Math CentralQuandaries & Queries


Question from Al:

i want to cut a 200 diameter pipe in 45 degrees. Can you demonstrate how to develop a flat rap around please


Hi Al,


We had a similar question a while ago and Edward showed that the curve is a cosine. For your question the curve you need is one period of the cosine. The length of the period is the circumference of the pipe which is 200 π and the amplitude is 200/2 = 100. (You didn't tell us the units but I assume they are millimeters.) Thus the curve is

y = 100 cos(x/100)

where the angle is measured in radians, not degrees. In the diagram the axes are in green. The red lines mark off one period.


I printed the diagram, cut along the curve and red lines and rolled it up to form the cut off cylinder in the image at the top of this page.


I hope this helps,

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