Why does the radius of a unit circle need to be 1?

[sysprog]

Put one jaw at any point on the circumference, and adjust the caliper opening so that the other jaw intersects a single point as the caliper is rotated through an arc.

This method makes good sense to me.

 

[mathwonk]

of course the assumption that caliper measure equals ruler measure is equivalent to the Side angle side axiom of euclidean geometry.

Pardon me, I am entranced by a thread that goes on this long, in answer to OP's question of "why is 1 = 1?"