# 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 OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length (see Fig) . Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in Fig.: Constructing this manner, you can get the line segment Pn-1Pn by square root spiral drawing a line segment of unit length perpendicular to OPn-1. In this manner, you will have created the points P2, P3,….,Pn,… ., and joined them to create a beautiful spiral depicting √2, √3, √4, …

Solution

Let us follow the following procedure to execute the activity

1: Mark a point O on the paper. Here, O will be the center of the square root spiral.

2: From O, draw a straight line, OA, of 1cm horizontally.

3: From A, draw a perpendicular line, AB, of 1 cm.

4: Join OB. Here, OB will be of √2

5: Now, from B, draw a perpendicular line of 1 cm and mark the end point C.

6: Join OC. Here, OC will be of √3 7: Repeat the s to draw √4, √5, √6….