Does a spiral staircase have a constant slope? - Answers

Previous answer: "No because the line is not straight and the points of the slop is in different ares." The above is ambiguous. You need to define the term slope. The slope of a helix (or any curve) is normally defined as the slope of a line that is tangent to the helix (curve). And then you need to define, slope with respect to what? Normally that would be slope with respect to a horizontal plane. That slope, by definition, is constant for a helix with a vertical axis. The value of the slope of such a helix is pitch / (2*pi*R), where R is the radius from the axis. Then you have to consider where on the staircase you are. A staircase is not a single helix. It has width, or different radii. If you are walking up stairs at a constant radius R from the axis (on a helix), then the slope is constant. In any case, the average slope of the stairs varies with the radius R on which you are walking, so that would not be a constant.