Or try this with out the maths...
my diagram is (kind of) to scale so just zoom it bigger and use a peice of string on your screen to compare those paths and see which is longer
??
How do you see your path shorter than the one going through the center of the web?
Approximation: "the web is made of circles"
length = 3/8*2*pi*R + R/3 = 9pi/4 + 1 = 8.06...
length = 3+2 = 5
Even considering my approximation increase the length a bit, it's clear that your path is longer.
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Or try this with out the maths...
my diagram is (kind of) to scale so just zoom it bigger and use a peice of string on your screen to compare those paths and see which is longer
??
How do you see your path shorter than the one going through the center of the web?
Approximation: "the web is made of circles"
length = 3/8*2*pi*R + R/3 = 9pi/4 + 1 = 8.06...length = 3+2 = 5Even considering my approximation increase the length a bit, it's clear that your path is longer.