{[ cos(t), sin(t), t ], [ cos(t+Pi), sin(t+Pi), t ]}


{[ x(t) = cos(t), y(t) = sin(t), z(t) = t ], [ x(t) = cos(t+Pi), y(t) = sin(t+Pi), z(t) = t ]}


t is an element of the set of all Real numbers



With respect to t: {[-sin(t), cos(t), 1], [sin(t), -cos(t), 1]}

Critical points are formed where all the derivatives equal 0. These critical points may be minimums, maximums, or saddle points. Since 1 will never equal 0, there will be no critical points. This means that there are no minimum or maximum points. This is the same for both equations.


With respect to t: {[sin(t), -cos(t), ( 1/2 )t2], [-sin(t), cos(t), ( 1/2 )t2]}

Interesting Features

This plot shows a double helix. The plot contains the standard helix and a second helix rotated Pi radians around. This is very similar to the double helix structure found in human DNA.

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