Our curve is closed for some value of T near 3.307. Is this a Lemniscate? Wolfram gives a parametric form for the lemniscate as:
x = (cos t)/(1 + sin2 t)
y = (cos t)(sin t)/(1 + sin2 t)
We take p = (x, y) to be the vector position on the curve as a function of t or λ, the arc length. The curvature is the magnitude of d2p/dλ2 = (d2p/dt2)/(dλ/dt)2.

We differentiate to find the tangent and then the derivative of its direction with respect to t.
Where r = 1/(1 + sin2 t), dr/dt = ((2cos2 t)(1 + sin2 t)–2)

dx/dt = –2(cos t)(1 + sin2 t)–2 (sin t)(cos t) – (sin t)/(1 + sin2 t) =(-2(cos t) – (sin t) – sin3 t)(1 + sin2 t)–2
dy/dt = (cos t)(sin t)/(1 + sin2 t)

This is too hard, but numerically:

```(define (sq x)(* x x))
(define (xf t) (/ (cos t) (+ 1 (sq (sin t)))))
(define (yf t) (/ (* (cos t)(sin t)) (+ 1 (sq (sin t)))))
(define (p t) (cons (xf t)(yf t)))
(define pi (* 4 (atan 1)))
(define dt .000001)
(define ((D f) t) (/ (- (f (+ t dt)) (f t)) dt))
(define xd (D xf))
(define yd (D yf))
(define (a t) (atan (/ (yd t) (xd t))))