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_1P_2` perpendicular to `OP_1` of unit length . Now draw a line segment `P_2P_3` perpendicular to `OP_2`. Then draw a line segment P3P 4 perpendicular to `OP_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,...., P_n,... ., `and joined them to create a beautiful spiral depicting `sqrt(2), sqrt(3), sqrt(4)..`

Explanation

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.


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