## The construction of circles to satisfy given conditions

About 6000 years ago, an unknown Mesopotamian made one of the greatest inventions of alt time, the wheel. This was the most important practical application ever made of a shape that fascinated early mathematicians. The shape is, of course, the circle. After tho wheel had been invented, the Mesopotamians found many more applications for the circle than just for transport. The potter's wheel was developed and vessels were made much more accurately and quickly. Pulleys were invented and engineers and builders were able to raise heavy weights. Since that time, the circle has been the most important geometric shape in the development of all forms of engineering

Apart from its practical applications, the circle has an aesthetic value which makes it unique amongst plane figures. The ervcients called it 'the perfect curve' and its symmetry and simplicity has led artists and craftsmen to use the circle as a basis for design for many thousands of years.

### Definitions

A circle is the locus of a point which moves so that it is always a fixed distance from another stationary point. Concentric circles are circles that have the same centre. Eccentric circles are circles that are not concentric. Fig. 4/1 shows some of the parts of the circle. Constructions

The length of the circumference of a circle is 110 or 2 flff. whoro D is the diameter and R the radius of the circle, n is the ratio of the diameter to the circumference and may be taken as 22/7 or. more accurately, as 3.142.

3 x GIVEN DIA

3 x GIVEN DIA

If you need to draw the circumference of a circle (this is required quite often in subsequent chapters), you should either calculate it or use the construction shown in Fig. 4/2. This construction is not exact but is accurate enough for most needs For the sake of thoroughness, the corresponding construction, that of finding the diameter from the circumference, is shown in Fig. 4/3.

To construct the circumference of a circle, given the diameter (Fig. 4/2)

1. Draw a semi- circle of the given diameter AB, centre 0

2. From B mark off three times the diameter. BC.

3. From O draw a line at 30* to OA to meet the semi-circle in D.

4. From D draw a line perpendicular to OA to meet OA m E.

EC is the required circumference.

To conetruct the diameter of a circle, given the

To conetruct the diameter of a circle, given the

0 0

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### Responses

• tyler
How to construct circles to satisfy certain conditions?
9 months ago