Wednesday Answer

You have a rotating barber’s pole, with painted red, white and blue helices. The cylinder is 4 feet tall. The red stripe cuts the vertical lines at a constant angle of 60 degrees. How long is the red stripe?

If you assume a right triangle wrapped around a cylinder, with the base of the triangle going around the base of the cylinder, you get a helix. Unwrap the red stripe from the cylinder, and it will form a triangle of 30 and 60 degrees. The hypotenuse of this triangle must be twice the altitude. The altitude is 4 feet, so the hypotenuse, or the length of the red strip, will be 8 feet. This solution is independent of the diameter and the shape of the object’s cross sections.

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