4. 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 \(OP_1\) 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 \(P_3P_4\) perpendicular to \(OP_3\).

Continuing in this manner, you can get the line segment \(P_(n-1)Pn\) by drawing a line segment of unit length perpendicular to \(OP_(n-1)\) .

In This manner, you will have created the points \(P_2\), \(P_3\), \(P_4\), \(P_5\),........ and joined them to create a beautiful spiral depicting \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{4}\),......