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I'm having a bit of trouble visualizing an object given $(a \cdot \cos(t), a \cdot \sin(t), ct)$ where c and a are constants. What object is described as c becomes large compared to a?

iamvegan
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user153509
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    It's a helix or corkscrew. The size of $a$ is the radius of the screw, and $c$ determines the pitch. The bigger $c$ gets, the steeper the pitch of the screw. – MPW Oct 06 '14 at 04:33
  • Oh ok. What is the object when c is equal to 0? – user153509 Oct 06 '14 at 04:36

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This is an equation of Helix where a is the radius .. Please see the figure enter image description here

Contribution from x and y shown here in red and blue. Middle you can see the helix. When c >>> it may look like a line (not exactly).. The length of winding will be less dense

Nirvana
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remember that $(cos(t),sin(t))$ describes a circle counterclockwise around the origin of radius 1 and period $2\pi$. adding a factor of $a$ scales the radius of the circle (and can change the direction of flow if a is negative$. $ct$ is linear in the z direction, so what you have is a spiral going out from the origin, along a cylinder of radius a.

Alan
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