Where designation of Mobius strip measured in π came from?

To physically make Mobius strip from strip of flexible material one will have to twist strip along length of it and glue ends. Amount of twist can be described in number of half turns. Half of turn equal 180°. 180° measured in radians equal 3.14159 equal π.

So, number of π in Mobius strip designation tells the number of half turns one has to make to strip of material to make this Mobius strip.