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 Fig.: Constructing this manner, you can get the line segment $P_{n-1}{P}_n$ by square root spiral drawing a line segment of unit length perpendicular to $O{P}_{n-1}$. In this manner, you will have created the points $P_2,P_3,P_4,\cdots$, and joined them to create a beautiful spiral depicting $\sqrt{2},\sqrt{3},\sqrt{4},...$.

Answer 1

Construct an activity.

To carry out the activity, please follow the steps below.

Make a mark on the paper with a point $O$. The square root spiral's center will be $O$ in this case.

From $O$, draw a horizontally $1$ cm straight line, $O{P}_1$.

Draw a $1$ cm perpendicular line from $P_1$ to $P_2$ from the point $P_1$.

Join $O{P}_2$, where $O{P}_2=\sqrt{2}$.

Draw a $1$ cm perpendicular line from $P_2$ to $P_3$ and indicate the end point $P_3$.

Join $O{P}_3$, where $O{P}_3=\sqrt{3}$.

Repeat the steps to draw $\sqrt{2},\sqrt{3},\sqrt{4},...$.

Hence, the required figure is as follows: