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May 12th, 2012, 11:50 AM  #1 
Newbie Joined: May 2012 Posts: 11 Thanks: 0  What curve is this?
Hello! Can somebody tell me what curve is this: (at; b sint; c cost), t e R 
May 12th, 2012, 11:57 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: What curve is this?
I believe it is an elliptical helix.

May 25th, 2012, 01:35 PM  #3 
Newbie Joined: May 2012 Posts: 11 Thanks: 0  Re: What curve is this?
Can someone plot this curve in http://www.wolframalpha.com/, or some other program?

May 25th, 2012, 02:42 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
For what values of a, b and c?

May 26th, 2012, 12:27 AM  #5  
Newbie Joined: May 2012 Posts: 11 Thanks: 0  Re: Quote:
 
May 26th, 2012, 12:35 AM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: What curve is this?
In order to plot a unique member of the family of curves given by the original parametric equations you have to choose values for a, b, and c. Suppose we choose a = 1, b = 2 and c = 3, where 0 < t < 2?. To plot the curve in WA, use the command: plot x=t, y=2*sin(t), z=3*cos(t) for 0<t<2*pi to get: [attachment=0:3abg6ouj]ellipticalhelix.jpg[/attachment:3abg6ouj] 
May 26th, 2012, 12:45 AM  #7 
Newbie Joined: May 2012 Posts: 11 Thanks: 0  Re: What curve is this?
Thank you. What wolud be equation of this curve without parameter t?

May 26th, 2012, 01:13 AM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: What curve is this?
You would have two equations by eliminating the parameter, but it is most often that a 3space curve such as a helix is represented parametrically I believe.

May 26th, 2012, 01:53 AM  #9  
Newbie Joined: May 2012 Posts: 11 Thanks: 0  Re: What curve is this? Quote:
what are flexion and torsion? Are they constant?  

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