Is it necessary for a helix to have constant pitch? If it is not so, what would be equation of a variable pitch helix?
2026-03-28 13:22:54.1774704174
Variable Pitch Helices
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You need to choose an increasing function in the z - direction. for example :
$$\mathbf{f}(t) = \left(10 \cos t, 10 \sin t, t\exp( -.01 t)\right) \qquad $$
Plot out your z-direction curve in the plane first, it shouldn't be too difficult to find what you are looking for.