The parabola r(t)=< t, t2 >, -3 ≤ t ≤ 3 .
  • Red: unit tangent vector, T(t)
  • Green: unit normal vector, N(t)

  • Yellow: Osculating Circle

(Repeating in an endless loop.)
The cubic r(t)=< t, t3 >, -2 ≤ t ≤ 2 .
  • Red: unit tangent vector, T(t)
  • Green: unit normal vector, N(t)

  • Yellow: Osculating Circle

(Repeating in an endless loop.)
The quartic r(t)=< t, t4 >, -1 ≤ t ≤ 1 .
  • Red: unit tangent vector, T(t)
  • Green: unit normal vector, N(t)

  • Yellow: Osculating Circle

(Repeating in an endless loop.)
The path r(t)=< 1+t3, t2 >, -1 ≤ t ≤ 1 .
  • Red: unit tangent vector, T(t)
  • Green: unit normal vector, N(t)

  • Yellow: Osculating Circle

(Repeating in an endless loop.)