Question

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 P₁ P₂ perpendicular to OP₁ of unit length. Now draw a line segment P₂ P₃ perpendicular to OP₂. Then draw a line segment P₃ P₄ perpendicular to OP₃. Continuing in this manner, you can get the line segment P_n–1P_n by drawing a line segment of unit length perpendicular to OP_n–1. In this manner, you will have created the points P₂, P₃,...., P_n,.... ., and joined them to create a beautiful spiral depicting `sqrt2, sqrt3, sqrt4,` ...

Answer 1

Starting with point O, draw a line segment OP₁ of unit length.

Now draw a line segment P₁P₂ perpendicular to OP₁ again of unit length.

Here, we need to keep in mind that the measure of the line segment would always be a constant, i.e., 1 unit.

Again, draw a line segment P₂P₃ perpendicular to OP₂ of unit length.

Again, a line segment P₃P₄ is drawn perpendicular to OP₃.

In this way, we have formed a figure, as shown in the figure.