### 18.2.1 Curvature of a curve

The curvature command finds the curvature of a curve. The curve can be given as an object or by a parameterization.

- To find the curvature from a parameterization, curvature takes two mandatory arguments and one optional argument:
  - C, a curve.
  - t, the parameter of the curve.
  - Optionally, t0, a value of the parameter.
- curvature(C,t ⟨,t0⟩) returns the curvature of the curve; if t0 is given, the curvature is given at the point it specifies, otherwise the curvature is given as a function of the parameter.
- To find the curvature from a curve object, curvature takes two arguments:
  - C, a curve.
  - p, a point on the curve.
- curvature(C,p) returns the curvature of C at the point p.

#### Examples

trigsimplify(curvature([5*cos(t),5*sin(t)],t))

1
5

trigsimplify(curvature([2*cos(t),3*sin(t)],t))

24 | √ |
2
|  | √ |
5 cos | ⎛ ⎝ | 2 t | ⎞ ⎠ | +13
260 cos | ⎛ ⎝ | 2 t | ⎞ ⎠ | +25 cos | ⎛ ⎝ | 4 t | ⎞ ⎠ | +363

curvature([2*cos(t),3*sin(t)],t,pi/2)

3
4

curvature(plot(x^2),point(1,1))

(see Section 19.2.3 and Section 26.5.2.)

2
25
|  | √ |
5