Construct the 'square root spiral'.
Answers
Answer:
A square root spiral is a spiral formed by many right angled triangles, where, the hypotenuse of each triangle is the square root of a number. the first triangle is always an isosceles triangle, with its hypotenuse equal to square root of 2.
Step-by-step explanation:
Take a piece of plywood having the dimensions 30 cm x 30 cm.
Draw a line segment PQ of length 1 unit by taking 2 cm as 1 unit, (see Fig. 1.2)
NCERT Class 9 Maths Lab Manual - Construct a Square Root Spiral 2
Construct a line QX perpendicular to the line segment PQ, by using compasses or a set square, (see Fig. 1.3)NCERT Class 9 Maths Lab Manual - Construct a Square Root Spiral 3
From Q, draw an arc of 1 unit, which cut QX at C(say). (see Fig. 1.4)
NCERT Class 9 Maths Lab Manual - Construct a Square Root Spiral 4
Join PC.
Taking PC as base, draw a perpendicular CY to PC, by using compasses or a set square.
From C, draw an arc of 1 unit, which cut CY at D (say).
Join PD. (see Fig. 1.5)
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Taking PD as base, draw a perpendicular DZ to PD, by using compasses or a set square.
From D, draw an arc of 1 unit, which cut DZ at E (say).
Join PE. (see Fig. 1.5)
Keep repeating the above process for sufficient number of times. Then, the figure so obtained is called a ‘square root spiral’.