CIRCLE 



1386 



CIRCLE 



ing measure 'through. The radius is one-half 

 the diameter. Any diameter of a circle divides 

 the circle into two equal parts. 



Arc. Any por- 

 tion of the cir- 

 cumference is 

 called an arc. 



Chord. A 

 straight line pass- 

 ing through a cir- 

 cle and terminat- 

 ing at both ends 

 in the circumfer- 

 ence is called a 

 chord. A diameter is the longest chord of a 

 circle. 



The curved line ab is an arc. The straight 

 line cd is a chord. The straight line ej is a 



chord; it is the longest chord of the circle, 

 being a diameter. 



Relation of Circumference to Diameter and 

 Radius. Measure the circumference of a cir- 

 cle; then measure its diameter; for example, 

 the circumference and diameter of a cylindrical 

 drinking glass; of a round dining table; a 

 bicycle wheel or wagon wheel; a barrel head, 

 and so on. By these measurements you will 

 discover an interesting fact, namely, that there 

 is always the same relation between the cir- 

 cumference and the diameter of a circle. Your 

 measurements must be carefully made to get 

 this relation. You will see very roughly at 

 first that the circumference is 3 and some frac- 

 tion times as great as the diameter. With 

 close work you will find the relation to be 

 about 3#. The fact has been proved that 

 the circumference is 3.14159+ times as great 

 as the diameter. The decimal has been car- 



ried out very many places, but for most prac- 

 tical uses 3.1416 is used. We state this fact in 

 mathematics in this way: 



Circumference = 3 . 1 4 1 6 X diameter 



or 



c = 3.1416xd 

 or 



In the last equation we use the Greek letter 

 v (pi) to stand for the number 3.1416. We 

 always find that mathematicians, when they 

 have to use a certain number many times, 

 find or invent some symbol for it, and so they 

 have chosen the symbol ir to mean 3.1416 or 

 the relation of the circumference to the diam- 

 eter of a circle. This relation is very generally 

 expressed in terms of radius instead of diam- 

 eter, and the desirable formula to remember is 



Circumference = 2 x v X radius, 

 using 2 X radius instead of diameter. It is 

 shortened to this form by omitting the times 



signs: 



Circumference = 2vr 



Many ancient peoples knew in a general 

 way of this relation, but for centuries the 

 Eastern peoples and the Greeks used it as 3. 

 The Jews used the value as 3, without the 

 added decimal, as indicated in the description 

 of Solomon's Temple in I Kings, VII. Hiram, 

 king of Tyre, it is related, made for the Tem- 

 ple a circular basin, called a "molten sea," which 

 was "10 cubits from the one brim to the 

 other"; while a "line of 30 cubits did compass 

 it round about." 



Area of Circle. Draw a circle; draw its 

 horizontal diameter and its vertical diameter; 

 draw a square on the radius, as in the figure 

 shown above. 



Compare the area of a (which is ^4 of the 



