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Contour and asymptotic angles in the Nyquist plot

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hanhan100

Joined Apr 8, 2022
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In this video, the professor is illustrating a Nyquist plot for the function G(s)H(s):

1699192602717.png

At the 25:37 mark, he draws a contour around the origin and says:
"The contour angle approaches the origin asymptotically, moving toward -180 degrees as it gets closer, and as it moves away, it approaches asymptotically to plus 180 degrees."
Click to expand...
I understand his previous explanation about why the phase should transition from -180 to 180 degrees via 0. However, I'm having trouble understanding the concept of asymptotes and how that relates to the drawing he is making.
 
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