Plotting a circle using differential equations?

Question

I was watching the MIT's SICP lecture where the lecturer talks about plotting a circle using a differential equation like this:

$\frac{dx}{dt} = -y$

$\frac{dy}{dt} = x$

$x(t+\delta t) = x(t) - y(t).\delta t$

$y(t+\delta t) = y(t) + x(t).\delta t$

There is a corresponding code in scheme as well which implements this algorithm:

(define (circle x y)
  (plot x y)
  (circle (- x (* y dt))
          (+ y (* x dt)))

Can someone explain the intuition behind this? Does it actually draw a circle?