why is it the formula of the centripetal acceleration a=v°2/r?

You need to do some vector calculus for that. The x and y coordinates of an object traveling around a circle of radius r can be written as

x=r sin(wt), y=r cos(wt)

where w is angular frequency and t is time. The V and A vectors are the first and second time derivatives of X=(x,y) so

V=rw[cos(wt),-sin(wt)]

A=-rw^2[sin(wt),cos(wt)]

These have magnitudes

v=rw

a=rw^2

Square the first and divide by r, and you get the second, so your formula results. Also notice that A is in the opposite direction as X, as viewed from the center of motion (origin). That means the acceleration is radially inward.