Below is the plot of a circle of radius 1 centered at the origin. It’s as curvy a graph as we can imagine. The key is that it’s differentiable, and thus, as we zoom in, begins to look like a straight line. Why? Calculus.

I don’t know why Mathematica insists on making it hard to see things in 1:1 ratio, but after plotting, at the bottom of the output, click around until the magic bar appears.

Once that occurs, click on the menu “image size,” choose “custom...” and then select 1:1.

Plot[Sqrt[1-x^2],{x,0,1}]

Plot[Sqrt[1-x^2],{x,.69,.71}]

Plot[Sqrt[1-x^2],{x,.69,.71}]