To construct a square root spiral.

OBJECTIVE

To construct a square root spiral

MATERIAL REQUIRED

Adhesive

Geometry box

White paper

A piece of plywood

PREREQUISITE KNOWLEDGE

Concept of number line.

Concept of irrational numbers.

The numbers which cannot be expressed in the form p/q where q ≠ 0 and both p and q are integers, are called irrational numbers, e.g. √3, π, etc

According to Pythagoras theorem, in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of other two sides.

Image 1

            Therefore, AC² = AB² +BC²                

PROCEDURE

Take a piece of plywood ,paste a white paper on it ..

Draw a line segment  PQ  of length 1 unit by taking 1 inch as 1 unit

       Image 2

Construct a line QX perpendicular to the line segment PQ.

                                                                           Image 3

From Q, draw an arc of 1 unit, which cut QX ,ie  C 

 Join PC.

                                                                          Image 4

Taking PC as base, draw a perpendicular CY to PC

From C, draw an arc of 1 unit, which cut CY at D 

Join PD. 

Taking PD as base, draw a perpendicular DZ to PD, 

From D, draw an arc of 1 unit, which cut DZ at E .

Join PE. 

                                                                   Image 5

Keep repeating the above process,as long as you wish.  The figure which  you get is called a ‘square root spiral'

OBSERVATION

Δ PQC is a right angled triangle

By Pythagoras theorem,

 PC² = PQ² + QC²          (Hypotenuse² = Perpendicular ² + Base²

 PC² = (1)² + (1)²   

PC = √2

In  Δ PCD 

PD² =PC² +CD²

PD²= (√2)² +(1)² 

PD² =2+1 = 3

PD = √3 and so on.

On actual measurement, we get

PC = √2

PD = √3

PE = √4

PF = √5

CONCLUSION

 In this way square root spiral can be constructed.