Question
Classroom activity (Constructing the 'square root spiral') : Take a large sheet of paper and construct the 'square root spiral' in the following fashion. Start with a point $O$ and draw a line segment $O P_1$ of unit length. Draw a line segment $P_1 P_2$ perpendicular to $O P_1$ of unit length (see Fig.). Now draw a line segment $P_2 P_3$ perpendicular to $O P_2$. Then draw a line segment $P_3 P_4$ perpendicular to $O P_3$. Continuing in this manner, you can get the line segment $P_{n-1} P_n$ by drawing a line segment of unit length perpendicular to $OP _{n-1}$. In this manner, you will have created the points $P _2$, $P_3, \ldots, P_n, \ldots$, and joined them to create a beautiful spiral depicting $\sqrt{2}, \sqrt{3}, \sqrt{4}, \ldots$
Fig. : Constructing square root spiral
Fig. : Constructing square root spiral
