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47. STAIRCASE This elaborate old staircase is found in the Queen Victoria Building in Sydney, Australia. It is commonly referred to as a spiral staircase, and this certainly conveys the idea. However, the term is mathematically incorrect. A spiral is the name given to a curve which lies within the plane. As an example, we might think of a watch spring lying on a flat surface, where the spring touches the level plane for its whole length. By contrast, the illustrated staircase is decidedly three dimensional – you should try climbing it! The curve it represents is called a helix. Points on this curve might be given coordinates x = r cos The first two equations here actually define a circle; the third coordinate lifts the points out of the circle plane (say z = 0). We might say that the picture shows a helical staircase!
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– Paul Scott |
, y = r sin
