Start date
Winding numbers are relative to where the point (observer) is. But it's easy, draw a helical curve around a point counterclockwise until you've rotated around a point the desired number of times, and then close it up. A clockwise turn gives a negative winding number (at least the way I remember learning it). To achieve a winding number of zero, just make sure the point isn't on the inside of the curve.
Its kind of hard visualizing. Would this wikipedia describe what you are referring to https://en.wikipedia.org/wiki/Winding_number ?
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Yes. Well, imagine an annulus around the origin being a "race track" for the curve.. You place your pencil on the annulus (say at the positive x-axis, call it the "finish line") and begin going around the race track counter-clockwise. Every time you reach the finish line again a counter goes up by +1. If you were to at any point go backwards through the finish line, it would mean adding a -1 to the counter.
When you're done driving you close the curve up, attaching it back to where it started. The counter gives the winding number of the curve around the origin.
When you're done driving you close the curve up, attaching it back to where it started. The counter gives the winding number of the curve around the origin.