Arc Length of a Curve in Space
Week 8
In this week I learned how to calculate
the arc-length of a space-curve. For example the arc length of helix. A helix is also known as a cylindrical coil or
solenoid coil. In mathematics,
a helix is a curve in 3-dimensional space.
To find the total length of the wire that is
used to make the spiral helix of the spring, we need to know the axial height
of the helix (h), the diameter of the helix (d), the number of turns in the
helix (n).
The formula for arc-length of a
helix or arc-length of a space-curve is
L = sqrt((n*Pi*d)^2 + h^2)
I noticed that the equation of calculating
the arc length for a curve in space is very similar to calculating the arc
length for a curve in the plane. We just need to add a z term to the formula
for the arc length of a plane curve.
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