A question about a dotted spiral

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A dotted spiral has the origin as its center. Its first point is one unit from the origin. Its second point has a distance of the square root of two from the origin and one unit from the first point. Its third point has a distance of the square root of three from the origin and one unit from the second point. Its fourth point has a distance of the square root of four from the origin and one unit from the third point. Is there a more elegant way to describe this emerging spiral? How many points are needed per revolution?