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 $$\sqrt{2}$$, $$\sqrt{3}$$, $$\sqrt{4}$$,......