# An arc length integral in 3D

edited February 11 in Problems

The groovy trefoil pic on our class web page is parameterized by
$$\begin{array}{l} x(t) = \sin(3t) \\ y(t) = \sin(t) + 2\sin(2t) \\ z(t) = \cos(t) - 2\cos(2t) \end{array}$$
over the interval $[0,2\pi]$.

• Type out an integral representing the arc length of the trefoil knot and
• Find a numerical estimate of your integral.

Of course, you can try to generate a 3D image of the trefoil knot on math3d.org if you like, but it might not look quite as groovy as the one on our web page!

• edited February 13

int_0^(2pi)sqrt(9cos(3t)^2+(cos(t)+4cos(2t))^2+(4sin(2t)-sin(t))^2)dt
~~28.83
Math3d is blocked at work, so I'll just refer to the webpage lol

• @fritz

Math3d is blocked at work, so I'll just refer to the webpage lol

I wonder why Math3d would be blocked?!