Example 1 Curvature

f(x) = (1 / 3 * x^(3))
g(x) = x^(2)
h(x) = (2 * x)
a = CurveCartesian(f(t), g(t), h(t), t, -15, 15)
v = -2.5 (slider from -2.5 to 2.4, step 0.1)
A: a(v)
u = Vector(a(v), a(v) + (2 * UnitVector[a'(v)]))
B: a(0)
k(x) = 2 / (x^(2) + 2)^(2)
d(x) = sqrt((f'(x))^(2) + (g'(x))^(2) + (h'(x))^(2))
b = CurveCartesian(f'(t) / d(t), g'(t) / d(t), h'(t) / d(t), t, 0, (2 * pi))
w = Vector(a(v), a(v) + (2 * UnitVector[b'(v)]))
α = Angle(u, w)