Q. 44.1( 249 Votes )

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 P1P2 perpendicular to OP1 of unit length (see Fig. 1.9). Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn-1Pn by 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

Answer :

Activity

For the square root spiral follow the given steps:-

1. Draw a line AB of length 1 unit.
2. Draw another line BC of length 1 unit perpendicular to AB.
3. Now, Join point A and point C forming a line AC.
    Here, AC represents a line of length √2 units.     (This can be easily found using Pythagoras Theorem in right ΔABC) 
                                               
4. Now, Draw a perpendicular CD of length 1 unit at point C and join points A and D.
    AD here represents length √3.

5. Similarly proceeding further we get Square Root Spiral.
 

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