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. 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 $O{P}_{n-1}$. In this manner, you will have created the points $P_2,P_3,.......,P_n,.....,$ and joined them to create a beautiful spiral depicting $\sqrt{2},\sqrt{3},\sqrt{4},.......$

Answer 1

Starting with point $O$, draw a line segment $O{P}_1$ of unit length.

Now draw a line segment $P_1{P}_2$ perpendicular to $O{P}_1$ again of unit length.

Here always we need to keep in mind that the measure of the line segment would always be a constant, i.e., $1$ unit.

Now again daw a line segment $P_2{P}_3$ perpendicular to $O{P}_2$ of unit length.

Again draw a line segment $P_3{P}_4$ perpendicular to $O{P}_3$.

In this way, we have formed a figure as shown in figure.