Is the perimeter of a square isometric to the circle? Homeomorphic? An isometry is defined as a function that preserves distances between points two metric spaces.

If make a circle with the same perimeter/circumference as the square, is it possible to find an explicit isometry between the two sets? 

As for homeomorphic, I can visualize a homeomorphism, but again, I cannot find an explicit function between the square and circle that is bicontinuous and bijective.
If the metric is minimal distance along the curve, then you find a isometric mapping by simply walking each curve with the same speed.
Isometric? No. Homeomorphic? Yes. Remember isometry is a distance preserving bijection.