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Radians, dimensions, & explanations

From <Mike Wilson mwilson@colosys.net>

Each year as I go through angular motion I realize
I do not have a simple explanation for why radians are a dimensionless
measurement.

I am always forced back into some discussion of the circumference of
a circle as 2 pi radi so the distance drops out.

My students routinely seem to have a rather blank expression at this
explanation. They are more than willing to just accept "because" as
an answer.

I hope I can provide a better answer.

Thanks for any ideas or feedback.



Best Wishes,

Mike Wilson
mwilson@colosys.net
Math/Science
West Grand HS
Kremmling, Colorado