easy way to draw a square root spiral
Answers
Answer:
Materials Required
AdhesiveGeometry boxMarkerA piece of plywood
Prerequisite Knowledge
Concept of number line.Concept of irrational numbers.Pythagoras theorem.
Theory
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.
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,
Construct a line QX perpendicular to the line segment PQ, by using compasses or a set square,
Q, draw an arc of 1 unit, which cut QX at C(say).
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.
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’.
Refer to the attachment
