\[\sqrt{n}\]
and \[\sqrt{n+1}\]
Spiral of Theodorus
A Pythagorean spiral, also called the 'Spiral of Theodorus' is a spiral formed by right angled triangles, with sides of length 1 forming the outer edge of the spiral. The side of length 1 is the shortest side of each triangle, and the hypotenuse of each triangle forms one of the two shorter sides of the next one in the spiral. The sides of the nth triangle are 1,