# 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 $\mathrm{O}$ and draw a line segment $\mathrm{OP}_{1}$ of unit length. Draw a line segment $\mathrm{P}_{1} \mathrm{P}_{2}$ perpendicular to $\mathrm{OP}_{1}$ of unit length (see figure below). Now draw a line segment $\mathrm{P}_{2} \mathrm{P}_{3}$ perpendicular to $\mathrm{OP}_{2}$. Then draw a line segment $\mathrm{P}_{3} \mathrm{P}_{4}$ perpendicular to $\mathrm{OP}_{3}$. Continuing in Fig. 1.9: Constructing this manner, you can get the line segment $\mathrm{P}_{\mathrm{a}-1} \mathrm{P}_{\mathrm{n}}$ by square root spiral drawing a line segment of unit length perpendicular to $\mathrm{OP}_{\mathrm{n}-1}$. In this manner, you will have created the points $\mathrm{P}_{2}, \mathrm{P}_{3}, \ldots, \mathrm{P}_{\mathrm{n}}, \ldots .$, , and joined them to create a beautiful spiral depicting $\sqrt{2}, \sqrt{3}, \sqrt{4}, \ldots$"

#### Complete Python Prime Pack

9 Courses     2 eBooks

#### Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

#### Java Prime Pack

9 Courses     2 eBooks

To do:

We have to construct a square root spiral as given in the question.

Solution:

Steps of construction:

1. Mark a point $A$ on a paper.

$A$ is the center of the square root spiral.

2. From $A$, draw a straight line $AB$ of $1\ cm$ horizontally.

3. From $B$, draw a perpendicular line $AC$ of $1\ cm$.

4. Join $AC$.

$AC^2=AB^2+BC^2$

$AC^2=1^2+1^2$

$AC=\sqrt{2}\ cm$

5. From $C$, draw a perpendicular line of $1\ cm$ and mark the end point $D$.

6. Join $AD$. $AD=\sqrt{3}\ cm$

7. Similarly, $AE=\sqrt{4}\ cm, AF=\sqrt5\ cm,.......$

Updated on 10-Oct-2022 13:38:03