. To construct a square-root spiral depicting, , …………………...
Answers
Answer:
A number line is a imaginary line whose each point represents a real number.
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 containing right angle. ΔABC is a right angled triangle having right angle at B. (see Fig. 1.1)
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Therefore, AC² = AB² +BC²
where, AC = hypotenuse, AB = perpendicular and BC = base
Procedure
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)
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Construct a line QX perpendicular to the line segment PQ, by using compasses or a set square, (see Fig. 1.3)
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From Q, draw an arc of 1 unit, which cut QX at C(say). (see Fig. 1.4)
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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’.