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

In summary, the discussion centers around the definition of the unit circle and why its radius is chosen to be 1. Some argue that using a circle of radius 1 simplifies the math and makes it easier to teach students about trigonometric functions, while others argue that it introduces unnecessary complications with the factor of 2. There is also mention of the debate between using pi versus tau as the fundamental constant in mathematics. Ultimately, it is suggested to have multiple memberships for the PF member @etotheipi, including @etothetau and @etothephi.
  • #36
Mark44 said:
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.
 
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  • #37
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?"
 
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