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| Math Central | Quandaries & Queries |
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Question from John: from the original question Al asked about cutting a 200 diameter pipe in 45 degrees. can someone explain the math steps required to creating the graph. I am trying to do the same thing only using a 150 degree cut. |
Hi John,
Most of the information you need is in Edwards response to Neal's question and my response to Al's question.
Suppose the diameter of the pipe is d units and the pipe is sliced by a plane in inclination φ degrees, in your case 150 degrees. Following Edward's development the equation of the intersecting plane is z = tan(φ) x which in your example is z = tan(150o) x = -1/√3 x. The equation of the curve you need is then
y = d/2 tan(φ) cos(2x/d)
where the angle 2x/d is in radians. In your case where the plane that slices the pipe has an inclination of 150o this is
y = -d/(2√3) cos(2x/d)
For example I took d = 10 units, graphed one period of y = -5/√3) cos(x/5)
cut it out and rolled it up to form the pipe
Harley
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